Atkin-Lehner |
3+ 11- 13+ |
Signs for the Atkin-Lehner involutions |
Class |
61347u |
Isogeny class |
Conductor |
61347 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
82944 |
Modular degree for the optimal curve |
Δ |
-15769185003 = -1 · 33 · 112 · 136 |
Discriminant |
Eigenvalues |
-2 3+ -4 1 11- 13+ -4 -3 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,1,620,912] |
[a1,a2,a3,a4,a6] |
Generators |
[-6:165:8] [9:-85:1] |
Generators of the group modulo torsion |
j |
45056/27 |
j-invariant |
L |
3.49384747388 |
L(r)(E,1)/r! |
Ω |
0.75966588936273 |
Real period |
R |
1.1497974052779 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
1.000000000003 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
61347q1 363b1 |
Quadratic twists by: -11 13 |