Atkin-Lehner |
2+ 3- 11- 37- |
Signs for the Atkin-Lehner involutions |
Class |
78144bq |
Isogeny class |
Conductor |
78144 |
Conductor |
∏ cp |
56 |
Product of Tamagawa factors cp |
deg |
344064 |
Modular degree for the optimal curve |
Δ |
21927272666112 = 210 · 314 · 112 · 37 |
Discriminant |
Eigenvalues |
2+ 3- -4 -4 11- -6 0 -6 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,0,-8885,-233541] |
[a1,a2,a3,a4,a6] |
Generators |
[-50:297:1] [-41:252:1] |
Generators of the group modulo torsion |
j |
75760866033664/21413352213 |
j-invariant |
L |
8.5138601126788 |
L(r)(E,1)/r! |
Ω |
0.50227942305058 |
Real period |
R |
1.2107461251384 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
0.9999999999936 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
78144bz1 4884b1 |
Quadratic twists by: -4 8 |