Atkin-Lehner |
2+ 3- 7+ 37- |
Signs for the Atkin-Lehner involutions |
Class |
12432m |
Isogeny class |
Conductor |
12432 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
3072 |
Modular degree for the optimal curve |
Δ |
12792528 = 24 · 32 · 74 · 37 |
Discriminant |
Eigenvalues |
2+ 3- 2 7+ -4 -6 6 0 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,0,-127,-568] |
[a1,a2,a3,a4,a6] |
Generators |
[-412:315:64] |
Generators of the group modulo torsion |
j |
14270199808/799533 |
j-invariant |
L |
5.8895921611001 |
L(r)(E,1)/r! |
Ω |
1.4261943701273 |
Real period |
R |
4.1295858996936 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
6216q1 49728cx1 37296r1 87024u1 |
Quadratic twists by: -4 8 -3 -7 |