Properties

Label 48400cp
Number of curves 4
Conductor 48400
CM no
Rank 1
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("48400.w1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 48400cp

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
48400.w4 48400cp1 [0, 1, 0, -137133, 19099738] [2] 414720 \(\Gamma_0(N)\)-optimal
48400.w3 48400cp2 [0, 1, 0, -303508, -36469512] [2] 829440  
48400.w2 48400cp3 [0, 1, 0, -1347133, -594672762] [2] 1244160  
48400.w1 48400cp4 [0, 1, 0, -21478508, -38320869512] [2] 2488320  

Rank

sage: E.rank()
 

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

Modular form 48400.2.a.w

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

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.