Atkin-Lehner |
2+ 3- 13+ 23- |
Signs for the Atkin-Lehner involutions |
Class |
69966o |
Isogeny class |
Conductor |
69966 |
Conductor |
∏ cp |
32 |
Product of Tamagawa factors cp |
deg |
688128 |
Modular degree for the optimal curve |
Δ |
-17725854670713072 = -1 · 24 · 310 · 138 · 23 |
Discriminant |
Eigenvalues |
2+ 3- 0 -2 6 13+ -6 -2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,0,-236547,44801797] |
[a1,a2,a3,a4,a6] |
Generators |
[114:4337:1] |
Generators of the group modulo torsion |
j |
-415996269625/5037552 |
j-invariant |
L |
4.1280431095635 |
L(r)(E,1)/r! |
Ω |
0.39009854045614 |
Real period |
R |
1.3227565224502 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.9999999998232 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
23322j1 5382n1 |
Quadratic twists by: -3 13 |