Atkin-Lehner |
2- 7+ 19- 23+ |
Signs for the Atkin-Lehner involutions |
Class |
12236a |
Isogeny class |
Conductor |
12236 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
4416 |
Modular degree for the optimal curve |
Δ |
-2349948272 = -1 · 24 · 72 · 194 · 23 |
Discriminant |
Eigenvalues |
2- -1 0 7+ 2 5 -4 19- |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-138,2461] |
[a1,a2,a3,a4,a6] |
Generators |
[27:133:1] |
Generators of the group modulo torsion |
j |
-18297184000/146871767 |
j-invariant |
L |
3.6639864264063 |
L(r)(E,1)/r! |
Ω |
1.2465597605375 |
Real period |
R |
0.36740982486336 |
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 |
48944w1 110124i1 85652a1 |
Quadratic twists by: -4 -3 -7 |