Atkin-Lehner |
2+ 11- 67+ |
Signs for the Atkin-Lehner involutions |
Class |
129712h |
Isogeny class |
Conductor |
129712 |
Conductor |
∏ cp |
2 |
Product of Tamagawa factors cp |
deg |
31488 |
Modular degree for the optimal curve |
Δ |
-2075392 = -1 · 28 · 112 · 67 |
Discriminant |
Eigenvalues |
2+ -2 4 -4 11- 4 -2 5 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,0,4,-68] |
[a1,a2,a3,a4,a6] |
j |
176/67 |
j-invariant |
L |
2.4500202566651 |
L(r)(E,1)/r! |
Ω |
1.2250102573195 |
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 |
64856l1 129712g1 |
Quadratic twists by: -4 -11 |