Properties

Label 44880by
Number of curves 2
Conductor 44880
CM no
Rank 1
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("44880.bf1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 44880by

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
44880.bf2 44880by1 [0, -1, 0, -14080, -278528] [2] 129024 \(\Gamma_0(N)\)-optimal
44880.bf1 44880by2 [0, -1, 0, -188160, -31334400] [2] 258048  

Rank

sage: E.rank()
 

The elliptic curves in class 44880by have rank \(1\).

Modular form 44880.2.a.bf

sage: E.q_eigenform(10)
 
\( q - q^{3} + q^{5} + 2q^{7} + q^{9} + q^{11} - 4q^{13} - q^{15} + q^{17} + 6q^{19} + O(q^{20}) \)

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.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.