Atkin-Lehner |
2- 3+ 5+ 7- 19- |
Signs for the Atkin-Lehner involutions |
Class |
127680eg |
Isogeny class |
Conductor |
127680 |
Conductor |
∏ cp |
24 |
Product of Tamagawa factors cp |
deg |
1105920 |
Modular degree for the optimal curve |
Δ |
-44835051405312000 = -1 · 223 · 38 · 53 · 73 · 19 |
Discriminant |
Eigenvalues |
2- 3+ 5+ 7- -5 -3 -5 19- |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,75999,6200001] |
[a1,a2,a3,a4,a6] |
Generators |
[-67:896:1] [-57:1296:1] |
Generators of the group modulo torsion |
j |
185183253170999/171032148000 |
j-invariant |
L |
9.11791482045 |
L(r)(E,1)/r! |
Ω |
0.23527126713328 |
Real period |
R |
1.6147875697087 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
0.99999999958497 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
127680cb1 31920by1 |
Quadratic twists by: -4 8 |