Atkin-Lehner |
2+ 11- 67+ |
Signs for the Atkin-Lehner involutions |
Class |
129712d |
Isogeny class |
Conductor |
129712 |
Conductor |
∏ cp |
1 |
Product of Tamagawa factors cp |
deg |
18624 |
Modular degree for the optimal curve |
Δ |
-2075392 = -1 · 28 · 112 · 67 |
Discriminant |
Eigenvalues |
2+ 0 2 -4 11- 4 5 -5 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-44,-132] |
[a1,a2,a3,a4,a6] |
j |
-304128/67 |
j-invariant |
L |
0.91607331434179 |
L(r)(E,1)/r! |
Ω |
0.91607582135947 |
Real period |
R |
1 |
Regulator |
r |
0 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
64856j1 129712c1 |
Quadratic twists by: -4 -11 |