Atkin-Lehner |
3- 7+ 11+ 89- |
Signs for the Atkin-Lehner involutions |
Class |
61677f |
Isogeny class |
Conductor |
61677 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
158400 |
Modular degree for the optimal curve |
Δ |
-384679449 = -1 · 36 · 72 · 112 · 89 |
Discriminant |
Eigenvalues |
1 3- 3 7+ 11+ 4 -7 7 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,0,-85293,9609138] |
[a1,a2,a3,a4,a6] |
Generators |
[10804:-5325:64] |
Generators of the group modulo torsion |
j |
-94132418755192273/527681 |
j-invariant |
L |
9.0289475134313 |
L(r)(E,1)/r! |
Ω |
1.1518929201065 |
Real period |
R |
1.9595891588469 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999998437 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
6853d1 |
Quadratic twists by: -3 |