Properties

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

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Show commands for: SageMath
sage: E = EllipticCurve("v1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 443760.v

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
443760.v1 443760v2 [0, -1, 0, -4904317800, -132193463330448] [2] 447068160 \(\Gamma_0(N)\)-optimal*
443760.v2 443760v1 [0, -1, 0, -303414120, -2109353043600] [2] 223534080 \(\Gamma_0(N)\)-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 443760.v1.

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 443760.2.a.v

sage: E.q_eigenform(10)
 
\( q - q^{3} + q^{5} - 4q^{7} + q^{9} + 4q^{11} + 4q^{13} - q^{15} + 4q^{17} + 4q^{19} + O(q^{20}) \)

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.

\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.