Atkin-Lehner |
2- 3+ 29+ 31+ |
Signs for the Atkin-Lehner involutions |
Class |
129456s |
Isogeny class |
Conductor |
129456 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
24576 |
Modular degree for the optimal curve |
Δ |
-12039408 = -1 · 24 · 33 · 29 · 312 |
Discriminant |
Eigenvalues |
2- 3+ -2 -5 -1 -1 -7 0 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-21,171] |
[a1,a2,a3,a4,a6] |
Generators |
[-6:9:1] [10:31:1] |
Generators of the group modulo torsion |
j |
-2370816/27869 |
j-invariant |
L |
8.4199187609024 |
L(r)(E,1)/r! |
Ω |
1.918237835811 |
Real period |
R |
1.0973507313287 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
0.99999999916204 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
32364c1 129456y1 |
Quadratic twists by: -4 -3 |