Properties

Label 8400.bj
Number of curves $2$
Conductor $8400$
CM no
Rank $0$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("bj1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 8400.bj

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
8400.bj1 8400by1 \([0, -1, 0, -288, -1728]\) \(5177717/189\) \(96768000\) \([2]\) \(3072\) \(0.30193\) \(\Gamma_0(N)\)-optimal
8400.bj2 8400by2 \([0, -1, 0, 112, -6528]\) \(300763/35721\) \(-18289152000\) \([2]\) \(6144\) \(0.64850\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 8400.2.a.bj

sage: E.q_eigenform(10)
 
\(q - q^{3} + q^{7} + q^{9} + 6 q^{11} - 2 q^{13} + 4 q^{17} + 6 q^{19} + O(q^{20})\)  Toggle raw display

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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.