# Properties

 Label 4730.h Number of curves 2 Conductor 4730 CM no Rank 1 Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("4730.h1")

sage: E.isogeny_class()

## Elliptic curves in class 4730.h

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
4730.h1 4730e1 [1, 0, 0, -3916, 96400] [3] 5760 $$\Gamma_0(N)$$-optimal
4730.h2 4730e2 [1, 0, 0, 17844, 373136] [] 17280

## Rank

sage: E.rank()

The elliptic curves in class 4730.h have rank $$1$$.

## Modular form4730.2.a.h

sage: E.q_eigenform(10)

$$q + q^{2} + q^{3} + q^{4} - q^{5} + q^{6} + 2q^{7} + q^{8} - 2q^{9} - q^{10} - q^{11} + q^{12} - 4q^{13} + 2q^{14} - q^{15} + q^{16} - 2q^{18} + 2q^{19} + O(q^{20})$$

## 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.

$$\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels.