Atkin-Lehner |
2- 3- 61+ |
Signs for the Atkin-Lehner involutions |
Class |
11712bi |
Isogeny class |
Conductor |
11712 |
Conductor |
∏ cp |
12 |
Product of Tamagawa factors cp |
deg |
13824 |
Modular degree for the optimal curve |
Δ |
-2074745664 = -1 · 26 · 312 · 61 |
Discriminant |
Eigenvalues |
2- 3- 3 -1 -5 -5 6 -2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,0,-6544,-205966] |
[a1,a2,a3,a4,a6] |
Generators |
[125:972:1] |
Generators of the group modulo torsion |
j |
-484328442184768/32417901 |
j-invariant |
L |
6.1894762375298 |
L(r)(E,1)/r! |
Ω |
0.26540033211012 |
Real period |
R |
1.9434402450062 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
11712v1 5856c1 35136ce1 |
Quadratic twists by: -4 8 -3 |