Atkin-Lehner |
2- 3+ 11- 43+ |
Signs for the Atkin-Lehner involutions |
Class |
68112bh |
Isogeny class |
Conductor |
68112 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
193536 |
Modular degree for the optimal curve |
Δ |
-610144026624 = -1 · 216 · 39 · 11 · 43 |
Discriminant |
Eigenvalues |
2- 3+ 3 3 11- -2 -7 4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-50571,4377402] |
[a1,a2,a3,a4,a6] |
Generators |
[133:64:1] |
Generators of the group modulo torsion |
j |
-177409591659/7568 |
j-invariant |
L |
9.2371958579574 |
L(r)(E,1)/r! |
Ω |
0.85985840511279 |
Real period |
R |
1.3428367685549 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000000938 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
8514f1 68112bc1 |
Quadratic twists by: -4 -3 |