Atkin-Lehner |
2- 3- 5+ 19+ |
Signs for the Atkin-Lehner involutions |
Class |
68400ek |
Isogeny class |
Conductor |
68400 |
Conductor |
∏ cp |
32 |
Product of Tamagawa factors cp |
deg |
221184 |
Modular degree for the optimal curve |
Δ |
-159563520000000 = -1 · 214 · 38 · 57 · 19 |
Discriminant |
Eigenvalues |
2- 3- 5+ -2 0 -6 8 19+ |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-75,-607750] |
[a1,a2,a3,a4,a6] |
Generators |
[181:2304:1] |
Generators of the group modulo torsion |
j |
-1/3420 |
j-invariant |
L |
5.5779752128719 |
L(r)(E,1)/r! |
Ω |
0.26359993942669 |
Real period |
R |
2.6450950750823 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000000566 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
8550bc1 22800br1 13680ba1 |
Quadratic twists by: -4 -3 5 |