Atkin-Lehner |
3- 13+ 59- |
Signs for the Atkin-Lehner involutions |
Class |
89739f |
Isogeny class |
Conductor |
89739 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
387072 |
Modular degree for the optimal curve |
Δ |
-1967480942756823 = -1 · 312 · 137 · 59 |
Discriminant |
Eigenvalues |
-1 3- 0 -2 -4 13+ -6 6 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,1,10615,-2094816] |
[a1,a2,a3,a4,a6] |
Generators |
[6176:482304:1] |
Generators of the group modulo torsion |
j |
37595375/559143 |
j-invariant |
L |
2.7363500776359 |
L(r)(E,1)/r! |
Ω |
0.22825145132156 |
Real period |
R |
5.9941569980793 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000033307 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
29913a1 6903f1 |
Quadratic twists by: -3 13 |