Properties

Label 4200o
Number of curves $6$
Conductor $4200$
CM no
Rank $1$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("4200.bb1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 4200o

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
4200.bb4 4200o1 [0, 1, 0, -4383, 110238] [2] 3072 \(\Gamma_0(N)\)-optimal
4200.bb3 4200o2 [0, 1, 0, -4508, 103488] [2, 2] 6144  
4200.bb2 4200o3 [0, 1, 0, -17008, -746512] [2, 2] 12288  
4200.bb5 4200o4 [0, 1, 0, 5992, 523488] [2] 12288  
4200.bb1 4200o5 [0, 1, 0, -262008, -51706512] [2] 24576  
4200.bb6 4200o6 [0, 1, 0, 27992, -3986512] [2] 24576  

Rank

sage: E.rank()
 

The elliptic curves in class 4200o have rank \(1\).

Modular form 4200.2.a.bb

sage: E.q_eigenform(10)
 
\( q + q^{3} + q^{7} + q^{9} - 4q^{11} + 2q^{13} - 2q^{17} - 4q^{19} + O(q^{20}) \)

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.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.