# Properties

 Label 262080c Number of curves 4 Conductor 262080 CM no Rank 1 Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("262080.c1")

sage: E.isogeny_class()

## Elliptic curves in class 262080c

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
262080.c3 262080c1 [0, 0, 0, -436908, -49912112]  5308416 $$\Gamma_0(N)$$-optimal
262080.c4 262080c2 [0, 0, 0, 1538772, -376294448]  10616832
262080.c1 262080c3 [0, 0, 0, -29648748, -62138026928]  15925248
262080.c2 262080c4 [0, 0, 0, -29487468, -62847465392]  31850496

## Rank

sage: E.rank()

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

## Modular form 262080.2.a.c

sage: E.q_eigenform(10)

$$q - q^{5} - q^{7} - 6q^{11} - q^{13} + 8q^{19} + O(q^{20})$$

## 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.

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

## Isogeny graph

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

The vertices are labelled with Cremona labels. 