Properties

Label 48400cd
Number of curves 2
Conductor 48400
CM no
Rank 1
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("48400.ba1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 48400cd

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
48400.ba2 48400cd1 [0, -1, 0, 482992, -521703488] [] 1382400 \(\Gamma_0(N)\)-optimal
48400.ba1 48400cd2 [0, -1, 0, -287497008, -1876186263488] [] 6912000  

Rank

sage: E.rank()
 

The elliptic curves in class 48400cd have rank \(1\).

Modular form 48400.2.a.ba

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

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.

\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.