Atkin-Lehner |
3+ 5- 13+ 17- |
Signs for the Atkin-Lehner involutions |
Class |
129285m |
Isogeny class |
Conductor |
129285 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
1032192 |
Modular degree for the optimal curve |
Δ |
-23200960144185135 = -1 · 39 · 5 · 138 · 172 |
Discriminant |
Eigenvalues |
1 3+ 5- -4 -2 13+ 17- -4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,0,54471,-5469112] |
[a1,a2,a3,a4,a6] |
Generators |
[85453236:28254734:970299] |
Generators of the group modulo torsion |
j |
188132517/244205 |
j-invariant |
L |
4.9735623520497 |
L(r)(E,1)/r! |
Ω |
0.20292063462017 |
Real period |
R |
12.254944644749 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000126578 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
129285e1 9945a1 |
Quadratic twists by: -3 13 |