Atkin-Lehner |
3+ 11- 67+ |
Signs for the Atkin-Lehner involutions |
Class |
24321j |
Isogeny class |
Conductor |
24321 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
28800 |
Modular degree for the optimal curve |
Δ |
-3916921371 = -1 · 3 · 117 · 67 |
Discriminant |
Eigenvalues |
-2 3+ -3 -3 11- 3 -6 0 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,1,-1492,22890] |
[a1,a2,a3,a4,a6] |
Generators |
[-42:98:1] [-7:181:1] |
Generators of the group modulo torsion |
j |
-207474688/2211 |
j-invariant |
L |
2.7292260026221 |
L(r)(E,1)/r! |
Ω |
1.3997668339347 |
Real period |
R |
0.48744296843872 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
1.0000000000005 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
72963o1 2211c1 |
Quadratic twists by: -3 -11 |