Atkin-Lehner |
2+ 3- 17+ 53+ |
Signs for the Atkin-Lehner involutions |
Class |
129744d |
Isogeny class |
Conductor |
129744 |
Conductor |
∏ cp |
32 |
Product of Tamagawa factors cp |
deg |
286720 |
Modular degree for the optimal curve |
Δ |
-50012662560768 = -1 · 211 · 313 · 172 · 53 |
Discriminant |
Eigenvalues |
2+ 3- -2 -1 -3 2 17+ 1 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-21891,-1292254] |
[a1,a2,a3,a4,a6] |
Generators |
[175:486:1] [661:16524:1] |
Generators of the group modulo torsion |
j |
-777075174146/33498279 |
j-invariant |
L |
10.382689026311 |
L(r)(E,1)/r! |
Ω |
0.19575339974825 |
Real period |
R |
1.6574886187841 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
0.99999999969553 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
64872a1 43248d1 |
Quadratic twists by: -4 -3 |