Atkin-Lehner |
2- 3- 5+ 11- 43- |
Signs for the Atkin-Lehner involutions |
Class |
42570w |
Isogeny class |
Conductor |
42570 |
Conductor |
∏ cp |
192 |
Product of Tamagawa factors cp |
deg |
1622016 |
Modular degree for the optimal curve |
Δ |
-2087571178452418560 = -1 · 224 · 314 · 5 · 112 · 43 |
Discriminant |
Eigenvalues |
2- 3- 5+ 0 11- 0 -8 4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,1,-10948568,-13941330213] |
[a1,a2,a3,a4,a6] |
Generators |
[9965:925833:1] |
Generators of the group modulo torsion |
j |
-199098554419711270541881/2863609298288640 |
j-invariant |
L |
8.2735979841557 |
L(r)(E,1)/r! |
Ω |
0.041498257129732 |
Real period |
R |
4.1535870803201 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000000003 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
14190e1 |
Quadratic twists by: -3 |