Atkin-Lehner |
2+ 7- 13+ 47+ |
Signs for the Atkin-Lehner involutions |
Class |
111202h |
Isogeny class |
Conductor |
111202 |
Conductor |
∏ cp |
24 |
Product of Tamagawa factors cp |
deg |
599040 |
Modular degree for the optimal curve |
Δ |
-1412728143548176 = -1 · 24 · 72 · 138 · 472 |
Discriminant |
Eigenvalues |
2+ 0 -3 7- 0 13+ 1 6 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,0,-55886,5411108] |
[a1,a2,a3,a4,a6] |
Generators |
[-272:794:1] [127:-655:1] |
Generators of the group modulo torsion |
j |
-23664119193/1731856 |
j-invariant |
L |
7.3912175588648 |
L(r)(E,1)/r! |
Ω |
0.47118313691067 |
Real period |
R |
0.65360445656777 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
1.0000000004599 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
111202p1 |
Quadratic twists by: 13 |