Properties

Label 8400bk
Number of curves $4$
Conductor $8400$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("bk1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 8400bk

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
8400.m3 8400bk1 [0, -1, 0, -1408, 13312] [2] 9216 \(\Gamma_0(N)\)-optimal
8400.m2 8400bk2 [0, -1, 0, -9408, -338688] [2, 2] 18432  
8400.m1 8400bk3 [0, -1, 0, -149408, -22178688] [2] 36864  
8400.m4 8400bk4 [0, -1, 0, 2592, -1154688] [2] 36864  

Rank

sage: E.rank()
 

The elliptic curves in class 8400bk have rank \(0\).

Complex multiplication

The elliptic curves in class 8400bk do not have complex multiplication.

Modular form 8400.2.a.bk

sage: E.q_eigenform(10)
 
\( q - q^{3} - q^{7} + q^{9} + 4q^{11} + 2q^{13} + 6q^{17} + O(q^{20}) \)

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.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.