# Properties

 Label 229320.ca Number of curves $2$ Conductor $229320$ CM no Rank $1$ Graph # Related objects

Show commands: SageMath
sage: E = EllipticCurve("ca1")

sage: E.isogeny_class()

## Elliptic curves in class 229320.ca

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
229320.ca1 229320bu1 $$[0, 0, 0, -1585983, 767896738]$$ $$20093868785104/26374985$$ $$579092519650095360$$ $$$$ $$4423680$$ $$2.3150$$ $$\Gamma_0(N)$$-optimal
229320.ca2 229320bu2 $$[0, 0, 0, -1153803, 1195668502]$$ $$-1934207124196/5912841025$$ $$-519292353335207961600$$ $$$$ $$8847360$$ $$2.6616$$

## Rank

sage: E.rank()

The elliptic curves in class 229320.ca have rank $$1$$.

## Complex multiplication

The elliptic curves in class 229320.ca do not have complex multiplication.

## Modular form 229320.2.a.ca

sage: E.q_eigenform(10)

$$q - q^{5} + 2 q^{11} + q^{13} + 6 q^{17} + 6 q^{19} + O(q^{20})$$ ## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 