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Properties

Label 117117.br
Number of curves $2$
Conductor $117117$
CM no
Rank $0$
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Show commands: SageMath
E = EllipticCurve("br1")
 
E.isogeny_class()
 

Elliptic curves in class 117117.br

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
117117.br1 117117bc2 \([1, -1, 0, -36130626, 83600024197]\) \(674733819141829/3361743\) \(25988559519515924331\) \([2]\) \(6469632\) \(2.9242\)  
117117.br2 117117bc1 \([1, -1, 0, -2219931, 1353024544]\) \(-156503678869/11647251\) \(-90041170860545071167\) \([2]\) \(3234816\) \(2.5777\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 117117.br have rank \(0\).

Complex multiplication

The elliptic curves in class 117117.br do not have complex multiplication.

Modular form 117117.2.a.br

sage: E.q_eigenform(10)
 
\(q + q^{2} - q^{4} + 2 q^{5} - q^{7} - 3 q^{8} + 2 q^{10} + q^{11} - q^{14} - q^{16} + 4 q^{19} + O(q^{20})\) 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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.