Atkin-Lehner |
2- 3- 13+ 23+ |
Signs for the Atkin-Lehner involutions |
Class |
69966bc |
Isogeny class |
Conductor |
69966 |
Conductor |
∏ cp |
64 |
Product of Tamagawa factors cp |
deg |
1032192 |
Modular degree for the optimal curve |
Δ |
-159532692036417648 = -1 · 24 · 312 · 138 · 23 |
Discriminant |
Eigenvalues |
2- 3- -4 -2 0 13+ 0 -2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,1,68413,-17957325] |
[a1,a2,a3,a4,a6] |
Generators |
[2129:97800:1] |
Generators of the group modulo torsion |
j |
10063705679/45337968 |
j-invariant |
L |
5.941000754973 |
L(r)(E,1)/r! |
Ω |
0.16336452927112 |
Real period |
R |
2.2729080102015 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000000611 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
23322f1 5382d1 |
Quadratic twists by: -3 13 |