Atkin-Lehner |
3- 5+ 13+ 17+ |
Signs for the Atkin-Lehner involutions |
Class |
129285t |
Isogeny class |
Conductor |
129285 |
Conductor |
∏ cp |
16 |
Product of Tamagawa factors cp |
deg |
1376256 |
Modular degree for the optimal curve |
Δ |
384408065134047825 = 38 · 52 · 1310 · 17 |
Discriminant |
Eigenvalues |
-1 3- 5+ -4 0 13+ 17+ -4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,1,-206888,-20492494] |
[a1,a2,a3,a4,a6] |
Generators |
[-384:1681:1] [-185:3472:1] |
Generators of the group modulo torsion |
j |
278317173889/109245825 |
j-invariant |
L |
5.8750932182467 |
L(r)(E,1)/r! |
Ω |
0.23149885547878 |
Real period |
R |
6.3446244803962 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
0.99999999925606 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
43095q1 9945i1 |
Quadratic twists by: -3 13 |