Atkin-Lehner |
2+ 3- 13+ 23- |
Signs for the Atkin-Lehner involutions |
Class |
69966n |
Isogeny class |
Conductor |
69966 |
Conductor |
∏ cp |
32 |
Product of Tamagawa factors cp |
deg |
294912 |
Modular degree for the optimal curve |
Δ |
-943980426250992 = -1 · 24 · 312 · 136 · 23 |
Discriminant |
Eigenvalues |
2+ 3- 0 -2 0 13+ 0 -2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,0,-54027,-5041035] |
[a1,a2,a3,a4,a6] |
Generators |
[594:12825:1] |
Generators of the group modulo torsion |
j |
-4956477625/268272 |
j-invariant |
L |
3.9360083770899 |
L(r)(E,1)/r! |
Ω |
0.15608172617135 |
Real period |
R |
3.1522014723828 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000001766 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
23322t1 414a1 |
Quadratic twists by: -3 13 |