# Properties

 Label 4560.h Number of curves $2$ Conductor $4560$ CM no Rank $0$ Graph # Related objects

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

sage: E.isogeny_class()

## Elliptic curves in class 4560.h

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
4560.h1 4560k2 $$[0, -1, 0, -1216, 1216]$$ $$48587168449/28048275$$ $$114885734400$$ $$$$ $$5120$$ $$0.81179$$
4560.h2 4560k1 $$[0, -1, 0, 304, 0]$$ $$756058031/438615$$ $$-1796567040$$ $$$$ $$2560$$ $$0.46522$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 4560.h have rank $$0$$.

## Complex multiplication

The elliptic curves in class 4560.h do not have complex multiplication.

## Modular form4560.2.a.h

sage: E.q_eigenform(10)

$$q - q^{3} - q^{5} + 2 q^{7} + q^{9} + 6 q^{11} + q^{15} - 6 q^{17} - q^{19} + O(q^{20})$$ ## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 