# Properties

 Label 16800j Number of curves $4$ Conductor $16800$ CM no Rank $0$ Graph

# Learn more

Show commands for: SageMath
sage: E = EllipticCurve("j1")

sage: E.isogeny_class()

## Elliptic curves in class 16800j

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
16800.x3 16800j1 $$[0, -1, 0, -1758, 28512]$$ $$601211584/11025$$ $$11025000000$$ $$[2, 2]$$ $$18432$$ $$0.72173$$ $$\Gamma_0(N)$$-optimal
16800.x2 16800j2 $$[0, -1, 0, -3633, -40863]$$ $$82881856/36015$$ $$2304960000000$$ $$[2]$$ $$36864$$ $$1.0683$$
16800.x1 16800j3 $$[0, -1, 0, -28008, 1813512]$$ $$303735479048/105$$ $$840000000$$ $$[2]$$ $$36864$$ $$1.0683$$
16800.x4 16800j4 $$[0, -1, 0, -8, 81012]$$ $$-8/354375$$ $$-2835000000000$$ $$[2]$$ $$36864$$ $$1.0683$$

## Rank

sage: E.rank()

The elliptic curves in class 16800j have rank $$0$$.

## Complex multiplication

The elliptic curves in class 16800j do not have complex multiplication.

## Modular form 16800.2.a.j

sage: E.q_eigenform(10)

$$q - q^{3} + q^{7} + q^{9} + 4q^{11} - 6q^{13} + 6q^{17} + 4q^{19} + O(q^{20})$$

## 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.

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

## Isogeny graph

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

The vertices are labelled with Cremona labels.