Atkin-Lehner |
2+ 3- 7- 31+ |
Signs for the Atkin-Lehner involutions |
Class |
109368o |
Isogeny class |
Conductor |
109368 |
Conductor |
∏ cp |
32 |
Product of Tamagawa factors cp |
deg |
294912 |
Modular degree for the optimal curve |
Δ |
385922843857152 = 28 · 310 · 77 · 31 |
Discriminant |
Eigenvalues |
2+ 3- -2 7- 0 -2 -2 0 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-37191,-2593766] |
[a1,a2,a3,a4,a6] |
Generators |
[-105:392:1] |
Generators of the group modulo torsion |
j |
259108432/17577 |
j-invariant |
L |
4.6106513091938 |
L(r)(E,1)/r! |
Ω |
0.34525419516274 |
Real period |
R |
1.6692958922701 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000067236 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
36456z1 15624j1 |
Quadratic twists by: -3 -7 |