Cremona's table of elliptic curves

Curve 31248r1

31248 = 24 · 32 · 7 · 31



Data for elliptic curve 31248r1

Field Data Notes
Atkin-Lehner 2+ 3- 7- 31+ Signs for the Atkin-Lehner involutions
Class 31248r Isogeny class
Conductor 31248 Conductor
∏ cp 8 Product of Tamagawa factors cp
deg 12288 Modular degree for the optimal curve
Δ 3280290048 = 28 · 310 · 7 · 31 Discriminant
Eigenvalues 2+ 3-  2 7-  0  2  2  0 Hecke eigenvalues for primes up to 20
Equation [0,0,0,-759,-7562] [a1,a2,a3,a4,a6]
Generators [81:680:1] Generators of the group modulo torsion
j 259108432/17577 j-invariant
L 7.085954025539 L(r)(E,1)/r!
Ω 0.91345673950237 Real period
R 3.8786478434651 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 15624j1 124992fz1 10416k1 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
Back to Tables and computations