# Properties

 Label 10560.bz Number of curves $4$ Conductor $10560$ CM no Rank $1$ Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("bz1")

sage: E.isogeny_class()

## Elliptic curves in class 10560.bz

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
10560.bz1 10560cn4 $$[0, 1, 0, -999985, 384558383]$$ $$6749703004355978704/5671875$$ $$92928000000$$ $$$$ $$55296$$ $$1.8401$$
10560.bz2 10560cn3 $$[0, 1, 0, -62485, 5995883]$$ $$-26348629355659264/24169921875$$ $$-24750000000000$$ $$$$ $$27648$$ $$1.4936$$
10560.bz3 10560cn2 $$[0, 1, 0, -12625, 498575]$$ $$13584145739344/1195803675$$ $$19592047411200$$ $$$$ $$18432$$ $$1.2908$$
10560.bz4 10560cn1 $$[0, 1, 0, 875, 36875]$$ $$72268906496/606436875$$ $$-620991360000$$ $$$$ $$9216$$ $$0.94425$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 10560.bz have rank $$1$$.

## Complex multiplication

The elliptic curves in class 10560.bz do not have complex multiplication.

## Modular form 10560.2.a.bz

sage: E.q_eigenform(10)

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

$$\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 