Properties

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

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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.