Atkin-Lehner |
2+ 13+ 29+ |
Signs for the Atkin-Lehner involutions |
Class |
24128b |
Isogeny class |
Conductor |
24128 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
239616 |
Modular degree for the optimal curve |
Δ |
-19745366966534144 = -1 · 231 · 13 · 294 |
Discriminant |
Eigenvalues |
2+ -1 -1 -1 6 13+ -7 2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-688481,220213729] |
[a1,a2,a3,a4,a6] |
Generators |
[425:2048:1] |
Generators of the group modulo torsion |
j |
-137676653031953881/75322597376 |
j-invariant |
L |
3.5308708658514 |
L(r)(E,1)/r! |
Ω |
0.38033727735279 |
Real period |
R |
1.1604407049011 |
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 |
24128n1 754b1 |
Quadratic twists by: -4 8 |