Atkin-Lehner |
2+ 3- 5- 7- 13- |
Signs for the Atkin-Lehner involutions |
Class |
57330cp |
Isogeny class |
Conductor |
57330 |
Conductor |
∏ cp |
140 |
Product of Tamagawa factors cp |
deg |
887040 |
Modular degree for the optimal curve |
Δ |
-756485924317987500 = -1 · 22 · 39 · 55 · 72 · 137 |
Discriminant |
Eigenvalues |
2+ 3- 5- 7- 1 13- 3 6 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,0,-160344,48639100] |
[a1,a2,a3,a4,a6] |
Generators |
[1166:37442:1] |
Generators of the group modulo torsion |
j |
-12763205672220241/21177624487500 |
j-invariant |
L |
5.5770251709102 |
L(r)(E,1)/r! |
Ω |
0.25458775016003 |
Real period |
R |
0.15647215568115 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000000094 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
19110bs1 57330m1 |
Quadratic twists by: -3 -7 |