Properties

Label 443760c
Number of curves $2$
Conductor $443760$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("c1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 443760c

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
443760.c2 443760c1 [0, -1, 0, 4584904, -1372340880] [] 24966144 \(\Gamma_0(N)\)-optimal*
443760.c1 443760c2 [0, -1, 0, -52660136, 172103028336] [] 74898432 \(\Gamma_0(N)\)-optimal*
*optimality has not been determined rigorously for conductors over 400000. In this case the optimal curve is certainly one of the 2 curves highlighted, and conditionally curve 443760c1.

Rank

sage: E.rank()
 

The elliptic curves in class 443760c have rank \(0\).

Complex multiplication

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

Modular form 443760.2.a.c

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 Cremona 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 Cremona labels.