# Properties

 Label 229320.n Number of curves $4$ Conductor $229320$ CM no Rank $0$ Graph

# Related objects

Show commands: SageMath
sage: E = EllipticCurve("n1")

sage: E.isogeny_class()

## Elliptic curves in class 229320.n

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
229320.n1 229320dq3 $$[0, 0, 0, -596239203, 5603751974702]$$ $$266912903848829942596/152163375$$ $$13363673530386816000$$ $$[2]$$ $$33030144$$ $$3.4309$$
229320.n2 229320dq2 $$[0, 0, 0, -37271703, 87525304202]$$ $$260798860029250384/196803140625$$ $$4321034744838084000000$$ $$[2, 2]$$ $$16515072$$ $$3.0843$$
229320.n3 229320dq4 $$[0, 0, 0, -29554203, 124811633702]$$ $$-32506165579682596/57814914850875$$ $$-5077566446289758418816000$$ $$[2]$$ $$33030144$$ $$3.4309$$
229320.n4 229320dq1 $$[0, 0, 0, -2818578, 751663577]$$ $$1804588288006144/866455078125$$ $$1188999857144531250000$$ $$[2]$$ $$8257536$$ $$2.7377$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form 229320.2.a.n

sage: E.q_eigenform(10)

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

## 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 LMFDB numbering.

$$\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels.