Atkin-Lehner |
2- 19- 61- |
Signs for the Atkin-Lehner involutions |
Class |
74176s |
Isogeny class |
Conductor |
74176 |
Conductor |
∏ cp |
16 |
Product of Tamagawa factors cp |
deg |
172032 |
Modular degree for the optimal curve |
Δ |
-33342959386624 = -1 · 222 · 194 · 61 |
Discriminant |
Eigenvalues |
2- -2 -1 -1 -1 -1 -8 19- |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,0,-7681,377343] |
[a1,a2,a3,a4,a6] |
Generators |
[1:608:1] [191:2432:1] |
Generators of the group modulo torsion |
j |
-191202526081/127193296 |
j-invariant |
L |
6.6444617100612 |
L(r)(E,1)/r! |
Ω |
0.60518755319253 |
Real period |
R |
0.68619860849531 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
0.99999999999862 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
74176c1 18544e1 |
Quadratic twists by: -4 8 |