# Properties

 Label 4730.a Number of curves 2 Conductor 4730 CM no Rank 0 Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("4730.a1")

sage: E.isogeny_class()

## Elliptic curves in class 4730.a

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
4730.a1 4730c2 [1, 0, 1, -117418, 15476508]  13536
4730.a2 4730c1 [1, 0, 1, -7338, 241436]  6768 $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 4730.a have rank $$0$$.

## Modular form4730.2.a.a

sage: E.q_eigenform(10)

$$q - q^{2} - 2q^{3} + q^{4} + q^{5} + 2q^{6} - q^{8} + q^{9} - q^{10} + q^{11} - 2q^{12} + 2q^{13} - 2q^{15} + q^{16} + 6q^{17} - q^{18} + 6q^{19} + O(q^{20})$$

## 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. 