Atkin-Lehner |
2- 3+ 13- 31+ |
Signs for the Atkin-Lehner involutions |
Class |
19344o |
Isogeny class |
Conductor |
19344 |
Conductor |
∏ cp |
12 |
Product of Tamagawa factors cp |
deg |
4608 |
Modular degree for the optimal curve |
Δ |
-156918528 = -1 · 28 · 32 · 133 · 31 |
Discriminant |
Eigenvalues |
2- 3+ -2 2 -3 13- 0 2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-189,1233] |
[a1,a2,a3,a4,a6] |
Generators |
[21:78:1] |
Generators of the group modulo torsion |
j |
-2932006912/612963 |
j-invariant |
L |
3.7244337193901 |
L(r)(E,1)/r! |
Ω |
1.744325540938 |
Real period |
R |
0.17793093624539 |
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 |
4836f1 77376bk1 58032bk1 |
Quadratic twists by: -4 8 -3 |