# Properties

 Label 229320cp Number of curves $2$ Conductor $229320$ CM no Rank $1$ Graph

# Related objects

Show commands: SageMath
sage: E = EllipticCurve("cp1")

sage: E.isogeny_class()

## Elliptic curves in class 229320cp

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
229320.y1 229320cp1 $$[0, 0, 0, -510678, -140239323]$$ $$397526095872/739375$$ $$27394556708610000$$ $$[2]$$ $$2064384$$ $$2.0448$$ $$\Gamma_0(N)$$-optimal
229320.y2 229320cp2 $$[0, 0, 0, -345303, -232617798]$$ $$-7680778992/34987225$$ $$-20740966775222803200$$ $$[2]$$ $$4128768$$ $$2.3913$$

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form 229320.2.a.cp

sage: E.q_eigenform(10)

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

## 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.