Atkin-Lehner |
2+ 7+ 13+ 89- |
Signs for the Atkin-Lehner involutions |
Class |
129584c |
Isogeny class |
Conductor |
129584 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
164352 |
Modular degree for the optimal curve |
Δ |
-1476220928 = -1 · 211 · 7 · 13 · 892 |
Discriminant |
Eigenvalues |
2+ -1 -2 7+ -3 13+ -6 -2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-25704,1594768] |
[a1,a2,a3,a4,a6] |
Generators |
[-96:1780:1] [82:178:1] |
Generators of the group modulo torsion |
j |
-917091764163794/720811 |
j-invariant |
L |
7.2397599110225 |
L(r)(E,1)/r! |
Ω |
1.2580393919994 |
Real period |
R |
0.71934948441441 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
1.0000000009614 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
64792d1 |
Quadratic twists by: -4 |