# Properties

 Label 18928.n Number of curves $4$ Conductor $18928$ CM no Rank $1$ Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("n1")

sage: E.isogeny_class()

## Elliptic curves in class 18928.n

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
18928.n1 18928b3 [0, 0, 0, -50531, -4372030]  36864
18928.n2 18928b4 [0, 0, 0, -9971, 303186]  36864
18928.n3 18928b2 [0, 0, 0, -3211, -65910] [2, 2] 18432
18928.n4 18928b1 [0, 0, 0, 169, -4394]  9216 $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 18928.n have rank $$1$$.

## Complex multiplication

The elliptic curves in class 18928.n do not have complex multiplication.

## Modular form 18928.2.a.n

sage: E.q_eigenform(10)

$$q - 2q^{5} - q^{7} - 3q^{9} - 4q^{11} - 6q^{17} + 8q^{19} + O(q^{20})$$

## 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 LMFDB numbering.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 