Atkin-Lehner |
2- 3+ 11+ 47- |
Signs for the Atkin-Lehner involutions |
Class |
12408b |
Isogeny class |
Conductor |
12408 |
Conductor |
∏ cp |
1 |
Product of Tamagawa factors cp |
deg |
10752 |
Modular degree for the optimal curve |
Δ |
-280191301632 = -1 · 211 · 37 · 113 · 47 |
Discriminant |
Eigenvalues |
2- 3+ 0 -2 11+ 0 -7 4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-848,27468] |
[a1,a2,a3,a4,a6] |
Generators |
[-11:188:1] |
Generators of the group modulo torsion |
j |
-32968057250/136812159 |
j-invariant |
L |
3.3444838963529 |
L(r)(E,1)/r! |
Ω |
0.8510188113747 |
Real period |
R |
3.929976460744 |
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 |
24816e1 99264v1 37224c1 |
Quadratic twists by: -4 8 -3 |