Atkin-Lehner |
2+ 3+ 13+ 47- |
Signs for the Atkin-Lehner involutions |
Class |
117312d |
Isogeny class |
Conductor |
117312 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
98304 |
Modular degree for the optimal curve |
Δ |
-81206181888 = -1 · 218 · 3 · 133 · 47 |
Discriminant |
Eigenvalues |
2+ 3+ 0 3 -1 13+ 0 -6 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-1953,-35295] |
[a1,a2,a3,a4,a6] |
j |
-3144219625/309777 |
j-invariant |
L |
1.4282854564125 |
L(r)(E,1)/r! |
Ω |
0.35707116725558 |
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 |
117312cn1 1833e1 |
Quadratic twists by: -4 8 |