Atkin-Lehner |
2+ 3- 7+ 37- |
Signs for the Atkin-Lehner involutions |
Class |
12432n |
Isogeny class |
Conductor |
12432 |
Conductor |
∏ cp |
34 |
Product of Tamagawa factors cp |
deg |
32640 |
Modular degree for the optimal curve |
Δ |
-68500074940416 = -1 · 211 · 317 · 7 · 37 |
Discriminant |
Eigenvalues |
2+ 3- -3 7+ 0 -2 -2 -1 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,0,-15912,-874476] |
[a1,a2,a3,a4,a6] |
Generators |
[180:1458:1] |
Generators of the group modulo torsion |
j |
-217568172289106/33447302217 |
j-invariant |
L |
4.1790985566572 |
L(r)(E,1)/r! |
Ω |
0.21075180682612 |
Real period |
R |
0.58321997463349 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
6216h1 49728cz1 37296s1 87024v1 |
Quadratic twists by: -4 8 -3 -7 |