Atkin-Lehner |
2- 3- 13- 89+ |
Signs for the Atkin-Lehner involutions |
Class |
83304s |
Isogeny class |
Conductor |
83304 |
Conductor |
∏ cp |
28 |
Product of Tamagawa factors cp |
deg |
284928 |
Modular degree for the optimal curve |
Δ |
1042223752058112 = 28 · 36 · 137 · 89 |
Discriminant |
Eigenvalues |
2- 3- 0 1 -2 13- -7 -7 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-39900,-2645372] |
[a1,a2,a3,a4,a6] |
Generators |
[-144:338:1] [-79:117:1] |
Generators of the group modulo torsion |
j |
37642192000000/5584618013 |
j-invariant |
L |
11.247164826988 |
L(r)(E,1)/r! |
Ω |
0.34115137390771 |
Real period |
R |
1.1774376093178 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
0.99999999999332 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
9256a1 |
Quadratic twists by: -3 |