Atkin-Lehner |
3+ 13+ 89+ |
Signs for the Atkin-Lehner involutions |
Class |
10413b |
Isogeny class |
Conductor |
10413 |
Conductor |
∏ cp |
2 |
Product of Tamagawa factors cp |
deg |
4032 |
Modular degree for the optimal curve |
Δ |
-22773231 = -1 · 39 · 13 · 89 |
Discriminant |
Eigenvalues |
-1 3+ -3 -1 5 13+ 4 -5 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,1,-434,3592] |
[a1,a2,a3,a4,a6] |
Generators |
[10:8:1] |
Generators of the group modulo torsion |
j |
-458314011/1157 |
j-invariant |
L |
2.1178006298176 |
L(r)(E,1)/r! |
Ω |
2.1461414248341 |
Real period |
R |
0.49339726760583 |
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 |
10413d1 |
Quadratic twists by: -3 |