Atkin-Lehner |
2- 3- 5+ 19+ |
Signs for the Atkin-Lehner involutions |
Class |
68400ep |
Isogeny class |
Conductor |
68400 |
Conductor |
∏ cp |
64 |
Product of Tamagawa factors cp |
deg |
491520 |
Modular degree for the optimal curve |
Δ |
-20464021440000000 = -1 · 212 · 311 · 57 · 192 |
Discriminant |
Eigenvalues |
2- 3- 5+ -2 -6 0 -6 19+ |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,68325,-341750] |
[a1,a2,a3,a4,a6] |
Generators |
[119:-3078:1] |
Generators of the group modulo torsion |
j |
756058031/438615 |
j-invariant |
L |
4.2160768327857 |
L(r)(E,1)/r! |
Ω |
0.22781506429512 |
Real period |
R |
1.1566610087075 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999993454 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
4275l1 22800cz1 13680bl1 |
Quadratic twists by: -4 -3 5 |