Atkin-Lehner |
2+ 5+ 23- |
Signs for the Atkin-Lehner involutions |
Class |
42320f |
Isogeny class |
Conductor |
42320 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
304128 |
Modular degree for the optimal curve |
Δ |
-851206361750000 = -1 · 24 · 56 · 237 |
Discriminant |
Eigenvalues |
2+ 3 5+ -2 0 1 0 0 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-98923,12057497] |
[a1,a2,a3,a4,a6] |
j |
-45198971136/359375 |
j-invariant |
L |
4.0248249584025 |
L(r)(E,1)/r! |
Ω |
0.50310311977798 |
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 |
21160d1 1840c1 |
Quadratic twists by: -4 -23 |