Atkin-Lehner |
2- 3+ 7- 13+ |
Signs for the Atkin-Lehner involutions |
Class |
122304fm |
Isogeny class |
Conductor |
122304 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
1658880 |
Modular degree for the optimal curve |
Δ |
1472477477732352 = 224 · 39 · 73 · 13 |
Discriminant |
Eigenvalues |
2- 3+ -2 7- 4 13+ 2 -4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-2387009,-1418683167] |
[a1,a2,a3,a4,a6] |
Generators |
[938862977261:-86984875698176:105823817] |
Generators of the group modulo torsion |
j |
16728308209329751/16376256 |
j-invariant |
L |
4.46622112326 |
L(r)(E,1)/r! |
Ω |
0.12146077584607 |
Real period |
R |
18.385446337469 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.9999999933746 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
122304dm1 30576db1 122304ih1 |
Quadratic twists by: -4 8 -7 |