Atkin-Lehner |
2- 23- 61- |
Signs for the Atkin-Lehner involutions |
Class |
5612a |
Isogeny class |
Conductor |
5612 |
Conductor |
∏ cp |
18 |
Product of Tamagawa factors cp |
deg |
4608 |
Modular degree for the optimal curve |
Δ |
-724374512 = -1 · 24 · 233 · 612 |
Discriminant |
Eigenvalues |
2- -3 0 0 -4 -5 -8 -4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-685,7021] |
[a1,a2,a3,a4,a6] |
Generators |
[-11:115:1] [5:61:1] |
Generators of the group modulo torsion |
j |
-2221648992000/45273407 |
j-invariant |
L |
3.3223493496724 |
L(r)(E,1)/r! |
Ω |
1.604500253745 |
Real period |
R |
0.11503579599935 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
0.99999999999986 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
22448d1 89792e1 50508a1 129076b1 |
Quadratic twists by: -4 8 -3 -23 |