Atkin-Lehner |
3- 11- 67+ |
Signs for the Atkin-Lehner involutions |
Class |
24321m |
Isogeny class |
Conductor |
24321 |
Conductor |
∏ cp |
20 |
Product of Tamagawa factors cp |
deg |
115200 |
Modular degree for the optimal curve |
Δ |
422287209928881 = 35 · 1110 · 67 |
Discriminant |
Eigenvalues |
-1 3- 2 4 11- -2 -6 -4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,0,0,-45922,3652595] |
[a1,a2,a3,a4,a6] |
Generators |
[-133:2789:1] |
Generators of the group modulo torsion |
j |
6045477024313/238370121 |
j-invariant |
L |
5.2133486991747 |
L(r)(E,1)/r! |
Ω |
0.5260877016758 |
Real period |
R |
1.9819314089906 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
72963j1 2211e1 |
Quadratic twists by: -3 -11 |