Cremona's table of elliptic curves

Curve 11712bb1

11712 = 26 · 3 · 61



Data for elliptic curve 11712bb1

Field Data Notes
Atkin-Lehner 2- 3+ 61- Signs for the Atkin-Lehner involutions
Class 11712bb Isogeny class
Conductor 11712 Conductor
∏ cp 4 Product of Tamagawa factors cp
deg 1536 Modular degree for the optimal curve
Δ 5059584 = 210 · 34 · 61 Discriminant
Eigenvalues 2- 3+ -2 -2  2  2 -2  4 Hecke eigenvalues for primes up to 20
Equation [0,-1,0,-69,-171] [a1,a2,a3,a4,a6]
Generators [-4:5:1] Generators of the group modulo torsion
j 35995648/4941 j-invariant
L 3.0532156448427 L(r)(E,1)/r!
Ω 1.6695516797955 Real period
R 1.8287637823926 Regulator
r 1 Rank of the group of rational points
S 1 (Analytic) order of Ш
t 2 Number of elements in the torsion subgroup
Twists 11712o1 2928m1 35136cn1 Quadratic twists by: -4 8 -3


Data from Elliptic Curve Data by J. E. Cremona.
Design inspired by The Modular Forms Explorer by William Stein.

Part of Computational Number Theory
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