Cremona's table of elliptic curves

Curve 8008c1

8008 = 23 · 7 · 11 · 13



Data for elliptic curve 8008c1

Field Data Notes
Atkin-Lehner 2- 7+ 11+ 13- Signs for the Atkin-Lehner involutions
Class 8008c Isogeny class
Conductor 8008 Conductor
∏ cp 4 Product of Tamagawa factors cp
deg 2944 Modular degree for the optimal curve
Δ -341076736 = -1 · 28 · 7 · 114 · 13 Discriminant
Eigenvalues 2- -2  1 7+ 11+ 13- -2 -5 Hecke eigenvalues for primes up to 20
Equation [0,1,0,175,67] [a1,a2,a3,a4,a6]
Generators [37:242:1] Generators of the group modulo torsion
j 2302045184/1332331 j-invariant
L 2.8880018783284 L(r)(E,1)/r!
Ω 1.0213273822393 Real period
R 0.70692363892087 Regulator
r 1 Rank of the group of rational points
S 1 (Analytic) order of Ш
t 1 Number of elements in the torsion subgroup
Twists 16016e1 64064f1 72072m1 56056o1 Quadratic twists by: -4 8 -3 -7


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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