Atkin-Lehner |
2- 3+ 7- 13+ |
Signs for the Atkin-Lehner involutions |
Class |
122304fp |
Isogeny class |
Conductor |
122304 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
1216512 |
Modular degree for the optimal curve |
Δ |
-17497173778366464 = -1 · 217 · 311 · 73 · 133 |
Discriminant |
Eigenvalues |
2- 3+ 3 7- 3 13+ -7 1 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-126849,18559521] |
[a1,a2,a3,a4,a6] |
Generators |
[635:13916:1] |
Generators of the group modulo torsion |
j |
-5020930768142/389191959 |
j-invariant |
L |
7.3717811819158 |
L(r)(E,1)/r! |
Ω |
0.38160177335518 |
Real period |
R |
4.8294987482304 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000047411 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
122304dq1 30576bf1 122304ir1 |
Quadratic twists by: -4 8 -7 |