Atkin-Lehner |
2- 3+ 5+ 13+ |
Signs for the Atkin-Lehner involutions |
Class |
18720w |
Isogeny class |
Conductor |
18720 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
3072 |
Modular degree for the optimal curve |
Δ |
-14040000 = -1 · 26 · 33 · 54 · 13 |
Discriminant |
Eigenvalues |
2- 3+ 5+ -2 -4 13+ -4 -2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,27,172] |
[a1,a2,a3,a4,a6] |
Generators |
[-3:8:1] [-1:12:1] |
Generators of the group modulo torsion |
j |
1259712/8125 |
j-invariant |
L |
6.568046225368 |
L(r)(E,1)/r! |
Ω |
1.6161999961325 |
Real period |
R |
2.0319410472361 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
0.99999999999988 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
18720a1 37440y2 18720c1 93600e1 |
Quadratic twists by: -4 8 -3 5 |