# Properties

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

# Learn more

Show commands for: SageMath
sage: E = EllipticCurve("i1")

sage: E.isogeny_class()

## Elliptic curves in class 16800i

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
16800.z3 16800i1 $$[0, -1, 0, -159468758, -775053481488]$$ $$448487713888272974160064/91549016015625$$ $$91549016015625000000$$ $$[2, 2]$$ $$2580480$$ $$3.2181$$ $$\Gamma_0(N)$$-optimal
16800.z1 16800i2 $$[0, -1, 0, -2551500008, -49605979418988]$$ $$229625675762164624948320008/9568125$$ $$76545000000000$$ $$[2]$$ $$5160960$$ $$3.5647$$
16800.z2 16800i3 $$[0, -1, 0, -160015633, -769469340863]$$ $$7079962908642659949376/100085966990454375$$ $$6405501887389080000000000$$ $$[2]$$ $$5160960$$ $$3.5647$$
16800.z4 16800i4 $$[0, -1, 0, -158922008, -780632518488]$$ $$-55486311952875723077768/801237030029296875$$ $$-6409896240234375000000000$$ $$[2]$$ $$5160960$$ $$3.5647$$

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form 16800.2.a.i

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.