Atkin-Lehner |
3+ 7+ 11+ 13- |
Signs for the Atkin-Lehner involutions |
Class |
39039c |
Isogeny class |
Conductor |
39039 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
404352 |
Modular degree for the optimal curve |
Δ |
-123513265926673623 = -1 · 32 · 76 · 11 · 139 |
Discriminant |
Eigenvalues |
-1 3+ -2 7+ 11+ 13- 0 4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,1,1,-246659,-50194240] |
[a1,a2,a3,a4,a6] |
j |
-156503678869/11647251 |
j-invariant |
L |
0.21331501958568 |
L(r)(E,1)/r! |
Ω |
0.10665750980661 |
Real period |
R |
1 |
Regulator |
r |
0 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
117117bc1 39039o1 |
Quadratic twists by: -3 13 |