# Properties

 Label 16184d Number of curves $4$ Conductor $16184$ CM no Rank $1$ Graph # Related objects

Show commands: SageMath
sage: E = EllipticCurve("d1")

sage: E.isogeny_class()

## Elliptic curves in class 16184d

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
16184.d4 16184d1 $$[0, 0, 0, 289, 9826]$$ $$432/7$$ $$-43254523648$$ $$$$ $$9216$$ $$0.72143$$ $$\Gamma_0(N)$$-optimal
16184.d3 16184d2 $$[0, 0, 0, -5491, 147390]$$ $$740772/49$$ $$1211126662144$$ $$[2, 2]$$ $$18432$$ $$1.0680$$
16184.d2 16184d3 $$[0, 0, 0, -17051, -677994]$$ $$11090466/2401$$ $$118690412890112$$ $$$$ $$36864$$ $$1.4146$$
16184.d1 16184d4 $$[0, 0, 0, -86411, 9776870]$$ $$1443468546/7$$ $$346036189184$$ $$$$ $$36864$$ $$1.4146$$

## Rank

sage: E.rank()

The elliptic curves in class 16184d have rank $$1$$.

## Complex multiplication

The elliptic curves in class 16184d do not have complex multiplication.

## Modular form 16184.2.a.d

sage: E.q_eigenform(10)

$$q - 2q^{5} + q^{7} - 3q^{9} + 4q^{11} + 2q^{13} + 8q^{19} + O(q^{20})$$ ## 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. 