Atkin-Lehner |
5- 11- 23+ |
Signs for the Atkin-Lehner involutions |
Class |
69575y |
Isogeny class |
Conductor |
69575 |
Conductor |
∏ cp |
12 |
Product of Tamagawa factors cp |
deg |
720000 |
Modular degree for the optimal curve |
Δ |
4101355265033125 = 54 · 1111 · 23 |
Discriminant |
Eigenvalues |
-2 1 5- 3 11- -6 3 0 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,1,-333758,74040544] |
[a1,a2,a3,a4,a6] |
Generators |
[62:7320:1] |
Generators of the group modulo torsion |
j |
3713504358400/3704173 |
j-invariant |
L |
3.5344038603109 |
L(r)(E,1)/r! |
Ω |
0.43682787866243 |
Real period |
R |
0.67425562646361 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000001413 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
69575r2 6325g1 |
Quadratic twists by: 5 -11 |