Atkin-Lehner |
2- 3+ 7- 23+ |
Signs for the Atkin-Lehner involutions |
Class |
108192bc |
Isogeny class |
Conductor |
108192 |
Conductor |
∏ cp |
2 |
Product of Tamagawa factors cp |
deg |
68096 |
Modular degree for the optimal curve |
Δ |
-8833660416 = -1 · 29 · 37 · 73 · 23 |
Discriminant |
Eigenvalues |
2- 3+ 1 7- 6 1 -4 2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-240,4824] |
[a1,a2,a3,a4,a6] |
Generators |
[61:462:1] |
Generators of the group modulo torsion |
j |
-8741816/50301 |
j-invariant |
L |
7.3698300270502 |
L(r)(E,1)/r! |
Ω |
1.1254099798148 |
Real period |
R |
3.2742867768141 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.9999999994906 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
108192bx1 108192bs1 |
Quadratic twists by: -4 -7 |