Atkin-Lehner |
2- 3+ 5- 19+ |
Signs for the Atkin-Lehner involutions |
Class |
6840l |
Isogeny class |
Conductor |
6840 |
Conductor |
∏ cp |
16 |
Product of Tamagawa factors cp |
deg |
15360 |
Modular degree for the optimal curve |
Δ |
239345280000 = 210 · 39 · 54 · 19 |
Discriminant |
Eigenvalues |
2- 3+ 5- 0 2 0 0 19+ |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-106947,-13461714] |
[a1,a2,a3,a4,a6] |
Generators |
[3267:185760:1] |
Generators of the group modulo torsion |
j |
6711788809548/11875 |
j-invariant |
L |
4.4913040415732 |
L(r)(E,1)/r! |
Ω |
0.26400214113533 |
Real period |
R |
4.2530943331166 |
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 |
13680d1 54720c1 6840a1 34200a1 |
Quadratic twists by: -4 8 -3 5 |