Atkin-Lehner |
2+ 3+ 5- 19- |
Signs for the Atkin-Lehner involutions |
Class |
13680d |
Isogeny class |
Conductor |
13680 |
Conductor |
∏ cp |
32 |
Product of Tamagawa factors cp |
deg |
30720 |
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 |
[193:100:1] |
Generators of the group modulo torsion |
j |
6711788809548/11875 |
j-invariant |
L |
5.085729121878 |
L(r)(E,1)/r! |
Ω |
0.84676072464388 |
Real period |
R |
0.75076243114855 |
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 |
6840l1 54720cr1 13680a1 68400d1 |
Quadratic twists by: -4 8 -3 5 |