Atkin-Lehner |
2+ 3+ 7+ 13+ |
Signs for the Atkin-Lehner involutions |
Class |
113568g |
Isogeny class |
Conductor |
113568 |
Conductor |
∏ cp |
16 |
Product of Tamagawa factors cp |
deg |
1357824 |
Modular degree for the optimal curve |
Δ |
-13261353908834304 = -1 · 212 · 34 · 72 · 138 |
Discriminant |
Eigenvalues |
2+ 3+ 3 7+ -6 13+ -3 -2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-530209,-148526639] |
[a1,a2,a3,a4,a6] |
Generators |
[1045:20916:1] |
Generators of the group modulo torsion |
j |
-4933544512/3969 |
j-invariant |
L |
5.6685596808916 |
L(r)(E,1)/r! |
Ω |
0.088457928397703 |
Real period |
R |
4.0051240887988 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000005217 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
113568cx1 113568cd1 |
Quadratic twists by: -4 13 |