# Properties

 Label 16184.b Number of curves $2$ Conductor $16184$ CM no Rank $0$ Graph # Related objects

Show commands: SageMath
sage: E = EllipticCurve("b1")

sage: E.isogeny_class()

## Elliptic curves in class 16184.b

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
16184.b1 16184b1 $$[0, 1, 0, -67144, 5551872]$$ $$275684/49$$ $$5950265291113472$$ $$$$ $$87040$$ $$1.7463$$ $$\Gamma_0(N)$$-optimal
16184.b2 16184b2 $$[0, 1, 0, 129376, 32121376]$$ $$986078/2401$$ $$-583125998529120256$$ $$$$ $$174080$$ $$2.0928$$

## Rank

sage: E.rank()

The elliptic curves in class 16184.b have rank $$0$$.

## Complex multiplication

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

## Modular form 16184.2.a.b

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 LMFDB 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 LMFDB labels. 