Atkin-Lehner |
2+ 3- 23- 71+ |
Signs for the Atkin-Lehner involutions |
Class |
78384f |
Isogeny class |
Conductor |
78384 |
Conductor |
∏ cp |
2 |
Product of Tamagawa factors cp |
deg |
12288 |
Modular degree for the optimal curve |
Δ |
1802832 = 24 · 3 · 232 · 71 |
Discriminant |
Eigenvalues |
2+ 3- 0 -2 0 6 6 -8 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,0,-63,-204] |
[a1,a2,a3,a4,a6] |
Generators |
[122980:1184004:1331] |
Generators of the group modulo torsion |
j |
1755904000/112677 |
j-invariant |
L |
7.9634578717753 |
L(r)(E,1)/r! |
Ω |
1.6991667214789 |
Real period |
R |
9.3733684518313 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.000000000128 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
39192b1 |
Quadratic twists by: -4 |