Atkin-Lehner |
2- 3+ 5+ 17- |
Signs for the Atkin-Lehner involutions |
Class |
12240bf |
Isogeny class |
Conductor |
12240 |
Conductor |
∏ cp |
16 |
Product of Tamagawa factors cp |
deg |
12288 |
Modular degree for the optimal curve |
Δ |
-116498165760 = -1 · 212 · 39 · 5 · 172 |
Discriminant |
Eigenvalues |
2- 3+ 5+ -4 -2 2 17- 0 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-2403,-48222] |
[a1,a2,a3,a4,a6] |
Generators |
[111:1026:1] |
Generators of the group modulo torsion |
j |
-19034163/1445 |
j-invariant |
L |
3.5278808278604 |
L(r)(E,1)/r! |
Ω |
0.33946238024967 |
Real period |
R |
2.5981382865353 |
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 |
765a1 48960dz1 12240bj1 61200dg1 |
Quadratic twists by: -4 8 -3 5 |