Atkin-Lehner |
2+ 3- 7- 19+ |
Signs for the Atkin-Lehner involutions |
Class |
89376q |
Isogeny class |
Conductor |
89376 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
1032192 |
Modular degree for the optimal curve |
Δ |
893170954880887872 = 26 · 3 · 714 · 193 |
Discriminant |
Eigenvalues |
2+ 3- 0 7- 4 -4 2 19+ |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,0,-257658,21515136] |
[a1,a2,a3,a4,a6] |
Generators |
[-15126670200:-969957773596:139798359] |
Generators of the group modulo torsion |
j |
251239591000000/118622310177 |
j-invariant |
L |
8.3022314524711 |
L(r)(E,1)/r! |
Ω |
0.25020959708744 |
Real period |
R |
16.590553574676 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000002068 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
89376bs1 12768c1 |
Quadratic twists by: -4 -7 |