Cremona's table of elliptic curves

Curve 69696j1

69696 = 26 · 32 · 112



Data for elliptic curve 69696j1

Field Data Notes
Atkin-Lehner 2+ 3+ 11- Signs for the Atkin-Lehner involutions
Class 69696j Isogeny class
Conductor 69696 Conductor
∏ cp 32 Product of Tamagawa factors cp
deg 368640 Modular degree for the optimal curve
Δ 6284345127616512 = 214 · 39 · 117 Discriminant
Eigenvalues 2+ 3+  0  2 11- -6 -6 -2 Hecke eigenvalues for primes up to 20
Equation [0,0,0,-65340,5174928] [a1,a2,a3,a4,a6]
Generators [36630:-418176:125] [-194:3248:1] Generators of the group modulo torsion
j 54000/11 j-invariant
L 10.823299426409 L(r)(E,1)/r!
Ω 0.40119157450083 Real period
R 3.3722353964836 Regulator
r 2 Rank of the group of rational points
S 0.99999999999881 (Analytic) order of Ш
t 2 Number of elements in the torsion subgroup
Twists 69696eh1 8712q1 69696i1 6336i1 Quadratic twists by: -4 8 -3 -11


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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