# Properties

 Label 4704.d Number of curves $2$ Conductor $4704$ CM no Rank $1$ Graph # Related objects

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

sage: E.isogeny_class()

## Elliptic curves in class 4704.d

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
4704.d1 4704w2 [0, -1, 0, -289, -1007]  1536
4704.d2 4704w1 [0, -1, 0, -254, -1476]  768 $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 4704.d have rank $$1$$.

## Complex multiplication

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

## Modular form4704.2.a.d

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. 