Atkin-Lehner |
3- 11- 17- 19- |
Signs for the Atkin-Lehner involutions |
Class |
31977x |
Isogeny class |
Conductor |
31977 |
Conductor |
∏ cp |
2 |
Product of Tamagawa factors cp |
deg |
4224 |
Modular degree for the optimal curve |
Δ |
-7770411 = -1 · 37 · 11 · 17 · 19 |
Discriminant |
Eigenvalues |
0 3- -2 -1 11- 3 17- 19- |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,1,24,126] |
[a1,a2,a3,a4,a6] |
Generators |
[2:13:1] |
Generators of the group modulo torsion |
j |
2097152/10659 |
j-invariant |
L |
3.5796332327394 |
L(r)(E,1)/r! |
Ω |
1.684287125565 |
Real period |
R |
1.0626552855525 |
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 |
10659f1 |
Quadratic twists by: -3 |