Properties

Label 296208.br
Number of curves $4$
Conductor $296208$
CM no
Rank $0$
Graph

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

Elliptic curves in class 296208.br

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
296208.br1 296208br4 \([0, 0, 0, -8432162211, -298021155868766]\) \(12534210458299016895673/315581882565708\) \(1669381705442637495529684992\) \([2]\) \(353894400\) \(4.3317\)  
296208.br2 296208br2 \([0, 0, 0, -547105251, -4282282960670]\) \(3423676911662954233/483711578981136\) \(2558763050961104073657483264\) \([2, 2]\) \(176947200\) \(3.9851\)  
296208.br3 296208br1 \([0, 0, 0, -144262371, 600092176354]\) \(62768149033310713/6915442583808\) \(36581673322277396668219392\) \([2]\) \(88473600\) \(3.6385\) \(\Gamma_0(N)\)-optimal
296208.br4 296208br3 \([0, 0, 0, 892465629, -23015418822110]\) \(14861225463775641287/51859390496937804\) \(-274328542079623849784115511296\) \([2]\) \(353894400\) \(4.3317\)  

Rank

sage: E.rank()
 

The elliptic curves in class 296208.br have rank \(0\).

Complex multiplication

The elliptic curves in class 296208.br do not have complex multiplication.

Modular form 296208.2.a.br

sage: E.q_eigenform(10)
 
\(q - 2 q^{5} + 4 q^{7} - 6 q^{13} - q^{17} + 4 q^{19} + O(q^{20})\) 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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.