# Properties

 Label 16184f Number of curves $2$ Conductor $16184$ CM no Rank $1$ Graph # Related objects

Show commands: SageMath
sage: E = EllipticCurve("f1")

sage: E.isogeny_class()

## Elliptic curves in class 16184f

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
16184.e1 16184f1 $$[0, -1, 0, -232, 1212]$$ $$275684/49$$ $$246514688$$ $$$$ $$5120$$ $$0.32965$$ $$\Gamma_0(N)$$-optimal
16184.e2 16184f2 $$[0, -1, 0, 448, 6380]$$ $$986078/2401$$ $$-24158439424$$ $$$$ $$10240$$ $$0.67622$$

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form 16184.2.a.f

sage: E.q_eigenform(10)

$$q + 2q^{3} + 2q^{5} + q^{7} + q^{9} - 2q^{11} - 2q^{13} + 4q^{15} + 4q^{19} + O(q^{20})$$ ## 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.

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

## Isogeny graph

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

The vertices are labelled with Cremona labels. 