Properties

Label 4800.br
Number of curves $2$
Conductor $4800$
CM no
Rank $1$
Graph

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

Elliptic curves in class 4800.br

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
4800.br1 4800cg2 \([0, 1, 0, -833, 9213]\) \(-102400/3\) \(-1875000000\) \([]\) \(2400\) \(0.55819\)  
4800.br2 4800cg1 \([0, 1, 0, 7, -27]\) \(20480/243\) \(-388800\) \([]\) \(480\) \(-0.24652\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 4800.br have rank \(1\).

Complex multiplication

The elliptic curves in class 4800.br do not have complex multiplication.

Modular form 4800.2.a.br

sage: E.q_eigenform(10)
 
\(q + q^{3} - 3 q^{7} + q^{9} + 2 q^{11} + q^{13} - 2 q^{17} - 5 q^{19} + O(q^{20})\) Copy content 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.

\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.