A005788 Conductors of elliptic curves.

11, 14, 15, 17, 19, 20, 21, 24, 26, 27, 30, 32, 33, 34, 35, 36, 37, 38, 39, 40, 42, 43, 44, 45, 46, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 61, 62, 63, 64, 65, 66, 67, 69, 70, 72, 73, 75, 76, 77, 78

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn

Comments

By the modularity of elliptic curves over Q (proved by Breuil-Conrad-Diamond-Taylor), these are equivalently the positive integers k such that there exists a rational weight 2 newform for Gamma_0(k). - Robin Visser, Nov 04 2024

Examples

			a(1) = 11, as there are no elliptic curves over Q of conductor less than 11, but there are exactly three elliptic curves over Q of conductor equal to 11, for example E : y^2 + y = x^3 - x^2. - _Robin Visser_, Nov 04 2024
		

References

• B. J. Birch and W. Kuyk, eds., Modular Functions of One Variable IV (Antwerp, 1972), Lect. Notes Math. 476 (1975), see pp. 82ff.
• N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

• J. E. Cremona, Table of n, a(n) for n = 1..10000
• J. E. Cremona, Elliptic Curve Data.
• Sean Howe and Kirti Joshi, Asymptotics of conductors of elliptic curves over Q, arXiv:1201.4566 [math.NT], 2012.
• LMFDB, Elliptic curves over Q.
• Eric Weisstein's World of Mathematics, Elliptic Curve.

Crossrefs

Cf. A060564, A110563, A110620, A217055.

Programs

Sage

# Uses Cremona's database of elliptic curves (works for all k < 500000)
def is_A005788(k):
    return CremonaDatabase().number_of_curves(k) > 0
print([k for k in range(1, 1000) if is_A005788(k)])  # Robin Visser, Nov 04 2024