Atkin-Lehner |
2- 3- 13+ |
Signs for the Atkin-Lehner involutions |
Class |
32448dh |
Isogeny class |
Conductor |
32448 |
Conductor |
∏ cp |
24 |
Product of Tamagawa factors cp |
deg |
129024 |
Modular degree for the optimal curve |
Δ |
-22553322974208 = -1 · 210 · 33 · 138 |
Discriminant |
Eigenvalues |
2- 3- -4 -4 2 13+ -6 -4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,0,3155,-217021] |
[a1,a2,a3,a4,a6] |
Generators |
[251:4056:1] |
Generators of the group modulo torsion |
j |
702464/4563 |
j-invariant |
L |
3.4157903012672 |
L(r)(E,1)/r! |
Ω |
0.33811049037791 |
Real period |
R |
1.6837643307317 |
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 |
32448n1 8112e1 97344gd1 2496bd1 |
Quadratic twists by: -4 8 -3 13 |