Properties

Label 44880.cc
Number of curves $2$
Conductor $44880$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("cc1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 44880.cc

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
44880.cc1 44880cc2 [0, 1, 0, -2296, -27820] [2] 49152  
44880.cc2 44880cc1 [0, 1, 0, 424, -2796] [2] 24576 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 44880.cc have rank \(0\).

Complex multiplication

The elliptic curves in class 44880.cc do not have complex multiplication.

Modular form 44880.2.a.cc

sage: E.q_eigenform(10)
 
\( q + q^{3} - q^{5} + 2q^{7} + q^{9} - q^{11} - q^{15} + q^{17} + O(q^{20}) \)

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.