Atkin-Lehner |
2+ 3- 7- 17+ |
Signs for the Atkin-Lehner involutions |
Class |
68544bv |
Isogeny class |
Conductor |
68544 |
Conductor |
∏ cp |
12 |
Product of Tamagawa factors cp |
deg |
245760 |
Modular degree for the optimal curve |
Δ |
-5804848674422784 = -1 · 214 · 311 · 76 · 17 |
Discriminant |
Eigenvalues |
2+ 3- -1 7- 1 3 17+ 5 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,4272,-3664096] |
[a1,a2,a3,a4,a6] |
Generators |
[145:63:1] |
Generators of the group modulo torsion |
j |
721888256/486008019 |
j-invariant |
L |
6.7846925263678 |
L(r)(E,1)/r! |
Ω |
0.1991914330544 |
Real period |
R |
2.8384305248361 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999999386 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
68544dk1 8568e1 22848p1 |
Quadratic twists by: -4 8 -3 |