# Properties

 Label 262080q Number of curves 4 Conductor 262080 CM no Rank 1 Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("262080.q1")

sage: E.isogeny_class()

## Elliptic curves in class 262080q

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
262080.q3 262080q1 [0, 0, 0, -80000722668, -8709408057888592] [2] 660602880 $$\Gamma_0(N)$$-optimal
262080.q2 262080q2 [0, 0, 0, -80578750188, -8577163916119888] [2, 2] 1321205760
262080.q1 262080q3 [0, 0, 0, -190627190508, 19913364837077168] [2] 2642411520
262080.q4 262080q4 [0, 0, 0, 20221249812, -28604067596119888] [2] 2642411520

## Rank

sage: E.rank()

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

## Modular form 262080.2.a.q

sage: E.q_eigenform(10)

$$q - q^{5} - q^{7} - 4q^{11} + q^{13} + 2q^{17} - 8q^{19} + O(q^{20})$$

## 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.

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

## Isogeny graph

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

The vertices are labelled with Cremona labels.