Atkin-Lehner |
2+ 29+ 59+ |
Signs for the Atkin-Lehner involutions |
Class |
3422b |
Isogeny class |
Conductor |
3422 |
Conductor |
∏ cp |
1 |
Product of Tamagawa factors cp |
deg |
13608 |
Modular degree for the optimal curve |
Δ |
229646532608 = 227 · 29 · 59 |
Discriminant |
Eigenvalues |
2+ -2 4 -2 5 -3 -6 0 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,0,1,-15989,-779136] |
[a1,a2,a3,a4,a6] |
Generators |
[-1986:1442:27] |
Generators of the group modulo torsion |
j |
452010552257419849/229646532608 |
j-invariant |
L |
2.2717578903218 |
L(r)(E,1)/r! |
Ω |
0.4245811664995 |
Real period |
R |
5.3505856349011 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
27376g1 109504m1 30798u1 85550q1 |
Quadratic twists by: -4 8 -3 5 |