Atkin-Lehner |
2- 3- 5+ 11+ 17+ |
Signs for the Atkin-Lehner involutions |
Class |
61710ce |
Isogeny class |
Conductor |
61710 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
218880 |
Modular degree for the optimal curve |
Δ |
-980880450000 = -1 · 24 · 3 · 55 · 113 · 173 |
Discriminant |
Eigenvalues |
2- 3- 5+ -5 11+ -7 17+ -1 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,0,0,-1856,-56880] |
[a1,a2,a3,a4,a6] |
Generators |
[54:6:1] |
Generators of the group modulo torsion |
j |
-531244194299/736950000 |
j-invariant |
L |
7.4776623883415 |
L(r)(E,1)/r! |
Ω |
0.34614012199238 |
Real period |
R |
2.7003740369611 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999996141 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
61710v1 |
Quadratic twists by: -11 |