Properties

Label 44100bg
Number of curves 4
Conductor 44100
CM no
Rank 0
Graph

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Show commands for: SageMath

sage: E = EllipticCurve("44100.ca1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 44100bg

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
44100.ca3 44100bg1 [0, 0, 0, -14700, 471625] [2] 103680 \(\Gamma_0(N)\)-optimal
44100.ca4 44100bg2 [0, 0, 0, 40425, 3172750] [2] 207360  
44100.ca1 44100bg3 [0, 0, 0, -455700, -118377875] [2] 311040  
44100.ca2 44100bg4 [0, 0, 0, -400575, -148090250] [2] 622080  

Rank

sage: E.rank()
 

The elliptic curves in class 44100bg have rank \(0\).

Modular form 44100.2.a.ca

sage: E.q_eigenform(10)
 
\( q + 2q^{13} + 6q^{17} + 4q^{19} + O(q^{20}) \)

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 Cremona numbering.

\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.