# Properties

 Label 20286.ca Number of curves $2$ Conductor $20286$ CM no Rank $1$ Graph

# Related objects

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

sage: E.isogeny_class()

## Elliptic curves in class 20286.ca

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
20286.ca1 20286co2 $$[1, -1, 1, -267035, 49791179]$$ $$24553362849625/1755162752$$ $$150533500962724992$$ $$[2]$$ $$258048$$ $$2.0430$$
20286.ca2 20286co1 $$[1, -1, 1, 15205, 3390923]$$ $$4533086375/60669952$$ $$-5203426444296192$$ $$[2]$$ $$129024$$ $$1.6964$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 20286.ca have rank $$1$$.

## Complex multiplication

The elliptic curves in class 20286.ca do not have complex multiplication.

## Modular form 20286.2.a.ca

sage: E.q_eigenform(10)

$$q + q^{2} + q^{4} + q^{8} - 4q^{11} + q^{16} + 6q^{17} + 6q^{19} + O(q^{20})$$

## 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.