Atkin-Lehner |
2- 3+ 19- 29- |
Signs for the Atkin-Lehner involutions |
Class |
6612b |
Isogeny class |
Conductor |
6612 |
Conductor |
∏ cp |
36 |
Product of Tamagawa factors cp |
deg |
5760 |
Modular degree for the optimal curve |
Δ |
-13290437376 = -1 · 28 · 32 · 193 · 292 |
Discriminant |
Eigenvalues |
2- 3+ -3 -3 -3 0 1 19- |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-1477,23041] |
[a1,a2,a3,a4,a6] |
Generators |
[-41:114:1] [-5:174:1] |
Generators of the group modulo torsion |
j |
-1392897753088/51915771 |
j-invariant |
L |
3.8691912816531 |
L(r)(E,1)/r! |
Ω |
1.2503669641533 |
Real period |
R |
0.085956794031492 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
0.99999999999966 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
26448r1 105792o1 19836g1 125628j1 |
Quadratic twists by: -4 8 -3 -19 |