Atkin-Lehner |
2+ 3+ 11+ 37- |
Signs for the Atkin-Lehner involutions |
Class |
19536c |
Isogeny class |
Conductor |
19536 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
1118208 |
Modular degree for the optimal curve |
Δ |
342613635408 = 24 · 314 · 112 · 37 |
Discriminant |
Eigenvalues |
2+ 3+ 2 -4 11+ 0 0 -6 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-58989947,-174367746138] |
[a1,a2,a3,a4,a6] |
j |
1418854149881269000523696128/21413352213 |
j-invariant |
L |
0.4902838209114 |
L(r)(E,1)/r! |
Ω |
0.054475980101267 |
Real period |
R |
1 |
Regulator |
r |
0 |
Rank of the group of rational points |
S |
9 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
9768k1 78144da1 58608r1 |
Quadratic twists by: -4 8 -3 |