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Properties

Label 92950bn
Number of curves $2$
Conductor $92950$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("bn1")
 
E.isogeny_class()
 

Elliptic curves in class 92950bn

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
92950.cp2 92950bn1 \([1, 0, 0, 42162, -13447708]\) \(109902239/1100000\) \(-82960779687500000\) \([]\) \(921600\) \(1.9275\) \(\Gamma_0(N)\)-optimal
92950.cp1 92950bn2 \([1, 0, 0, -25096588, -48393711458]\) \(-23178622194826561/1610510\) \(-121462877540468750\) \([]\) \(4608000\) \(2.7323\)  

Rank

sage: E.rank()
 

The elliptic curves in class 92950bn have rank \(0\).

Complex multiplication

The elliptic curves in class 92950bn do not have complex multiplication.

Modular form 92950.2.a.bn

sage: E.q_eigenform(10)
 
\(q + q^{2} + q^{3} + q^{4} + q^{6} + 3 q^{7} + q^{8} - 2 q^{9} - q^{11} + q^{12} + 3 q^{14} + q^{16} + 7 q^{17} - 2 q^{18} - 5 q^{19} + O(q^{20})\) 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 Cremona 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 Cremona labels.