# Properties

 Label 262080.k Number of curves 2 Conductor 262080 CM no Rank 1 Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("262080.k1")

sage: E.isogeny_class()

## Elliptic curves in class 262080.k

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
262080.k1 262080k1 [0, 0, 0, -32763, -2051012]  1105920 $$\Gamma_0(N)$$-optimal
262080.k2 262080k2 [0, 0, 0, 44412, -10262432]  2211840

## Rank

sage: E.rank()

The elliptic curves in class 262080.k have rank $$1$$.

## Modular form 262080.2.a.k

sage: E.q_eigenform(10)

$$q - q^{5} - q^{7} - 4q^{11} + q^{13} - 6q^{17} + O(q^{20})$$

## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 