# Properties

 Label 145728.ed Number of curves 2 Conductor 145728 CM no Rank 0 Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("145728.ed1")

sage: E.isogeny_class()

## Elliptic curves in class 145728.ed

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
145728.ed1 145728bq2 [0, 0, 0, -713100, -229975792]  1310720
145728.ed2 145728bq1 [0, 0, 0, -13260, -8546416]  655360 $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 145728.ed have rank $$0$$.

## Modular form 145728.2.a.ed

sage: E.q_eigenform(10)

$$q + 2q^{7} - q^{11} - 2q^{13} + 2q^{19} + O(q^{20})$$

## 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. 