# Properties

 Label 250173x Number of curves 2 Conductor 250173 CM no Rank 1 Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("250173.x1")

sage: E.isogeny_class()

## Elliptic curves in class 250173x

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
250173.x2 250173x1 [0, 0, 1, 249090, -75066611] [] 2903040 $$\Gamma_0(N)$$-optimal
250173.x1 250173x2 [0, 0, 1, -9010560, -10444578260] [] 8709120

## Rank

sage: E.rank()

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

## Modular form 250173.2.a.x

sage: E.q_eigenform(10)

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

## 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.

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

## Isogeny graph

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

The vertices are labelled with Cremona labels. 