# Properties

 Label 218010.cb Number of curves $2$ Conductor $218010$ CM no Rank $1$ Graph # Related objects

Show commands: SageMath
sage: E = EllipticCurve("cb1")

sage: E.isogeny_class()

## Elliptic curves in class 218010.cb

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
218010.cb1 218010p2 $$[1, 0, 0, -40141, -2999959]$$ $$1481933914201/53916840$$ $$260246288563560$$ $$$$ $$1327104$$ $$1.5358$$
218010.cb2 218010p1 $$[1, 0, 0, -6341, 129921]$$ $$5841725401/1857600$$ $$8966280398400$$ $$$$ $$663552$$ $$1.1892$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 218010.cb have rank $$1$$.

## Complex multiplication

The elliptic curves in class 218010.cb do not have complex multiplication.

## Modular form 218010.2.a.cb

sage: E.q_eigenform(10)

$$q + q^{2} + q^{3} + q^{4} - q^{5} + q^{6} + 2q^{7} + q^{8} + q^{9} - q^{10} + 2q^{11} + q^{12} + 2q^{14} - q^{15} + q^{16} - 4q^{17} + q^{18} + 6q^{19} + O(q^{20})$$ ## 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. 