Atkin-Lehner |
3+ 5- 7+ 11- 17+ |
Signs for the Atkin-Lehner involutions |
Class |
58905i |
Isogeny class |
Conductor |
58905 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
1152000 |
Modular degree for the optimal curve |
Δ |
7511923397540972025 = 39 · 52 · 710 · 11 · 173 |
Discriminant |
Eigenvalues |
-1 3+ 5- 7+ 11- 0 17+ 8 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,1,-608717,-126442916] |
[a1,a2,a3,a4,a6] |
Generators |
[1609706:107856958:343] |
Generators of the group modulo torsion |
j |
1267295938283304747/381645247042675 |
j-invariant |
L |
4.0673953375024 |
L(r)(E,1)/r! |
Ω |
0.17490614657357 |
Real period |
R |
11.62736535417 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.9999999999264 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
58905b1 |
Quadratic twists by: -3 |