Atkin-Lehner |
2+ 3- 11- 37- |
Signs for the Atkin-Lehner involutions |
Class |
9768k |
Isogeny class |
Conductor |
9768 |
Conductor |
∏ cp |
56 |
Product of Tamagawa factors cp |
deg |
559104 |
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 |
4.7014005511314 |
L(r)(E,1)/r! |
Ω |
0.33581432508081 |
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 |
19536c1 78144f1 29304l1 107448bb1 |
Quadratic twists by: -4 8 -3 -11 |