Atkin-Lehner |
3- 5+ 7- 13- 17+ |
Signs for the Atkin-Lehner involutions |
Class |
69615o |
Isogeny class |
Conductor |
69615 |
Conductor |
∏ cp |
16 |
Product of Tamagawa factors cp |
deg |
819200 |
Modular degree for the optimal curve |
Δ |
83257246153935945 = 322 · 5 · 74 · 13 · 17 |
Discriminant |
Eigenvalues |
1 3- 5+ 7- -4 13- 17+ 4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,0,-517140,-142335765] |
[a1,a2,a3,a4,a6] |
j |
20980751961338245441/114207470718705 |
j-invariant |
L |
2.8494418517757 |
L(r)(E,1)/r! |
Ω |
0.17809011616751 |
Real period |
R |
1 |
Regulator |
r |
0 |
Rank of the group of rational points |
S |
4 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
23205o1 |
Quadratic twists by: -3 |