Atkin-Lehner |
2- 3+ 7- 13- 23+ |
Signs for the Atkin-Lehner involutions |
Class |
12558n |
Isogeny class |
Conductor |
12558 |
Conductor |
∏ cp |
768 |
Product of Tamagawa factors cp |
deg |
258048 |
Modular degree for the optimal curve |
Δ |
-1660616206139584512 = -1 · 212 · 32 · 74 · 138 · 23 |
Discriminant |
Eigenvalues |
2- 3+ 2 7- 0 13- 2 8 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,1,1,-598947,-189130047] |
[a1,a2,a3,a4,a6] |
j |
-23762325430118066146993/1660616206139584512 |
j-invariant |
L |
4.1022134836621 |
L(r)(E,1)/r! |
Ω |
0.085462780909627 |
Real period |
R |
1 |
Regulator |
r |
0 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
4 |
Number of elements in the torsion subgroup |
Twists |
100464bs1 37674k1 87906bn1 |
Quadratic twists by: -4 -3 -7 |