Atkin-Lehner |
2+ 3- 7- 43+ |
Signs for the Atkin-Lehner involutions |
Class |
86688r |
Isogeny class |
Conductor |
86688 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
737280 |
Modular degree for the optimal curve |
Δ |
-76323620036063232 = -1 · 212 · 314 · 72 · 433 |
Discriminant |
Eigenvalues |
2+ 3- 2 7- -1 -3 5 8 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,81096,-9882448] |
[a1,a2,a3,a4,a6] |
Generators |
[3316:191628:1] |
Generators of the group modulo torsion |
j |
19753066976768/25560625923 |
j-invariant |
L |
8.8386093450013 |
L(r)(E,1)/r! |
Ω |
0.18378760584421 |
Real period |
R |
6.0114291309332 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000004062 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
86688l1 28896k1 |
Quadratic twists by: -4 -3 |