Atkin-Lehner |
2- 3+ 5- 19+ |
Signs for the Atkin-Lehner involutions |
Class |
68400dy |
Isogeny class |
Conductor |
68400 |
Conductor |
∏ cp |
6 |
Product of Tamagawa factors cp |
deg |
172800 |
Modular degree for the optimal curve |
Δ |
-37397700000000 = -1 · 28 · 39 · 58 · 19 |
Discriminant |
Eigenvalues |
2- 3+ 5- -4 -5 2 0 19+ |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-3375,-303750] |
[a1,a2,a3,a4,a6] |
Generators |
[450:9450:1] |
Generators of the group modulo torsion |
j |
-2160/19 |
j-invariant |
L |
3.975216091743 |
L(r)(E,1)/r! |
Ω |
0.27450157636437 |
Real period |
R |
2.4135963951826 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000001593 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
17100k1 68400dx1 68400dk1 |
Quadratic twists by: -4 -3 5 |