V. A. Abrashkin, Galois modules of group schemes of period p over the ring of Witt vectors, Izv. Akad. Nauk SSSR
Ser. Mat., 51 (1987) 691–736.
 D. J. Bernstein and T. Lange, A complete set of addition laws for incomplete Edwards curves, J. Number Theory,
131 (2011) 858–872.
 W. Bosma and H. W. Lenstra, Complete systems of two addition laws for elliptic curves, J. Number Theory, 53
 C. Breuil, B. Conrad, F. Diamond and R. Taylor, On the modularity of elliptic curves over Q: wild 3-adic exercises,
J. Amer. Math. Soc., 14 (2001) 843–939.
 A. Chillali and L. El Fadil, Elliptic Curve over a Local Finite Ring Rn, in Number Theory and Its Applications,
 M. Chou, Torsion of rational elliptic curves over the maximal abelian extension of Q, Pacific J. Math., 302 (2019)
 A. Clemm and S. Trebat-Leder, Elliptic curves with everywhere good reduction, J. Number Theory, 161 (2016)
 H. Cohen, A course in computational algebraic number theory, Graduate Texts in Mathematics, 138, Springer-
Verlag, Berlin, 1993.
 J. E. Cremona and M. P. Lingham, Finding all elliptic curves with good reduction outside a given set of primes,
Experiment. Math., 16 (2007) 303–312.
 H. B. Daniels, A. Lozano-Robledo, F. Najman and A. V. Sutherland, Torsion subgroups of rational elliptic curves
over the compositum of all cubic fields, Math. Comp., 87 (2018) 425–458.
 M. Derickx, S. Kamienny, W. Stein and M. Stoll, Torsion points on elliptic curves over number fields of small degree,
 M. Derickx and F. Najman, Torsion of elliptic curves over cyclic cubic fields, Math. Comp., 88 (2019) 2443–2459.
 M. Derickx and A. V. Sutherland, Torsion subgroups of elliptic curves over quintic and sextic number fields, Proc.
Amer. Math. Soc., 145 (2017) 4233–4245.
 N. D. Elkies, Z28 in E(Q), etc., Number Theory Listserver, 2006.
 N. D. Elkies and Z. Klagsbrun, New rank records for elliptic curves having rational torsion, arXiv:2003.00077 (2020).
 R. R. Farashahi and I. E. Shparlinski, On group structures realized by elliptic curves over a fixed finite field, Exp.
Math., 21 (2012) 1–10.
 J. M. Fontaine, Il n’y a pas de variété abélienne sur Z, Invent. Math., 81 (1985) 515–538.
 Y. Fujita, Torsion subgroups of elliptic curves with non-cyclic torsion over Q in elementary abelian 2-extensions of
Q, Acta Arith., 115 (2004) 29–45.
 Y. Fujita, Torsion subgroups of elliptic curves in elementary abelian 2-extensions of Q, J. Number Theory, 114
 T. Kagawa, Determination of elliptic curves with everywhere good reduction over Q( 37), Acta Arith., 83 (1998)
 T. Kagawa, Determination of elliptic curves with everywhere good reduction over real quadratic fields, Arch. Math.
(Basel), 73 (1999) 25–32.
 T. Kagawa, Determination of elliptic curves with everywhere good reduction over real quadratic fields Q( 3p), Acta.
Arith., 96 (2001) 231–245.
 T. Kagawa, Torsion Groups of Elliptic Curves with Everywhere Good Reduction over Quadratic Fields, Int. J.
Algebra, 10 (2016) 461–467.
 S. Kamienny, Torsion points on elliptic curves and q-coefficients of modular forms, Invent. Math., 109 (1992)
 N. M. Katz and B. Mazur, Arithmetic Moduli of Elliptic Curves, Annals of Mathematics Studies, 108, Princeton
University Press, Princeton, NJ, 1985.
 M. A. Kenku and F. Momose, Torsion points on elliptic curves defined over quadratic fields, Nagoya Math. J., 109
 M. Kida, Computing elliptic curves having good reduction everywhere over quadratic fields, Tokyo J. Math., 24
 M. Kida, Reduction of elliptic curves over certain real quadratic number fields, Math. Comp., 68 (1999) 1679–1685.
 Z. Klagsbrun, T. Sherman and J. Weigandt, The Elkies curve has rank 28 subject only to GRH, Math. Comp., 88
 E. Kobayashi, A remark on the Mordell-Weil rank of elliptic curves over the maximal abelian extension of the
rational number field, Tokyo J. Math., 29 (2006) 295–300.
 N. Koblitz, Elliptic curve cryptosystems, Math. Comp., 48 (1987) 203–209.
 M. Kosters and R. Pannekoek, On the structure of elliptic curves over finite extensions of Qp with additive reduction,
 D. Jeon, C. H. Kim and A. Schweizer, On the torsion of elliptic curves over cubic number fields, Acta Arith., 113
 D. Jeon, C. H. Kim and E. Park, On the torsion of elliptic curves over quartic number fields, J. London Math. Soc.
(2), 74 (2006), pp. 1–12.
 D. Johnson, A. Menezes and S. Vanstone, The Elliptic Curve Digital Signature Algorithm (ECDSA), Int. J. Inf.
Secur., (2001) 36–63.
 S. Lang and A. Néron, Rational points of abelian varieties over function fields, Amer. J. Math., 81 (1959) 95–118.
 H. Lange and W. Ruppert, Complete systems of addition laws on abelian varieties, Invent. Math., 79 (1985) 603–610.
 H. Lange and W. Ruppert, Addition laws on elliptic curves in arbitrary characteristics, J. Algebra, 107 (1987)
 M. Laska and M. Lorenz, Rational points on elliptic curves over Q in elementary abelian 2-extensions of Q, J. Reine
Angew. Math., 355 (1985) 163–172.
 H. W. Lenstra, Elliptic curves and number-theoretic algorithms, Proceedings of the International Congress of Math-
ematicians, 1, 2 (1986) 99–120.
 H. W. Lenstra, Factoring integers with elliptic curves, Ann. of Math. (2), 126 (1987) 649–673.
 H. W. Lenstra and J. Pila, Does the set of points of an elliptic curve determine the group?, Computational algebra
and number theory (Sydney, 1992), Math. Appl., 325, Kluwer Acad. Publ., Dordrecht, 1995 111–118.
 E. Lutz, Sur l’équation y 2 = x3 − Ax − B dans les corps p-adiques, J. Reine Angew. Math., 177 (1937) 237–247.
 B. Mazur, Modular curves and the Eisenstein ideal, Inst. Hautes Études Sci. Publ. Math., no. 47 (1977) 33–186.
 B. Mazur, Rational isogenies of prime degree, Invent. Math., 44 (1978) 129–162.
 R. J. S. McDonald, Torsion subgroups of elliptic curves over function fields of genus 0, J. Number Theory, 193
 A. Meneghetti, M. Sala and D. Taufer, A survey on PoW-based consensus, AETiC, 4 (2020) 8–18.
 A. Meneghetti, M. Sala and D. Taufer, A New ECDLP-Based PoW Model, Mathematicsl, 8 (2020) pp. 11.
 B. Meyer and V. Müller, A public key cryptosystem based on elliptic curves over Z/nZ equivalent to factoring.,
Advances in cryptology—EUROCRYPT ’96, Lecture Notes in Comput. Sci., 1070, Springer, Berlin, 1996 49–59.
 L. Merel, Bornes pour la torsion des courbes elliptiques sur les corps de nombres, Invent. Math., 124 (1996) 437–449.
 V. S. Miller, Use of elliptic curves in cryptography, Advances in cryptology—CRYPTO ’85 (Santa Barbara, Calif.,
1985), Lecture Notes in Comput. Sci., 218, Springer, Berlin, 1986 417–426.
 L. J. Mordell, On the rational solutions of the indeterminate equations of the third and fourth degrees, Proc. Camb.
Phil. Soc., 21 (1922) 179–192.
 F. Najman, Torsion of rational elliptic curves over cubic fields and sporadic points on X1 (n), Math. Res. Lett., 23
 J. Neukirch, Algebraische Zahlentheorie, Springer-Verlag (1999).
 A. Ogg, Abelian curves of 2-power conductor, Proc. Cambridge Philos. Soc., 62 (1966) 143–148.
 K. Ribet, Torsion points of abelian varieties in cyclotomic extensions, Enseign. Math., 27 (1981) 315–319.
 H. G. Rück, A Note on Elliptic Curves Over Finite Fields, Math. Comp., 49 (1987) 301–304.
 M. Sala and D. Taufer, The group structure of elliptic curves over Z/N Z, (2020), arXiv:2010.15543.
 R. Schoof, Abelian varieties over cyclotomic fields with good reduction everywhere, Math. Ann., 325 (2003) 413–448.
 B. Setzer, Elliptic curves over complex quadratic fields, Pacific J. Math., 74 (1978) 235–250.
 J. H. Silverman, Advanced topics in the arithmetic of elliptic curves, Graduate Texts in Mathematics, 151, Springer-
Verlag, New York, 1994.
 J. H. Silverman, The arithmetic of elliptic curves Second edition, Graduate Texts in Mathematics, 106, Springer,
 R. J. Stroeker,Reduction of elliptic curves over imaginary quadratic number fields, Pacific J. Math., 108 (1983)
 A. V. Sutherland, Torsion subgroups of elliptic curves over number fields, Preprint (2012).
 N. Takeshi, Elliptic curves with good reduction everywhere over cubic fields, Int. J. Number Theory, 11 (2015)
 N. Takeshi, Family of elliptic curves with good reduction everywhere over number fields of given degree, Funct.
Approx. Comment. Math., 56 (2017) 61–65.
 J. T. Tate, The arithmetic of elliptic curves, Invent. Math., 23 (1974) 179–206.
 J. F. Voloch, A note on elliptic curves over finite fields, Bull. Soc. Math. France, 116 (1988) 455–458.
 L. C. Washington, Elliptic curves, number theory and cryptography, Chapman & Hall / CRC, 2008.
 W. C. Waterhouse, Abelian varieties over finite fields, Ann. Sci. École Norm. Sup. (4), 2 (1969) 521–560.
 A. Weil, L’arithmétique sur les courbes algébriques, Acta Arith., 52 (1929) 281–315.
 A. Wiles, Modular elliptic curves and Fermat’s Last Theorem, Ann. Math., 142 (1995) 443–551.