# Properties

 Label 4730.g Number of curves 4 Conductor 4730 CM no Rank 0 Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("4730.g1")

sage: E.isogeny_class()

## Elliptic curves in class 4730.g

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
4730.g1 4730g4 [1, -1, 1, -630667, 192931441]  18816
4730.g2 4730g3 [1, -1, 1, -39847, 2952969]  18816
4730.g3 4730g2 [1, -1, 1, -39417, 3021941] [2, 2] 9408
4730.g4 4730g1 [1, -1, 1, -2437, 48749]  4704 $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

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

## Modular form4730.2.a.g

sage: E.q_eigenform(10)

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

## 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.

$$\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 