Atkin-Lehner |
2+ 3- 5- 29+ |
Signs for the Atkin-Lehner involutions |
Class |
83520cf |
Isogeny class |
Conductor |
83520 |
Conductor |
∏ cp |
16 |
Product of Tamagawa factors cp |
deg |
1032192 |
Modular degree for the optimal curve |
Δ |
167740550306795520 = 212 · 324 · 5 · 29 |
Discriminant |
Eigenvalues |
2+ 3- 5- -2 -2 4 -6 0 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-474132,-124105376] |
[a1,a2,a3,a4,a6] |
Generators |
[-570020:-842148:1331] |
Generators of the group modulo torsion |
j |
3947608165749184/56175970905 |
j-invariant |
L |
6.3356886956305 |
L(r)(E,1)/r! |
Ω |
0.1820953830222 |
Real period |
R |
8.6983104474414 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000008427 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
83520bx1 41760z1 27840bs1 |
Quadratic twists by: -4 8 -3 |