Atkin-Lehner |
2+ 3- 5+ 11- 19+ |
Signs for the Atkin-Lehner involutions |
Class |
68970w |
Isogeny class |
Conductor |
68970 |
Conductor |
∏ cp |
48 |
Product of Tamagawa factors cp |
deg |
1382400 |
Modular degree for the optimal curve |
Δ |
-4490740851855637500 = -1 · 22 · 36 · 55 · 1110 · 19 |
Discriminant |
Eigenvalues |
2+ 3- 5+ -2 11- 2 0 19+ |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,0,1,-113864,-103033438] |
[a1,a2,a3,a4,a6] |
Generators |
[7054:172161:8] |
Generators of the group modulo torsion |
j |
-92155535561809/2534906137500 |
j-invariant |
L |
4.7106624076108 |
L(r)(E,1)/r! |
Ω |
0.1063472404399 |
Real period |
R |
3.6912589269628 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000000066 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
6270o1 |
Quadratic twists by: -11 |