Atkin-Lehner |
3- 11+ 17+ 43+ |
Signs for the Atkin-Lehner involutions |
Class |
72369i |
Isogeny class |
Conductor |
72369 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
219456 |
Modular degree for the optimal curve |
Δ |
-8814329046963 = -1 · 36 · 113 · 173 · 432 |
Discriminant |
Eigenvalues |
2 3- -2 3 11+ -2 17+ -8 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,1,-9651,391887] |
[a1,a2,a3,a4,a6] |
j |
-136368207106048/12090986347 |
j-invariant |
L |
2.8658846030802 |
L(r)(E,1)/r! |
Ω |
0.71647115767522 |
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 |
8041b1 |
Quadratic twists by: -3 |