Atkin-Lehner |
2- 3+ 7+ 17+ |
Signs for the Atkin-Lehner involutions |
Class |
4998y |
Isogeny class |
Conductor |
4998 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
24192 |
Modular degree for the optimal curve |
Δ |
493815251817216 = 28 · 39 · 78 · 17 |
Discriminant |
Eigenvalues |
2- 3+ 3 7+ -2 1 17+ 0 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,1,1,-19944,-187671] |
[a1,a2,a3,a4,a6] |
j |
152186997697/85660416 |
j-invariant |
L |
3.4592758808382 |
L(r)(E,1)/r! |
Ω |
0.43240948510477 |
Real period |
R |
1 |
Regulator |
r |
0 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
39984cs1 14994r1 124950cl1 4998br1 |
Quadratic twists by: -4 -3 5 -7 |