Atkin-Lehner |
3- 11- 67- |
Signs for the Atkin-Lehner involutions |
Class |
24321p |
Isogeny class |
Conductor |
24321 |
Conductor |
∏ cp |
36 |
Product of Tamagawa factors cp |
deg |
51840 |
Modular degree for the optimal curve |
Δ |
-25698921115131 = -1 · 39 · 117 · 67 |
Discriminant |
Eigenvalues |
0 3- -3 1 11- -5 -6 -2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,1,-3307,-255755] |
[a1,a2,a3,a4,a6] |
Generators |
[650:1085:8] [95:-545:1] |
Generators of the group modulo torsion |
j |
-2258403328/14506371 |
j-invariant |
L |
6.7799880119162 |
L(r)(E,1)/r! |
Ω |
0.28059162395155 |
Real period |
R |
0.67119965193097 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
0.99999999999989 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
72963t1 2211f1 |
Quadratic twists by: -3 -11 |