Atkin-Lehner |
2- 3- 13+ 37- |
Signs for the Atkin-Lehner involutions |
Class |
69264w |
Isogeny class |
Conductor |
69264 |
Conductor |
∏ cp |
2 |
Product of Tamagawa factors cp |
deg |
354816 |
Modular degree for the optimal curve |
Δ |
-254428849778688 = -1 · 212 · 317 · 13 · 37 |
Discriminant |
Eigenvalues |
2- 3- -4 4 -3 13+ -3 -1 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,15648,-146000] |
[a1,a2,a3,a4,a6] |
j |
141909917696/85207707 |
j-invariant |
L |
0.64466536106 |
L(r)(E,1)/r! |
Ω |
0.32233267345024 |
Real period |
R |
1 |
Regulator |
r |
0 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
4329c1 23088r1 |
Quadratic twists by: -4 -3 |