Atkin-Lehner |
2+ 3- 5- 11+ |
Signs for the Atkin-Lehner involutions |
Class |
31680bc |
Isogeny class |
Conductor |
31680 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
8192 |
Modular degree for the optimal curve |
Δ |
320760000 = 26 · 36 · 54 · 11 |
Discriminant |
Eigenvalues |
2+ 3- 5- 0 11+ 2 2 -4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-207,-756] |
[a1,a2,a3,a4,a6] |
Generators |
[24:90:1] |
Generators of the group modulo torsion |
j |
21024576/6875 |
j-invariant |
L |
6.0880384173869 |
L(r)(E,1)/r! |
Ω |
1.2914883886636 |
Real period |
R |
2.3569853476138 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
31680bq1 15840i2 3520d1 |
Quadratic twists by: -4 8 -3 |