Atkin-Lehner |
2+ 29- 37+ |
Signs for the Atkin-Lehner involutions |
Class |
68672k |
Isogeny class |
Conductor |
68672 |
Conductor |
∏ cp |
2 |
Product of Tamagawa factors cp |
deg |
337920 |
Modular degree for the optimal curve |
Δ |
955486500241408 = 214 · 292 · 375 |
Discriminant |
Eigenvalues |
2+ -1 2 1 -3 0 -6 -6 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-134837,-18954323] |
[a1,a2,a3,a4,a6] |
Generators |
[428:1247:1] [-1622:725:8] |
Generators of the group modulo torsion |
j |
16547570407186432/58318267837 |
j-invariant |
L |
9.8310531900994 |
L(r)(E,1)/r! |
Ω |
0.24919484616418 |
Real period |
R |
19.725635063126 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
1.0000000000007 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
68672ba1 4292a1 |
Quadratic twists by: -4 8 |