Atkin-Lehner |
2+ 3+ 19+ |
Signs for the Atkin-Lehner involutions |
Class |
2736b |
Isogeny class |
Conductor |
2736 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
384 |
Modular degree for the optimal curve |
Δ |
95738112 = 28 · 39 · 19 |
Discriminant |
Eigenvalues |
2+ 3+ 0 0 -2 -2 4 19+ |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-135,-378] |
[a1,a2,a3,a4,a6] |
Generators |
[13:8:1] |
Generators of the group modulo torsion |
j |
54000/19 |
j-invariant |
L |
3.2526713342321 |
L(r)(E,1)/r! |
Ω |
1.4411502557823 |
Real period |
R |
2.2569966741368 |
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 |
1368b1 10944bq1 2736a1 68400b1 |
Quadratic twists by: -4 8 -3 5 |