# Properties

 Label 250173o Number of curves 3 Conductor 250173 CM no Rank 1 Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("250173.o1")

sage: E.isogeny_class()

## Elliptic curves in class 250173o

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
250173.o1 250173o1 [0, 0, 1, -290244, 60186010] [] 1425600 $$\Gamma_0(N)$$-optimal
250173.o2 250173o2 [0, 0, 1, -160284, 114200635] [] 4276800
250173.o3 250173o3 [0, 0, 1, 1431726, -2955990650] [] 12830400

## Rank

sage: E.rank()

The elliptic curves in class 250173o have rank $$1$$.

## Modular form 250173.2.a.o

sage: E.q_eigenform(10)

$$q - 2q^{4} - 3q^{5} + q^{7} + q^{11} + 4q^{13} + 4q^{16} + 6q^{17} + O(q^{20})$$

## 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.

$$\left(\begin{array}{rrr} 1 & 3 & 9 \\ 3 & 1 & 3 \\ 9 & 3 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with Cremona labels. 