Atkin-Lehner |
3- 7- 19+ 31+ |
Signs for the Atkin-Lehner involutions |
Class |
12369i |
Isogeny class |
Conductor |
12369 |
Conductor |
∏ cp |
24 |
Product of Tamagawa factors cp |
deg |
13056 |
Modular degree for the optimal curve |
Δ |
-144311089671 = -1 · 36 · 72 · 194 · 31 |
Discriminant |
Eigenvalues |
1 3- -2 7- 6 0 0 19+ |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,0,1,-372,-18515] |
[a1,a2,a3,a4,a6] |
Generators |
[35:90:1] |
Generators of the group modulo torsion |
j |
-5671177348537/144311089671 |
j-invariant |
L |
6.2881422584392 |
L(r)(E,1)/r! |
Ω |
0.44719602757325 |
Real period |
R |
2.3435443186449 |
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 |
37107l1 86583o1 |
Quadratic twists by: -3 -7 |