Atkin-Lehner |
2+ 7+ 13+ 17- |
Signs for the Atkin-Lehner involutions |
Class |
99008h |
Isogeny class |
Conductor |
99008 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
52377600 |
Modular degree for the optimal curve |
Δ |
-298984846311424 = -1 · 214 · 75 · 13 · 174 |
Discriminant |
Eigenvalues |
2+ 2 -1 7+ 0 13+ 17- 5 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-25575542021,1574300868678557] |
[a1,a2,a3,a4,a6] |
j |
-112921935191145358638804243137536/18248586811 |
j-invariant |
L |
3.4321772807722 |
L(r)(E,1)/r! |
Ω |
0.095338270003829 |
Real period |
R |
1 |
Regulator |
r |
0 |
Rank of the group of rational points |
S |
9 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
99008cw1 12376j1 |
Quadratic twists by: -4 8 |