Atkin-Lehner |
2+ 3- 5- 13+ 59+ |
Signs for the Atkin-Lehner involutions |
Class |
69030o |
Isogeny class |
Conductor |
69030 |
Conductor |
∏ cp |
3 |
Product of Tamagawa factors cp |
deg |
2096640 |
Modular degree for the optimal curve |
Δ |
-2763649499839488000 = -1 · 213 · 36 · 53 · 137 · 59 |
Discriminant |
Eigenvalues |
2+ 3- 5- 0 -2 13+ 6 1 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,0,-5487849,4950265293] |
[a1,a2,a3,a4,a6] |
Generators |
[8966:110497:8] |
Generators of the group modulo torsion |
j |
-25072791410715995199889/3791014403072000 |
j-invariant |
L |
5.0988528030872 |
L(r)(E,1)/r! |
Ω |
0.24654537427652 |
Real period |
R |
6.8937314525081 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999994625 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
7670e1 |
Quadratic twists by: -3 |