Atkin-Lehner |
2- 3+ 5+ 13+ |
Signs for the Atkin-Lehner involutions |
Class |
121680cm |
Isogeny class |
Conductor |
121680 |
Conductor |
∏ cp |
64 |
Product of Tamagawa factors cp |
deg |
2322432 |
Modular degree for the optimal curve |
Δ |
-433717749504000000 = -1 · 214 · 33 · 56 · 137 |
Discriminant |
Eigenvalues |
2- 3+ 5+ -4 0 13+ 6 -4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-673803,-215231302] |
[a1,a2,a3,a4,a6] |
j |
-63378025803/812500 |
j-invariant |
L |
1.3320643231791 |
L(r)(E,1)/r! |
Ω |
0.083253968716335 |
Real period |
R |
1 |
Regulator |
r |
0 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
15210ba1 121680cz3 9360bh1 |
Quadratic twists by: -4 -3 13 |