Atkin-Lehner |
3+ 7- 11+ 89+ |
Signs for the Atkin-Lehner involutions |
Class |
20559c |
Isogeny class |
Conductor |
20559 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
10880 |
Modular degree for the optimal curve |
Δ |
-21155211 = -1 · 32 · 74 · 11 · 89 |
Discriminant |
Eigenvalues |
-2 3+ -3 7- 11+ -5 4 -8 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,1,-82,390] |
[a1,a2,a3,a4,a6] |
Generators |
[18:-67:1] [-5:25:1] |
Generators of the group modulo torsion |
j |
-61723537408/21155211 |
j-invariant |
L |
2.9099314528721 |
L(r)(E,1)/r! |
Ω |
2.0310272214083 |
Real period |
R |
0.17909234685525 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
1.0000000000003 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
61677o1 |
Quadratic twists by: -3 |