# Properties

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

# Related objects

Show commands: SageMath
sage: E = EllipticCurve("bg1")

sage: E.isogeny_class()

## Elliptic curves in class 229320bg

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
229320.j4 229320bg1 $$[0, 0, 0, 36897, 1925602]$$ $$253012016/219375$$ $$-4816625355360000$$ $$[2]$$ $$1179648$$ $$1.6968$$ $$\Gamma_0(N)$$-optimal
229320.j3 229320bg2 $$[0, 0, 0, -183603, 17051902]$$ $$7793764996/3080025$$ $$270501679957017600$$ $$[2, 2]$$ $$2359296$$ $$2.0433$$
229320.j1 229320bg3 $$[0, 0, 0, -2565003, 1580679142]$$ $$10625310339698/3855735$$ $$677256057966458880$$ $$[2]$$ $$4718592$$ $$2.3899$$
229320.j2 229320bg4 $$[0, 0, 0, -1330203, -578492138]$$ $$1481943889298/34543665$$ $$6067560759651256320$$ $$[2]$$ $$4718592$$ $$2.3899$$

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form 229320.2.a.bg

sage: E.q_eigenform(10)

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

## 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.

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

## Isogeny graph

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

The vertices are labelled with Cremona labels.