Atkin-Lehner |
2- 3- 7- 11- 13+ |
Signs for the Atkin-Lehner involutions |
Class |
42042dk |
Isogeny class |
Conductor |
42042 |
Conductor |
∏ cp |
2 |
Product of Tamagawa factors cp |
deg |
159936 |
Modular degree for the optimal curve |
Δ |
405857407956 = 22 · 3 · 72 · 11 · 137 |
Discriminant |
Eigenvalues |
2- 3- -1 7- 11- 13+ -3 -1 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,0,0,-72521,-7522971] |
[a1,a2,a3,a4,a6] |
Generators |
[-495105715230:233360129351:3176523000] |
Generators of the group modulo torsion |
j |
860833894093732321/8282804244 |
j-invariant |
L |
10.184167526694 |
L(r)(E,1)/r! |
Ω |
0.29092686576839 |
Real period |
R |
17.502968486248 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
126126bs1 42042bw1 |
Quadratic twists by: -3 -7 |