Atkin-Lehner |
2- 3+ 7+ 11- 13+ |
Signs for the Atkin-Lehner involutions |
Class |
48048bh |
Isogeny class |
Conductor |
48048 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
403200 |
Modular degree for the optimal curve |
Δ |
-6394276586041344 = -1 · 212 · 310 · 75 · 112 · 13 |
Discriminant |
Eigenvalues |
2- 3+ -1 7+ 11- 13+ -4 -7 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-524501,-146082723] |
[a1,a2,a3,a4,a6] |
Generators |
[26796562:895479057:17576] |
Generators of the group modulo torsion |
j |
-3895861901277528064/1561102682139 |
j-invariant |
L |
3.5985189665098 |
L(r)(E,1)/r! |
Ω |
0.088699765365805 |
Real period |
R |
10.142413995255 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000000061 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
3003h1 |
Quadratic twists by: -4 |