# Properties

 Label 443760.dc Number of curves $2$ Conductor $443760$ CM no Rank $1$ Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("dc1")

sage: E.isogeny_class()

## Elliptic curves in class 443760.dc

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
443760.dc1 443760dc2 [0, 1, 0, -28480, -2173900] [] 1741824
443760.dc2 443760dc1 [0, 1, 0, 2480, 18068] [] 580608 $$\Gamma_0(N)$$-optimal*
*optimality has not been determined rigorously for conductors over 400000. In this case the optimal curve is certainly one of the 0 curves highlighted, and conditionally curve 443760.dc1.

## Rank

sage: E.rank()

The elliptic curves in class 443760.dc have rank $$1$$.

## Complex multiplication

The elliptic curves in class 443760.dc do not have complex multiplication.

## Modular form 443760.2.a.dc

sage: E.q_eigenform(10)

$$q + q^{3} + q^{5} + 2q^{7} + q^{9} + 3q^{11} - 4q^{13} + q^{15} - 3q^{17} - q^{19} + O(q^{20})$$

## 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.

$$\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels.