Atkin-Lehner |
2- 3+ 7- 17+ |
Signs for the Atkin-Lehner involutions |
Class |
39984bl |
Isogeny class |
Conductor |
39984 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
138240 |
Modular degree for the optimal curve |
Δ |
-111478575366144 = -1 · 215 · 35 · 77 · 17 |
Discriminant |
Eigenvalues |
2- 3+ -1 7- -3 3 17+ 6 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-29416,-1997456] |
[a1,a2,a3,a4,a6] |
Generators |
[852:24304:1] |
Generators of the group modulo torsion |
j |
-5841725401/231336 |
j-invariant |
L |
4.372806252182 |
L(r)(E,1)/r! |
Ω |
0.18185090138985 |
Real period |
R |
3.0057633882755 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000000004 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
4998n1 119952ga1 5712ba1 |
Quadratic twists by: -4 -3 -7 |