Atkin-Lehner |
2+ 5- 13+ 41+ |
Signs for the Atkin-Lehner involutions |
Class |
69290k |
Isogeny class |
Conductor |
69290 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
122880 |
Modular degree for the optimal curve |
Δ |
1266554681600 = 28 · 52 · 136 · 41 |
Discriminant |
Eigenvalues |
2+ -2 5- 2 -2 13+ -6 2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,0,1,-2708,2706] |
[a1,a2,a3,a4,a6] |
Generators |
[-48:174:1] [-330:1851:8] |
Generators of the group modulo torsion |
j |
454756609/262400 |
j-invariant |
L |
6.2730401140806 |
L(r)(E,1)/r! |
Ω |
0.73232954666857 |
Real period |
R |
4.2829352868766 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
0.99999999999719 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
410d1 |
Quadratic twists by: 13 |