Atkin-Lehner |
2+ 3- 19- 89- |
Signs for the Atkin-Lehner involutions |
Class |
40584i |
Isogeny class |
Conductor |
40584 |
Conductor |
∏ cp |
288 |
Product of Tamagawa factors cp |
deg |
221184 |
Modular degree for the optimal curve |
Δ |
-7391555430476544 = -1 · 28 · 312 · 193 · 892 |
Discriminant |
Eigenvalues |
2+ 3- -1 -1 -3 -2 -7 19- |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,0,12519,4105323] |
[a1,a2,a3,a4,a6] |
Generators |
[-117:1026:1] [-81:1602:1] |
Generators of the group modulo torsion |
j |
847535647609856/28873263400299 |
j-invariant |
L |
9.699329142669 |
L(r)(E,1)/r! |
Ω |
0.31550137307019 |
Real period |
R |
0.10674510181081 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
0.99999999999987 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
81168e1 121752bd1 |
Quadratic twists by: -4 -3 |