Atkin-Lehner |
2- 3- 23+ 83+ |
Signs for the Atkin-Lehner involutions |
Class |
68724b |
Isogeny class |
Conductor |
68724 |
Conductor |
∏ cp |
6 |
Product of Tamagawa factors cp |
deg |
36960 |
Modular degree for the optimal curve |
Δ |
-512131248 = -1 · 24 · 36 · 232 · 83 |
Discriminant |
Eigenvalues |
2- 3- -2 3 3 4 5 2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-1116,-14391] |
[a1,a2,a3,a4,a6] |
Generators |
[67:460:1] |
Generators of the group modulo torsion |
j |
-13178585088/43907 |
j-invariant |
L |
7.1602128219476 |
L(r)(E,1)/r! |
Ω |
0.41292091090403 |
Real period |
R |
2.890066286406 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000000856 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
7636f1 |
Quadratic twists by: -3 |