Cremona's table of elliptic curves

Curve 117312bm1

117312 = 26 · 3 · 13 · 47



Data for elliptic curve 117312bm1

Field Data Notes
Atkin-Lehner 2+ 3- 13- 47- Signs for the Atkin-Lehner involutions
Class 117312bm Isogeny class
Conductor 117312 Conductor
∏ cp 6 Product of Tamagawa factors cp
deg 34560 Modular degree for the optimal curve
Δ 13725504 = 26 · 33 · 132 · 47 Discriminant
Eigenvalues 2+ 3- -3 -1 -5 13- -2 -2 Hecke eigenvalues for primes up to 20
Equation [0,1,0,-137,-639] [a1,a2,a3,a4,a6]
Generators [-8:3:1] [16:39:1] Generators of the group modulo torsion
j 4475809792/214461 j-invariant
L 11.13265606717 L(r)(E,1)/r!
Ω 1.3987620091968 Real period
R 1.3264891846966 Regulator
r 2 Rank of the group of rational points
S 1.000000000376 (Analytic) order of Ш
t 1 Number of elements in the torsion subgroup
Twists 117312cg1 1833b1 Quadratic twists by: -4 8


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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