Atkin-Lehner |
2- 3- 7- 17- |
Signs for the Atkin-Lehner involutions |
Class |
68544ex |
Isogeny class |
Conductor |
68544 |
Conductor |
∏ cp |
24 |
Product of Tamagawa factors cp |
deg |
589824 |
Modular degree for the optimal curve |
Δ |
2457845172038592 = 26 · 318 · 73 · 172 |
Discriminant |
Eigenvalues |
2- 3- -2 7- -4 -2 17- 4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-1191711,500725384] |
[a1,a2,a3,a4,a6] |
Generators |
[636:238:1] |
Generators of the group modulo torsion |
j |
4011705594213827392/52680152007 |
j-invariant |
L |
4.6906222359774 |
L(r)(E,1)/r! |
Ω |
0.41736080061661 |
Real period |
R |
1.8731284093446 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000001038 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
68544eb1 34272t4 22848cs1 |
Quadratic twists by: -4 8 -3 |