Atkin-Lehner |
2- 3- 23- 83- |
Signs for the Atkin-Lehner involutions |
Class |
68724g |
Isogeny class |
Conductor |
68724 |
Conductor |
∏ cp |
30 |
Product of Tamagawa factors cp |
deg |
417600 |
Modular degree for the optimal curve |
Δ |
-24304889161714608 = -1 · 24 · 36 · 232 · 835 |
Discriminant |
Eigenvalues |
2- 3- 0 -3 5 4 1 2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-112080,-16274063] |
[a1,a2,a3,a4,a6] |
Generators |
[1278:43907:1] |
Generators of the group modulo torsion |
j |
-13349363777536000/2083752500147 |
j-invariant |
L |
6.7212863126242 |
L(r)(E,1)/r! |
Ω |
0.12935139450185 |
Real period |
R |
1.7320484093284 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999998276 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
7636b1 |
Quadratic twists by: -3 |