# Properties

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

Show commands for: SageMath
sage: E = EllipticCurve("250173.b1")

sage: E.isogeny_class()

## Elliptic curves in class 250173.b

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
250173.b1 250173b2 [0, 0, 1, -170508603, -856585839470] [] 74880000
250173.b2 250173b1 [0, 0, 1, -6076713, 5759809240] [] 14976000 $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 250173.b have rank $$2$$.

## Modular form 250173.2.a.b

sage: E.q_eigenform(10)

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

## 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.

$$\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 