Atkin-Lehner |
2- 3+ 7- 83+ |
Signs for the Atkin-Lehner involutions |
Class |
97608m |
Isogeny class |
Conductor |
97608 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
333312 |
Modular degree for the optimal curve |
Δ |
-486164761350912 = -1 · 28 · 34 · 710 · 83 |
Discriminant |
Eigenvalues |
2- 3+ 0 7- -3 4 2 6 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,16007,714253] |
[a1,a2,a3,a4,a6] |
Generators |
[-33:386:1] |
Generators of the group modulo torsion |
j |
6272000/6723 |
j-invariant |
L |
5.9679950394045 |
L(r)(E,1)/r! |
Ω |
0.34758777984499 |
Real period |
R |
4.2924373159058 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000020721 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
97608s1 |
Quadratic twists by: -7 |