Atkin-Lehner |
2- 3- 13+ |
Signs for the Atkin-Lehner involutions |
Class |
8112bi |
Isogeny class |
Conductor |
8112 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
8064 |
Modular degree for the optimal curve |
Δ |
9035786448 = 24 · 32 · 137 |
Discriminant |
Eigenvalues |
2- 3- 4 -2 -4 13+ 2 -2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,0,-901,-9658] |
[a1,a2,a3,a4,a6] |
Generators |
[4270:3042:125] |
Generators of the group modulo torsion |
j |
1048576/117 |
j-invariant |
L |
5.974216750706 |
L(r)(E,1)/r! |
Ω |
0.87763929876234 |
Real period |
R |
3.4035718085613 |
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 |
2028c1 32448cr1 24336cb1 624j1 |
Quadratic twists by: -4 8 -3 13 |