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Properties

Label 91035.br
Number of curves $2$
Conductor $91035$
CM no
Rank $0$
Graph

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

Elliptic curves in class 91035.br

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
91035.br1 91035bq2 \([1, -1, 0, -26634294, 50610317683]\) \(24170156844497/1191196125\) \(102979574418344426137125\) \([2]\) \(7520256\) \(3.1750\)  
91035.br2 91035bq1 \([1, -1, 0, 1001331, 3082569808]\) \(1284365503/48234375\) \(-4169888824843878609375\) \([2]\) \(3760128\) \(2.8284\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 91035.br have rank \(0\).

Complex multiplication

The elliptic curves in class 91035.br do not have complex multiplication.

Modular form 91035.2.a.br

sage: E.q_eigenform(10)
 
\(q + q^{2} - q^{4} + q^{5} + q^{7} - 3 q^{8} + q^{10} + 2 q^{11} - 4 q^{13} + q^{14} - q^{16} + 4 q^{19} + O(q^{20})\) 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.