Atkin-Lehner |
3+ 11- 67+ |
Signs for the Atkin-Lehner involutions |
Class |
24321i |
Isogeny class |
Conductor |
24321 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
2056320 |
Modular degree for the optimal curve |
Δ |
-2.0401885193801E+19 |
Discriminant |
Eigenvalues |
2 3+ -3 3 11- 5 -2 -4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,1,-11634432,15279885587] |
[a1,a2,a3,a4,a6] |
j |
-98311244861358051328/11516332315851 |
j-invariant |
L |
3.322250572349 |
L(r)(E,1)/r! |
Ω |
0.20764066077182 |
Real period |
R |
1 |
Regulator |
r |
0 |
Rank of the group of rational points |
S |
4 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
72963r1 2211d1 |
Quadratic twists by: -3 -11 |