# Properties

 Label 288990.ej Number of curves $4$ Conductor $288990$ CM no Rank $0$ Graph

# Related objects

Show commands: SageMath
sage: E = EllipticCurve("ej1")

sage: E.isogeny_class()

## Elliptic curves in class 288990.ej

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
288990.ej1 288990ej3 $$[1, -1, 1, -944573, 353069331]$$ $$26487576322129/44531250$$ $$156694058107031250$$ $$[2]$$ $$4718592$$ $$2.1947$$
288990.ej2 288990ej2 $$[1, -1, 1, -77603, 1773087]$$ $$14688124849/8122500$$ $$28580996198722500$$ $$[2, 2]$$ $$2359296$$ $$1.8481$$
288990.ej3 288990ej1 $$[1, -1, 1, -47183, -3909369]$$ $$3301293169/22800$$ $$80227357750800$$ $$[2]$$ $$1179648$$ $$1.5016$$ $$\Gamma_0(N)$$-optimal
288990.ej4 288990ej4 $$[1, -1, 1, 302647, 13788987]$$ $$871257511151/527800050$$ $$-1857193132992988050$$ $$[2]$$ $$4718592$$ $$2.1947$$

## Rank

sage: E.rank()

The elliptic curves in class 288990.ej have rank $$0$$.

## Complex multiplication

The elliptic curves in class 288990.ej do not have complex multiplication.

## Modular form 288990.2.a.ej

sage: E.q_eigenform(10)

$$q + q^{2} + q^{4} - q^{5} + q^{8} - q^{10} + 4q^{11} + q^{16} - 2q^{17} + q^{19} + O(q^{20})$$

## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels.