Atkin-Lehner |
2- 3- 13- 23- |
Signs for the Atkin-Lehner involutions |
Class |
86112bo |
Isogeny class |
Conductor |
86112 |
Conductor |
∏ cp |
32 |
Product of Tamagawa factors cp |
deg |
196608 |
Modular degree for the optimal curve |
Δ |
-22342731982272 = -1 · 26 · 312 · 134 · 23 |
Discriminant |
Eigenvalues |
2- 3- 2 2 2 13- -4 4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-27309,-1751852] |
[a1,a2,a3,a4,a6] |
Generators |
[7068:81172:27] |
Generators of the group modulo torsion |
j |
-48276258286528/478882287 |
j-invariant |
L |
9.1339886293602 |
L(r)(E,1)/r! |
Ω |
0.18558216431459 |
Real period |
R |
6.152253816327 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000000205 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
86112m1 28704j1 |
Quadratic twists by: -4 -3 |