Atkin-Lehner |
2+ 3- 5- 19+ |
Signs for the Atkin-Lehner involutions |
Class |
68400ck |
Isogeny class |
Conductor |
68400 |
Conductor |
∏ cp |
16 |
Product of Tamagawa factors cp |
deg |
368640 |
Modular degree for the optimal curve |
Δ |
-85034148289632000 = -1 · 28 · 318 · 53 · 193 |
Discriminant |
Eigenvalues |
2+ 3- 5- 2 -4 2 0 19+ |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,59145,12891350] |
[a1,a2,a3,a4,a6] |
Generators |
[1781:75944:1] |
Generators of the group modulo torsion |
j |
980844844912/3645153819 |
j-invariant |
L |
6.6767421506788 |
L(r)(E,1)/r! |
Ω |
0.24248476273053 |
Real period |
R |
6.8836718600411 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999998374 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
34200bo1 22800k1 68400cn1 |
Quadratic twists by: -4 -3 5 |