# Properties

 Label 262080.n Number of curves 4 Conductor 262080 CM no Rank 0 Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("262080.n1")

sage: E.isogeny_class()

## Elliptic curves in class 262080.n

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
262080.n1 262080n4 [0, 0, 0, -62807148, -191579351472]  23592960
262080.n2 262080n2 [0, 0, 0, -4101228, -2710665648] [2, 2] 11796480
262080.n3 262080n1 [0, 0, 0, -1152108, 435455568]  5898240 $$\Gamma_0(N)$$-optimal
262080.n4 262080n3 [0, 0, 0, 7418772, -15193737648]  23592960

## Rank

sage: E.rank()

The elliptic curves in class 262080.n have rank $$0$$.

## Modular form 262080.2.a.n

sage: E.q_eigenform(10)

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

## 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 LMFDB 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 LMFDB labels. 