Atkin-Lehner |
2+ 3+ 7- 17+ |
Signs for the Atkin-Lehner involutions |
Class |
68544q |
Isogeny class |
Conductor |
68544 |
Conductor |
∏ cp |
24 |
Product of Tamagawa factors cp |
deg |
92160 |
Modular degree for the optimal curve |
Δ |
-82542329856 = -1 · 219 · 33 · 73 · 17 |
Discriminant |
Eigenvalues |
2+ 3+ -3 7- -3 -5 17+ -2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-10764,430064] |
[a1,a2,a3,a4,a6] |
Generators |
[-83:867:1] [-2:672:1] |
Generators of the group modulo torsion |
j |
-19486825371/11662 |
j-invariant |
L |
8.5845493804769 |
L(r)(E,1)/r! |
Ω |
1.0689008580705 |
Real period |
R |
0.33463305302835 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
0.99999999999751 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
68544cv1 2142b1 68544w2 |
Quadratic twists by: -4 8 -3 |