# Properties

 Label 4598.h Number of curves $2$ Conductor $4598$ CM no Rank $1$ Graph # Related objects

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

sage: E.isogeny_class()

## Elliptic curves in class 4598.h

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
4598.h1 4598i1 $$[1, 0, 1, -971, 12340]$$ $$-471625/38$$ $$-8145637478$$ $$$$ $$3168$$ $$0.64815$$ $$\Gamma_0(N)$$-optimal
4598.h2 4598i2 $$[1, 0, 1, 5684, 4354]$$ $$94766375/54872$$ $$-11762300518232$$ $$[]$$ $$9504$$ $$1.1975$$

## Rank

sage: E.rank()

The elliptic curves in class 4598.h have rank $$1$$.

## Complex multiplication

The elliptic curves in class 4598.h do not have complex multiplication.

## Modular form4598.2.a.h

sage: E.q_eigenform(10)

$$q - q^{2} + q^{3} + q^{4} - q^{6} - q^{7} - q^{8} - 2 q^{9} + q^{12} + 2 q^{13} + q^{14} + q^{16} + 6 q^{17} + 2 q^{18} + q^{19} + O(q^{20})$$

## 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. 