Atkin-Lehner |
2+ 3- 7+ 13- |
Signs for the Atkin-Lehner involutions |
Class |
13104w |
Isogeny class |
Conductor |
13104 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
36864 |
Modular degree for the optimal curve |
Δ |
-306819035136432 = -1 · 24 · 39 · 78 · 132 |
Discriminant |
Eigenvalues |
2+ 3- 2 7+ -4 13- 6 -4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,6486,-818417] |
[a1,a2,a3,a4,a6] |
Generators |
[1520101:51484680:1331] |
Generators of the group modulo torsion |
j |
2587063175168/26304786963 |
j-invariant |
L |
5.1096815065256 |
L(r)(E,1)/r! |
Ω |
0.26880323864972 |
Real period |
R |
9.5045013821135 |
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 |
6552m1 52416eu1 4368k1 91728bb1 |
Quadratic twists by: -4 8 -3 -7 |