# Properties

 Label 212160.ek Number of curves 2 Conductor 212160 CM no Rank 1 Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("212160.ek1")

sage: E.isogeny_class()

## Elliptic curves in class 212160.ek

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
212160.ek1 212160fl1 [0, 1, 0, -871681, 309383519]  2949120 $$\Gamma_0(N)$$-optimal
212160.ek2 212160fl2 [0, 1, 0, -134401, 816779615]  5898240

## Rank

sage: E.rank()

The elliptic curves in class 212160.ek have rank $$1$$.

## Modular form 212160.2.a.ek

sage: E.q_eigenform(10)

$$q + q^{3} - q^{5} - 2q^{7} + q^{9} + q^{13} - q^{15} - q^{17} - 2q^{19} + O(q^{20})$$

## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 