Properties

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

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Show commands for: SageMath

sage: E = EllipticCurve("48400.l1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 48400cn

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
48400.l3 48400cn1 [0, 1, 0, -4033, 66438] [2] 69120 \(\Gamma_0(N)\)-optimal
48400.l4 48400cn2 [0, 1, 0, 11092, 459688] [2] 138240  
48400.l1 48400cn3 [0, 1, 0, -125033, -17055062] [2] 207360  
48400.l2 48400cn4 [0, 1, 0, -109908, -21320312] [2] 414720  

Rank

sage: E.rank()
 

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

Modular form 48400.2.a.l

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

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.