# Properties

 Label 229320.k Number of curves $2$ Conductor $229320$ CM no Rank $0$ Graph # Related objects

Show commands: SageMath
sage: E = EllipticCurve("k1")

sage: E.isogeny_class()

## Elliptic curves in class 229320.k

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
229320.k1 229320bh1 $$[0, 0, 0, -393078, 19143173]$$ $$14270199808/7921875$$ $$3728703552005250000$$ $$$$ $$3096576$$ $$2.2540$$ $$\Gamma_0(N)$$-optimal
229320.k2 229320bh2 $$[0, 0, 0, 1536297, 151498298]$$ $$53247522512/32131125$$ $$-241977945710932704000$$ $$$$ $$6193152$$ $$2.6005$$

## Rank

sage: E.rank()

The elliptic curves in class 229320.k have rank $$0$$.

## Complex multiplication

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

## Modular form 229320.2.a.k

sage: E.q_eigenform(10)

$$q - q^{5} - 4q^{11} - q^{13} + 2q^{17} + 2q^{19} + O(q^{20})$$ ## 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. 