Properties

Label 48400k
Number of curves 4
Conductor 48400
CM no
Rank 0
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("48400.cd1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 48400k

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
48400.cd3 48400k1 [0, 0, 0, -6050, 166375] [2] 61440 \(\Gamma_0(N)\)-optimal
48400.cd2 48400k2 [0, 0, 0, -21175, -998250] [2, 2] 122880  
48400.cd4 48400k3 [0, 0, 0, 39325, -5656750] [2] 245760  
48400.cd1 48400k4 [0, 0, 0, -323675, -70875750] [2] 245760  

Rank

sage: E.rank()
 

The elliptic curves in class 48400k have rank \(0\).

Modular form 48400.2.a.cd

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

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.

\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.