Atkin-Lehner |
2- 31- |
Signs for the Atkin-Lehner involutions |
Class |
61504ca |
Isogeny class |
Conductor |
61504 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
184320 |
Modular degree for the optimal curve |
Δ |
-28172916849664 = -1 · 210 · 317 |
Discriminant |
Eigenvalues |
2- 2 3 1 6 2 -6 -1 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-8969,417857] |
[a1,a2,a3,a4,a6] |
Generators |
[-48024:617923:729] |
Generators of the group modulo torsion |
j |
-87808/31 |
j-invariant |
L |
12.750111048725 |
L(r)(E,1)/r! |
Ω |
0.6265331851777 |
Real period |
R |
5.0875641349605 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999997135 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
61504bb1 15376y1 1984h1 |
Quadratic twists by: -4 8 -31 |