Atkin-Lehner |
5- 7+ 17+ 31- |
Signs for the Atkin-Lehner involutions |
Class |
129115p |
Isogeny class |
Conductor |
129115 |
Conductor |
∏ cp |
3 |
Product of Tamagawa factors cp |
deg |
836640 |
Modular degree for the optimal curve |
Δ |
-1268704923285835 = -1 · 5 · 78 · 175 · 31 |
Discriminant |
Eigenvalues |
-2 0 5- 7+ -3 5 17+ 3 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,1,-81977,-9195230] |
[a1,a2,a3,a4,a6] |
Generators |
[11515:1235265:1] |
Generators of the group modulo torsion |
j |
-10568551182336/220077835 |
j-invariant |
L |
2.8621669033403 |
L(r)(E,1)/r! |
Ω |
0.14089998506404 |
Real period |
R |
6.7711550106436 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999431977 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
129115j1 |
Quadratic twists by: -7 |