# Properties

 Label 4704.n Number of curves $2$ Conductor $4704$ CM no Rank $0$ Graph # Related objects

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

sage: E.isogeny_class()

## Elliptic curves in class 4704.n

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
4704.n1 4704e2 [0, -1, 0, -14177, -373743]  10752
4704.n2 4704e1 [0, -1, 0, -12462, -531180]  5376 $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 4704.n have rank $$0$$.

## Complex multiplication

The elliptic curves in class 4704.n do not have complex multiplication.

## Modular form4704.2.a.n

sage: E.q_eigenform(10)

$$q - q^{3} + 2q^{5} + q^{9} - 2q^{11} - 2q^{15} + 2q^{17} + O(q^{20})$$

## 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. 