Atkin-Lehner |
2+ 3+ 13+ |
Signs for the Atkin-Lehner involutions |
Class |
32448n |
Isogeny class |
Conductor |
32448 |
Conductor |
∏ cp |
8 |
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 |
[1335:18928:27] |
Generators of the group modulo torsion |
j |
702464/4563 |
j-invariant |
L |
3.6335734860306 |
L(r)(E,1)/r! |
Ω |
0.49140569375297 |
Real period |
R |
3.6971218813932 |
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 |
32448dh1 4056h1 97344cw1 2496g1 |
Quadratic twists by: -4 8 -3 13 |