Atkin-Lehner |
2- 5+ 23+ 37- |
Signs for the Atkin-Lehner involutions |
Class |
68080l |
Isogeny class |
Conductor |
68080 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
207360 |
Modular degree for the optimal curve |
Δ |
-118011723776000 = -1 · 221 · 53 · 233 · 37 |
Discriminant |
Eigenvalues |
2- -1 5+ 4 3 2 6 -2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,9504,-385280] |
[a1,a2,a3,a4,a6] |
Generators |
[2704:140672:1] |
Generators of the group modulo torsion |
j |
23175939596831/28811456000 |
j-invariant |
L |
6.2872430775639 |
L(r)(E,1)/r! |
Ω |
0.31598746292138 |
Real period |
R |
4.9742820647707 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999992922 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
8510f1 |
Quadratic twists by: -4 |