Properties

Label 87120.br
Number of curves $6$
Conductor $87120$
CM no
Rank $1$
Graph

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

Elliptic curves in class 87120.br

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
87120.br1 87120s6 \([0, 0, 0, -84332523, 298085433338]\) \(25078144523224322/1815\) \(4800541416929280\) \([2]\) \(3932160\) \(2.9066\)  
87120.br2 87120s4 \([0, 0, 0, -5271123, 4656953378]\) \(12247559771044/3294225\) \(4356491335863321600\) \([2, 2]\) \(1966080\) \(2.5600\)  
87120.br3 87120s5 \([0, 0, 0, -4617723, 5854374218]\) \(-4117122162722/3215383215\) \(-8504451953116652206080\) \([2]\) \(3932160\) \(2.9066\)  
87120.br4 87120s3 \([0, 0, 0, -2526843, -1507248358]\) \(1349195526724/38671875\) \(51142131572400000000\) \([2]\) \(1966080\) \(2.5600\)  
87120.br5 87120s2 \([0, 0, 0, -370623, 53423678]\) \(17029316176/6125625\) \(2025228410267040000\) \([2, 2]\) \(983040\) \(2.2134\)  
87120.br6 87120s1 \([0, 0, 0, 70422, 5879027]\) \(1869154304/1804275\) \(-37282613916279600\) \([2]\) \(491520\) \(1.8668\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 87120.br have rank \(1\).

Complex multiplication

The elliptic curves in class 87120.br do not have complex multiplication.

Modular form 87120.2.a.br

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

\(\left(\begin{array}{rrrrrr} 1 & 2 & 4 & 8 & 4 & 8 \\ 2 & 1 & 2 & 4 & 2 & 4 \\ 4 & 2 & 1 & 8 & 4 & 8 \\ 8 & 4 & 8 & 1 & 2 & 4 \\ 4 & 2 & 4 & 2 & 1 & 2 \\ 8 & 4 & 8 & 4 & 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.