Atkin-Lehner |
2- 3- 5- 43- |
Signs for the Atkin-Lehner involutions |
Class |
61920cd |
Isogeny class |
Conductor |
61920 |
Conductor |
∏ cp |
84 |
Product of Tamagawa factors cp |
deg |
817152 |
Modular degree for the optimal curve |
Δ |
-187792353720000000 = -1 · 29 · 310 · 57 · 433 |
Discriminant |
Eigenvalues |
2- 3- 5- 3 4 -1 -4 -5 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-623307,190553294] |
[a1,a2,a3,a4,a6] |
Generators |
[553:-3870:1] |
Generators of the group modulo torsion |
j |
-71751706663500872/503130234375 |
j-invariant |
L |
7.9633336668461 |
L(r)(E,1)/r! |
Ω |
0.32094099227104 |
Real period |
R |
0.2953863593365 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000000337 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
61920bx1 123840et1 20640b1 |
Quadratic twists by: -4 8 -3 |