Atkin-Lehner |
2+ 3- 11+ 43+ |
Signs for the Atkin-Lehner involutions |
Class |
68112d |
Isogeny class |
Conductor |
68112 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
23552 |
Modular degree for the optimal curve |
Δ |
-264819456 = -1 · 28 · 37 · 11 · 43 |
Discriminant |
Eigenvalues |
2+ 3- -3 -1 11+ 0 -1 -8 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-399,3166] |
[a1,a2,a3,a4,a6] |
Generators |
[5:-36:1] [-15:76:1] |
Generators of the group modulo torsion |
j |
-37642192/1419 |
j-invariant |
L |
8.3678904976552 |
L(r)(E,1)/r! |
Ω |
1.7325427400346 |
Real period |
R |
0.60372900941632 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
0.99999999999464 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
34056l1 22704n1 |
Quadratic twists by: -4 -3 |