# Properties

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

Show commands for: SageMath
sage: E = EllipticCurve("262080.l1")

sage: E.isogeny_class()

## Elliptic curves in class 262080l

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
262080.l3 262080l1 [0, 0, 0, -13085868, -16432837328]  18874368 $$\Gamma_0(N)$$-optimal
262080.l2 262080l2 [0, 0, 0, -49212588, 115169578288] [2, 2] 37748736
262080.l1 262080l3 [0, 0, 0, -757876908, 8030383101232]  75497472
262080.l4 262080l4 [0, 0, 0, 81424212, 622510654768]  75497472

## Rank

sage: E.rank()

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

## Modular form 262080.2.a.l

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 Cremona 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 Cremona labels. 