Properties

Label 20400cx
Number of curves 6
Conductor 20400
CM no
Rank 1
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("20400.dc1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 20400cx

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
20400.dc5 20400cx1 [0, 1, 0, -13608, -571212] [2] 49152 \(\Gamma_0(N)\)-optimal
20400.dc4 20400cx2 [0, 1, 0, -45608, 3076788] [2, 2] 98304  
20400.dc2 20400cx3 [0, 1, 0, -693608, 222100788] [2, 2] 196608  
20400.dc6 20400cx4 [0, 1, 0, 90392, 18036788] [2] 196608  
20400.dc1 20400cx5 [0, 1, 0, -11097608, 14225884788] [2] 393216  
20400.dc3 20400cx6 [0, 1, 0, -657608, 246220788] [2] 393216  

Rank

sage: E.rank()
 

The elliptic curves in class 20400cx have rank \(1\).

Modular form 20400.2.a.dc

sage: E.q_eigenform(10)
 
\( q + q^{3} + q^{9} + 4q^{11} + 2q^{13} - q^{17} - 4q^{19} + O(q^{20}) \)

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.

\(\left(\begin{array}{rrrrrr} 1 & 2 & 4 & 4 & 8 & 8 \\ 2 & 1 & 2 & 2 & 4 & 4 \\ 4 & 2 & 1 & 4 & 2 & 2 \\ 4 & 2 & 4 & 1 & 8 & 8 \\ 8 & 4 & 2 & 8 & 1 & 4 \\ 8 & 4 & 2 & 8 & 4 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.