# Properties

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

Show commands: SageMath
sage: E = EllipticCurve("z1")

sage: E.isogeny_class()

## Elliptic curves in class 229320z

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
229320.b1 229320z1 $$[0, 0, 0, -210063, 34277362]$$ $$46689225424/3901625$$ $$85664573912736000$$ $$$$ $$2654208$$ $$1.9910$$ $$\Gamma_0(N)$$-optimal
229320.b2 229320z2 $$[0, 0, 0, 222117, 157102918]$$ $$13799183324/129390625$$ $$-11363667968016000000$$ $$$$ $$5308416$$ $$2.3376$$

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form 229320.2.a.z

sage: E.q_eigenform(10)

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