# Properties

 Label 258570.fh Number of curves 2 Conductor 258570 CM no Rank 1 Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("258570.fh1")

sage: E.isogeny_class()

## Elliptic curves in class 258570.fh

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
258570.fh1 258570fh1 [1, -1, 1, -20716052, -35872861449]  20643840 $$\Gamma_0(N)$$-optimal
258570.fh2 258570fh2 [1, -1, 1, -3194132, -94634372361]  41287680

## Rank

sage: E.rank()

The elliptic curves in class 258570.fh have rank $$1$$.

## Modular form 258570.2.a.fh

sage: E.q_eigenform(10)

$$q + q^{2} + q^{4} + q^{5} + 2q^{7} + q^{8} + q^{10} + 2q^{14} + q^{16} + q^{17} - 2q^{19} + O(q^{20})$$

## 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. 