Atkin-Lehner |
2+ 3+ 11+ 37+ |
Signs for the Atkin-Lehner involutions |
Class |
78144f |
Isogeny class |
Conductor |
78144 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
8945664 |
Modular degree for the optimal curve |
Δ |
21927272666112 = 210 · 314 · 112 · 37 |
Discriminant |
Eigenvalues |
2+ 3+ -2 4 11+ 0 0 -6 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-235959789,1395177928893] |
[a1,a2,a3,a4,a6] |
Generators |
[271956113436:-907226649:30664297] |
Generators of the group modulo torsion |
j |
1418854149881269000523696128/21413352213 |
j-invariant |
L |
4.9842003137098 |
L(r)(E,1)/r! |
Ω |
0.23745658648423 |
Real period |
R |
10.494971707825 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999994635 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
78144da1 9768k1 |
Quadratic twists by: -4 8 |