# Properties

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

Show commands for: SageMath
sage: E = EllipticCurve("250173.g1")

sage: E.isogeny_class()

## Elliptic curves in class 250173.g

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
250173.g1 250173g1 [1, -1, 1, -672611, -211460934]  2918400 $$\Gamma_0(N)$$-optimal
250173.g2 250173g2 [1, -1, 1, -363956, -406530894]  5836800

## Rank

sage: E.rank()

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

## Modular form 250173.2.a.g

sage: E.q_eigenform(10)

$$q - q^{2} - q^{4} - 2q^{5} + q^{7} + 3q^{8} + 2q^{10} - q^{11} - 2q^{13} - q^{14} - q^{16} - 6q^{17} + O(q^{20})$$

## 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 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. 