Atkin-Lehner |
2- 3- 5- 7- 13- |
Signs for the Atkin-Lehner involutions |
Class |
21840cl |
Isogeny class |
Conductor |
21840 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
196608 |
Modular degree for the optimal curve |
Δ |
-72040001851883520 = -1 · 244 · 32 · 5 · 7 · 13 |
Discriminant |
Eigenvalues |
2- 3- 5- 7- -4 13- 2 4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,0,-348160,-80234572] |
[a1,a2,a3,a4,a6] |
j |
-1139466686381936641/17587891077120 |
j-invariant |
L |
3.1417844275253 |
L(r)(E,1)/r! |
Ω |
0.098180763360165 |
Real period |
R |
1 |
Regulator |
r |
0 |
Rank of the group of rational points |
S |
16 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
2730v1 87360eo1 65520de1 109200cz1 |
Quadratic twists by: -4 8 -3 5 |