# Properties

 Label 350064co Number of curves $2$ Conductor $350064$ CM no Rank $1$ Graph # Related objects

Show commands: SageMath
sage: E = EllipticCurve("co1")

sage: E.isogeny_class()

## Elliptic curves in class 350064co

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
350064.co1 350064co1 $$[0, 0, 0, -5681883, 4464288650]$$ $$6793805286030262681/1048227429629952$$ $$3129990333236162592768$$ $$$$ $$28901376$$ $$2.8480$$ $$\Gamma_0(N)$$-optimal
350064.co2 350064co2 $$[0, 0, 0, 9893157, 24633965450]$$ $$35862531227445945959/108547797844556928$$ $$-324121987599081474097152$$ $$$$ $$57802752$$ $$3.1946$$

## Rank

sage: E.rank()

The elliptic curves in class 350064co have rank $$1$$.

## Complex multiplication

The elliptic curves in class 350064co do not have complex multiplication.

## Modular form 350064.2.a.co

sage: E.q_eigenform(10)

$$q + 4 q^{5} + 2 q^{7} + q^{11} - q^{13} + q^{17} + 4 q^{19} + O(q^{20})$$ ## 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 Cremona 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 Cremona labels. 