Atkin-Lehner |
3- 7- 67+ |
Signs for the Atkin-Lehner involutions |
Class |
4221h |
Isogeny class |
Conductor |
4221 |
Conductor |
∏ cp |
16 |
Product of Tamagawa factors cp |
deg |
6144 |
Modular degree for the optimal curve |
Δ |
-2534131577187 = -1 · 38 · 78 · 67 |
Discriminant |
Eigenvalues |
2 3- 0 7- -2 -4 3 -5 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,1,-615,-76815] |
[a1,a2,a3,a4,a6] |
Generators |
[514:3083:8] |
Generators of the group modulo torsion |
j |
-35287552000/3476175003 |
j-invariant |
L |
6.8281902769999 |
L(r)(E,1)/r! |
Ω |
0.35964064033275 |
Real period |
R |
1.1866342244237 |
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 |
67536bp1 1407f1 105525s1 29547t1 |
Quadratic twists by: -4 -3 5 -7 |