Atkin-Lehner |
2- 3- 5- 11- 13+ |
Signs for the Atkin-Lehner involutions |
Class |
128700bx |
Isogeny class |
Conductor |
128700 |
Conductor |
∏ cp |
12 |
Product of Tamagawa factors cp |
deg |
691200 |
Modular degree for the optimal curve |
Δ |
-709531143750000 = -1 · 24 · 38 · 58 · 113 · 13 |
Discriminant |
Eigenvalues |
2- 3- 5- 1 11- 13+ 2 1 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-373125,87735625] |
[a1,a2,a3,a4,a6] |
Generators |
[344:297:1] |
Generators of the group modulo torsion |
j |
-1260895840000/155727 |
j-invariant |
L |
7.7803187678258 |
L(r)(E,1)/r! |
Ω |
0.48903870068911 |
Real period |
R |
1.3257844226709 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000090413 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
42900bh1 128700z1 |
Quadratic twists by: -3 5 |