Atkin-Lehner |
3- 23+ 67- |
Signs for the Atkin-Lehner involutions |
Class |
13869a |
Isogeny class |
Conductor |
13869 |
Conductor |
∏ cp |
2 |
Product of Tamagawa factors cp |
deg |
41472 |
Modular degree for the optimal curve |
Δ |
11697071148423 = 315 · 233 · 67 |
Discriminant |
Eigenvalues |
1 3- 4 -2 1 -4 3 -5 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,0,-10260,367173] |
[a1,a2,a3,a4,a6] |
Generators |
[124:933:1] |
Generators of the group modulo torsion |
j |
163855897047361/16045365087 |
j-invariant |
L |
6.785762480554 |
L(r)(E,1)/r! |
Ω |
0.69541170656066 |
Real period |
R |
4.8789532995603 |
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 |
4623c1 |
Quadratic twists by: -3 |