Atkin-Lehner |
2- 3- 5+ 7- 13- |
Signs for the Atkin-Lehner involutions |
Class |
57330en |
Isogeny class |
Conductor |
57330 |
Conductor |
∏ cp |
10 |
Product of Tamagawa factors cp |
deg |
1075200 |
Modular degree for the optimal curve |
Δ |
-503577908199843750 = -1 · 2 · 311 · 57 · 72 · 135 |
Discriminant |
Eigenvalues |
2- 3- 5+ 7- -4 13- 5 -7 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,1,-59828,34618637] |
[a1,a2,a3,a4,a6] |
Generators |
[-330:48833:8] |
Generators of the group modulo torsion |
j |
-662989657192009/14097531093750 |
j-invariant |
L |
8.5743216824232 |
L(r)(E,1)/r! |
Ω |
0.24704414924743 |
Real period |
R |
3.4707649254073 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000000085 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
19110bk1 57330eq1 |
Quadratic twists by: -3 -7 |