Properties

Label 8400.l
Number of curves $6$
Conductor $8400$
CM no
Rank $1$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("8400.l1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 8400.l

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
8400.l1 8400c5 [0, -1, 0, -262008, 51706512] [2] 49152  
8400.l2 8400c3 [0, -1, 0, -17008, 746512] [2, 2] 24576  
8400.l3 8400c2 [0, -1, 0, -4508, -103488] [2, 2] 12288  
8400.l4 8400c1 [0, -1, 0, -4383, -110238] [2] 6144 \(\Gamma_0(N)\)-optimal
8400.l5 8400c4 [0, -1, 0, 5992, -523488] [2] 24576  
8400.l6 8400c6 [0, -1, 0, 27992, 3986512] [2] 49152  

Rank

sage: E.rank()
 

The elliptic curves in class 8400.l have rank \(1\).

Modular form 8400.2.a.l

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 LMFDB numbering.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.