Atkin-Lehner |
2- 3+ 5+ 7+ 13- |
Signs for the Atkin-Lehner involutions |
Class |
21840bd |
Isogeny class |
Conductor |
21840 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
165888 |
Modular degree for the optimal curve |
Δ |
-12424028718366720 = -1 · 220 · 312 · 5 · 73 · 13 |
Discriminant |
Eigenvalues |
2- 3+ 5+ 7+ 0 13- -6 4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-54776,-7269264] |
[a1,a2,a3,a4,a6] |
Generators |
[140083020:-991692288:456533] |
Generators of the group modulo torsion |
j |
-4437543642183289/3033210136320 |
j-invariant |
L |
3.644933026092 |
L(r)(E,1)/r! |
Ω |
0.15143543721342 |
Real period |
R |
12.034610567918 |
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 |
2730n1 87360gr1 65520du1 109200fy1 |
Quadratic twists by: -4 8 -3 5 |