Atkin-Lehner |
3- 37+ 83- |
Signs for the Atkin-Lehner involutions |
Class |
27639i |
Isogeny class |
Conductor |
27639 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
130176 |
Modular degree for the optimal curve |
Δ |
-867341106533151 = -1 · 324 · 37 · 83 |
Discriminant |
Eigenvalues |
1 3- -2 -4 4 2 -4 0 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,0,-58473,5638360] |
[a1,a2,a3,a4,a6] |
Generators |
[-7548:11342:27] |
Generators of the group modulo torsion |
j |
-30329586561339793/1189768321719 |
j-invariant |
L |
4.0866948704561 |
L(r)(E,1)/r! |
Ω |
0.49602122628781 |
Real period |
R |
8.2389515889081 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
9213b1 |
Quadratic twists by: -3 |