# Properties

 Label 222768cl Number of curves $2$ Conductor $222768$ CM no Rank $0$ Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("cl1")

sage: E.isogeny_class()

## Elliptic curves in class 222768cl

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
222768.fz1 222768cl1 $$[0, 0, 0, -65523, 6452210]$$ $$10418796526321/6390657$$ $$19082399551488$$ $$$$ $$1146880$$ $$1.4911$$ $$\Gamma_0(N)$$-optimal
222768.fz2 222768cl2 $$[0, 0, 0, -53283, 8936930]$$ $$-5602762882081/8312741073$$ $$-24821711840120832$$ $$$$ $$2293760$$ $$1.8377$$

## Rank

sage: E.rank()

The elliptic curves in class 222768cl have rank $$0$$.

## Complex multiplication

The elliptic curves in class 222768cl do not have complex multiplication.

## Modular form 222768.2.a.cl

sage: E.q_eigenform(10)

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