# Properties

 Label 11560.g Number of curves 4 Conductor 11560 CM no Rank 1 Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("11560.g1")

sage: E.isogeny_class()

## Elliptic curves in class 11560.g

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
11560.g1 11560a3 [0, 0, 0, -30923, -2092938] [2] 20480
11560.g2 11560a2 [0, 0, 0, -2023, -29478] [2, 2] 10240
11560.g3 11560a1 [0, 0, 0, -578, 4913] [2] 5120 $$\Gamma_0(N)$$-optimal
11560.g4 11560a4 [0, 0, 0, 3757, -167042] [2] 20480

## Rank

sage: E.rank()

The elliptic curves in class 11560.g have rank $$1$$.

## Modular form 11560.2.a.g

sage: E.q_eigenform(10)

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

## 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.

$$\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels.