Atkin-Lehner |
2+ 3- 29+ 31- |
Signs for the Atkin-Lehner involutions |
Class |
129456i |
Isogeny class |
Conductor |
129456 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
221184 |
Modular degree for the optimal curve |
Δ |
54359092224 = 210 · 310 · 29 · 31 |
Discriminant |
Eigenvalues |
2+ 3- 1 -4 6 0 -1 -1 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-27147,-1721558] |
[a1,a2,a3,a4,a6] |
Generators |
[707:18234:1] |
Generators of the group modulo torsion |
j |
2963887778596/72819 |
j-invariant |
L |
7.2832851326426 |
L(r)(E,1)/r! |
Ω |
0.37193730006957 |
Real period |
R |
4.8955060533334 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999998858187 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
64728l1 43152j1 |
Quadratic twists by: -4 -3 |