Atkin-Lehner |
3+ 7- 17+ 19+ |
Signs for the Atkin-Lehner involutions |
Class |
128877f |
Isogeny class |
Conductor |
128877 |
Conductor |
∏ cp |
21 |
Product of Tamagawa factors cp |
deg |
197568 |
Modular degree for the optimal curve |
Δ |
-5473572312453 = -1 · 3 · 77 · 17 · 194 |
Discriminant |
Eigenvalues |
1 3+ 0 7- -2 -2 17+ 19+ |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,1,0,-6505,228502] |
[a1,a2,a3,a4,a6] |
Generators |
[-738:2231:8] [18:334:1] |
Generators of the group modulo torsion |
j |
-233644479625/42000693 |
j-invariant |
L |
12.162424609637 |
L(r)(E,1)/r! |
Ω |
0.73266710921073 |
Real period |
R |
0.79048597884798 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
0.99999999940467 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
128877p1 |
Quadratic twists by: -19 |