Atkin-Lehner |
2+ 3- 23- 71+ |
Signs for the Atkin-Lehner involutions |
Class |
78384i |
Isogeny class |
Conductor |
78384 |
Conductor |
∏ cp |
56 |
Product of Tamagawa factors cp |
deg |
1132544 |
Modular degree for the optimal curve |
Δ |
194558317783645392 = 24 · 37 · 238 · 71 |
Discriminant |
Eigenvalues |
2+ 3- -2 4 -4 6 6 -4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,0,-145039,1235912] |
[a1,a2,a3,a4,a6] |
Generators |
[8:276:1] |
Generators of the group modulo torsion |
j |
21089248978550536192/12159894861477837 |
j-invariant |
L |
8.560904618288 |
L(r)(E,1)/r! |
Ω |
0.27093266021345 |
Real period |
R |
2.256993256665 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999985038 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
39192g1 |
Quadratic twists by: -4 |