Atkin-Lehner |
2+ 3- 13- 23+ |
Signs for the Atkin-Lehner involutions |
Class |
86112m |
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 |
[121:468:1] |
Generators of the group modulo torsion |
j |
-48276258286528/478882287 |
j-invariant |
L |
6.3221994152807 |
L(r)(E,1)/r! |
Ω |
0.68100884013965 |
Real period |
R |
1.1604473826443 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.000000001028 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
86112bo1 28704p1 |
Quadratic twists by: -4 -3 |