Properties

Label 8400.br
Number of curves $2$
Conductor $8400$
CM no
Rank $1$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("br1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 8400.br

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
8400.br1 8400bb1 \([0, 1, 0, -385708, 92072588]\) \(12692020761488/9261\) \(4630500000000\) \([2]\) \(46080\) \(1.7414\) \(\Gamma_0(N)\)-optimal
8400.br2 8400bb2 \([0, 1, 0, -383208, 93327588]\) \(-3111705953492/85766121\) \(-171532242000000000\) \([2]\) \(92160\) \(2.0880\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 8400.2.a.br

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