# Properties

 Label 4560.w Number of curves $4$ Conductor $4560$ CM no Rank $1$ Graph # Related objects

Show commands: SageMath
sage: E = EllipticCurve("w1")

sage: E.isogeny_class()

## Elliptic curves in class 4560.w

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
4560.w1 4560bd4 $$[0, 1, 0, -96120, 11438100]$$ $$23977812996389881/146611125$$ $$600519168000$$ $$$$ $$18432$$ $$1.4473$$
4560.w2 4560bd3 $$[0, 1, 0, -19800, -875052]$$ $$209595169258201/41748046875$$ $$171000000000000$$ $$$$ $$18432$$ $$1.4473$$
4560.w3 4560bd2 $$[0, 1, 0, -6120, 170100]$$ $$6189976379881/456890625$$ $$1871424000000$$ $$[2, 2]$$ $$9216$$ $$1.1007$$
4560.w4 4560bd1 $$[0, 1, 0, 360, 11988]$$ $$1256216039/15582375$$ $$-63825408000$$ $$$$ $$4608$$ $$0.75414$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 4560.w have rank $$1$$.

## Complex multiplication

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

## Modular form4560.2.a.w

sage: E.q_eigenform(10)

$$q + q^{3} + q^{5} - 4 q^{7} + q^{9} - 4 q^{11} + 2 q^{13} + q^{15} + 2 q^{17} + q^{19} + O(q^{20})$$

## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 