# Properties

 Label 6160.j Number of curves 4 Conductor 6160 CM no Rank 1 Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("6160.j1")

sage: E.isogeny_class()

## Elliptic curves in class 6160.j

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
6160.j1 6160g4 [0, -1, 0, -417856, 101158656]  82944
6160.j2 6160g2 [0, -1, 0, -57216, -5201920]  27648
6160.j3 6160g1 [0, -1, 0, -896, -200704]  13824 $$\Gamma_0(N)$$-optimal
6160.j4 6160g3 [0, -1, 0, 8064, 5411840]  41472

## Rank

sage: E.rank()

The elliptic curves in class 6160.j have rank $$1$$.

## Modular form6160.2.a.j

sage: E.q_eigenform(10)

$$q + 2q^{3} - q^{5} - q^{7} + q^{9} + q^{11} - 4q^{13} - 2q^{15} + 4q^{19} + O(q^{20})$$

## Isogeny matrix

sage: E.isogeny_class().matrix()

The $$i,j$$ entry is the smallest degree of a cyclic isogeny between the $$i$$-th and $$j$$-th curve in the isogeny class, in the LMFDB numbering.

$$\left(\begin{array}{rrrr} 1 & 3 & 6 & 2 \\ 3 & 1 & 2 & 6 \\ 6 & 2 & 1 & 3 \\ 2 & 6 & 3 & 1 \end{array}\right)$$

## Isogeny graph

sage: E.isogeny_graph().plot(edge_labels=True)

The vertices are labelled with LMFDB labels. 