Atkin-Lehner |
3- 7+ 11- 89+ |
Signs for the Atkin-Lehner involutions |
Class |
61677j |
Isogeny class |
Conductor |
61677 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
27648 |
Modular degree for the optimal curve |
Δ |
-34970859 = -1 · 36 · 72 · 11 · 89 |
Discriminant |
Eigenvalues |
-2 3- 3 7+ 11- -3 -2 4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,1,-531,4718] |
[a1,a2,a3,a4,a6] |
Generators |
[18:31:1] |
Generators of the group modulo torsion |
j |
-22713274368/47971 |
j-invariant |
L |
3.7897706976172 |
L(r)(E,1)/r! |
Ω |
2.0684633510777 |
Real period |
R |
0.45804179898311 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999994304 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
6853c1 |
Quadratic twists by: -3 |