Atkin-Lehner |
2+ 3- 5+ 47+ |
Signs for the Atkin-Lehner involutions |
Class |
67680d |
Isogeny class |
Conductor |
67680 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
2523136 |
Modular degree for the optimal curve |
Δ |
-1942268051520000000 = -1 · 212 · 317 · 57 · 47 |
Discriminant |
Eigenvalues |
2+ 3- 5+ 3 -6 -5 7 7 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-1953948,1053414272] |
[a1,a2,a3,a4,a6] |
j |
-276296409398322496/650461640625 |
j-invariant |
L |
2.1069799265266 |
L(r)(E,1)/r! |
Ω |
0.26337249267461 |
Real period |
R |
1 |
Regulator |
r |
0 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
67680f1 22560r1 |
Quadratic twists by: -4 -3 |