Atkin-Lehner |
2- 7- 17- |
Signs for the Atkin-Lehner involutions |
Class |
53312ca |
Isogeny class |
Conductor |
53312 |
Conductor |
∏ cp |
28 |
Product of Tamagawa factors cp |
deg |
258048 |
Modular degree for the optimal curve |
Δ |
-329426452103168 = -1 · 214 · 72 · 177 |
Discriminant |
Eigenvalues |
2- -1 -4 7- -3 -5 17- -6 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-17425,1249361] |
[a1,a2,a3,a4,a6] |
Generators |
[-5:1156:1] [41:776:1] |
Generators of the group modulo torsion |
j |
-728871512656/410338673 |
j-invariant |
L |
5.5680915573074 |
L(r)(E,1)/r! |
Ω |
0.50280109070013 |
Real period |
R |
0.39550513401615 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
1.0000000000008 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
53312t1 13328r1 53312bh1 |
Quadratic twists by: -4 8 -7 |