Atkin-Lehner |
2+ 3- 61- |
Signs for the Atkin-Lehner involutions |
Class |
11712n |
Isogeny class |
Conductor |
11712 |
Conductor |
∏ cp |
52 |
Product of Tamagawa factors cp |
deg |
69888 |
Modular degree for the optimal curve |
Δ |
-3263292764061696 = -1 · 225 · 313 · 61 |
Discriminant |
Eigenvalues |
2+ 3- 1 2 -2 -4 1 -4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,0,-454145,-117982113] |
[a1,a2,a3,a4,a6] |
Generators |
[811:6912:1] |
Generators of the group modulo torsion |
j |
-39515579724486529/12448473984 |
j-invariant |
L |
6.0377730174025 |
L(r)(E,1)/r! |
Ω |
0.091952308704555 |
Real period |
R |
1.2627308786612 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
11712z1 366d1 35136w1 |
Quadratic twists by: -4 8 -3 |