Atkin-Lehner |
3+ 23+ 31- |
Signs for the Atkin-Lehner involutions |
Class |
66309b |
Isogeny class |
Conductor |
66309 |
Conductor |
∏ cp |
2 |
Product of Tamagawa factors cp |
deg |
17280 |
Modular degree for the optimal curve |
Δ |
-13725963 = -1 · 33 · 232 · 312 |
Discriminant |
Eigenvalues |
-2 3+ 0 0 -2 -5 6 -1 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,1,52,-124] |
[a1,a2,a3,a4,a6] |
Generators |
[4:11:1] [18:79:1] |
Generators of the group modulo torsion |
j |
15872000/14283 |
j-invariant |
L |
4.5939062400698 |
L(r)(E,1)/r! |
Ω |
1.2253742302824 |
Real period |
R |
1.8744911254585 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
1.0000000000021 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
66309k1 |
Quadratic twists by: -31 |