Atkin-Lehner |
2- 3+ 5+ 31- |
Signs for the Atkin-Lehner involutions |
Class |
111600cx |
Isogeny class |
Conductor |
111600 |
Conductor |
∏ cp |
32 |
Product of Tamagawa factors cp |
deg |
165888 |
Modular degree for the optimal curve |
Δ |
-2142720000000 = -1 · 215 · 33 · 57 · 31 |
Discriminant |
Eigenvalues |
2- 3+ 5+ -3 5 0 2 1 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-675,-70750] |
[a1,a2,a3,a4,a6] |
Generators |
[65:400:1] |
Generators of the group modulo torsion |
j |
-19683/1240 |
j-invariant |
L |
7.2951758905092 |
L(r)(E,1)/r! |
Ω |
0.36257665768488 |
Real period |
R |
0.62876151159683 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999659059 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
13950e1 111600cy1 22320bc1 |
Quadratic twists by: -4 -3 5 |