# Properties

 Label 164080.n Number of curves 2 Conductor 164080 CM no Rank 1 Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("164080.n1")

sage: E.isogeny_class()

## Elliptic curves in class 164080.n

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
164080.n1 164080j2 [0, 0, 0, -88735387, 321922512074] [] 66382848
164080.n2 164080j1 [0, 0, 0, 153413, -149478166] [] 9483264 $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 164080.n have rank $$1$$.

## Modular form 164080.2.a.n

sage: E.q_eigenform(10)

$$q + 3q^{3} + q^{5} - q^{7} + 6q^{9} - 5q^{11} + 7q^{13} + 3q^{15} - 3q^{17} + 8q^{19} + O(q^{20})$$

## 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 LMFDB numbering.

$$\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 