Properties

Label 400e
Number of curves 4
Conductor 400
CM no
Rank 0
Graph

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Show commands for: SageMath

sage: E = EllipticCurve("400.c1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 400e

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
400.c3 400e1 [0, 1, 0, -33, -62] [2] 48 \(\Gamma_0(N)\)-optimal
400.c4 400e2 [0, 1, 0, 92, -312] [2] 96  
400.c1 400e3 [0, 1, 0, -1033, 12438] [2] 144  
400.c2 400e4 [0, 1, 0, -908, 15688] [2] 288  

Rank

sage: E.rank()
 

The elliptic curves in class 400e have rank \(0\).

Modular form 400.2.a.c

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.