Atkin-Lehner |
2- 3+ 29- 31+ |
Signs for the Atkin-Lehner involutions |
Class |
129456z |
Isogeny class |
Conductor |
129456 |
Conductor |
∏ cp |
48 |
Product of Tamagawa factors cp |
deg |
995328 |
Modular degree for the optimal curve |
Δ |
-1327122629001216 = -1 · 221 · 33 · 293 · 312 |
Discriminant |
Eigenvalues |
2- 3+ -3 1 6 -4 -3 7 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-227259,-41736214] |
[a1,a2,a3,a4,a6] |
Generators |
[685:11136:1] |
Generators of the group modulo torsion |
j |
-11737166732534979/12000168448 |
j-invariant |
L |
5.9149194777493 |
L(r)(E,1)/r! |
Ω |
0.10932328216443 |
Real period |
R |
1.1271842906711 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000232045 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
16182k1 129456t2 |
Quadratic twists by: -4 -3 |