Atkin-Lehner |
2+ 3+ 7- 11- |
Signs for the Atkin-Lehner involutions |
Class |
81312m |
Isogeny class |
Conductor |
81312 |
Conductor |
∏ cp |
30 |
Product of Tamagawa factors cp |
deg |
144000 |
Modular degree for the optimal curve |
Δ |
-3401689471488 = -1 · 29 · 33 · 75 · 114 |
Discriminant |
Eigenvalues |
2+ 3+ -2 7- 11- 1 6 0 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-7784,-276252] |
[a1,a2,a3,a4,a6] |
Generators |
[136:1078:1] |
Generators of the group modulo torsion |
j |
-6959007176/453789 |
j-invariant |
L |
4.5975433391168 |
L(r)(E,1)/r! |
Ω |
0.25318099021043 |
Real period |
R |
0.60530391561629 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999936863 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
81312bm1 81312bb1 |
Quadratic twists by: -4 -11 |