Atkin-Lehner |
2- 3- 5+ 19+ |
Signs for the Atkin-Lehner involutions |
Class |
6840q |
Isogeny class |
Conductor |
6840 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
53760 |
Modular degree for the optimal curve |
Δ |
-1352636718750000 = -1 · 24 · 36 · 514 · 19 |
Discriminant |
Eigenvalues |
2- 3- 5+ 4 -4 -4 2 19+ |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-234318,43693117] |
[a1,a2,a3,a4,a6] |
Generators |
[282:203:1] |
Generators of the group modulo torsion |
j |
-121981271658244096/115966796875 |
j-invariant |
L |
4.1336061701338 |
L(r)(E,1)/r! |
Ω |
0.47887170173426 |
Real period |
R |
4.3159850072198 |
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 |
13680r1 54720cm1 760b1 34200y1 |
Quadratic twists by: -4 8 -3 5 |