Atkin-Lehner |
2+ 3- 19- |
Signs for the Atkin-Lehner involutions |
Class |
51984x |
Isogeny class |
Conductor |
51984 |
Conductor |
∏ cp |
16 |
Product of Tamagawa factors cp |
deg |
276480 |
Modular degree for the optimal curve |
Δ |
4504083824316672 = 28 · 39 · 197 |
Discriminant |
Eigenvalues |
2+ 3- -2 0 0 -2 -2 19- |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-559911,161227654] |
[a1,a2,a3,a4,a6] |
Generators |
[389:1512:1] |
Generators of the group modulo torsion |
j |
2211014608/513 |
j-invariant |
L |
4.4758995249536 |
L(r)(E,1)/r! |
Ω |
0.42433932014651 |
Real period |
R |
2.6369813687213 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999999659 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
25992k1 17328m1 2736j1 |
Quadratic twists by: -4 -3 -19 |