# Properties

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

Show commands for: SageMath
sage: E = EllipticCurve("262080.g1")

sage: E.isogeny_class()

## Elliptic curves in class 262080g

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
262080.g2 262080g1 [0, 0, 0, -783, -4968]  172032 $$\Gamma_0(N)$$-optimal
262080.g1 262080g2 [0, 0, 0, -5508, 153792]  344064

## Rank

sage: E.rank()

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

## Modular form 262080.2.a.g

sage: E.q_eigenform(10)

$$q - q^{5} - q^{7} - 6q^{11} + q^{13} + 4q^{19} + O(q^{20})$$

## 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 Cremona 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 Cremona labels. 