Properties

Label 88445bn
Number of curves $3$
Conductor $88445$
CM no
Rank $2$
Graph

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

Elliptic curves in class 88445bn

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
88445.w2 88445bn1 \([0, 1, 1, -23585, 1538779]\) \(-262144/35\) \(-193721529881915\) \([]\) \(228096\) \(1.4740\) \(\Gamma_0(N)\)-optimal
88445.w3 88445bn2 \([0, 1, 1, 153305, -3891744]\) \(71991296/42875\) \(-237308874105345875\) \([]\) \(684288\) \(2.0233\)  
88445.w1 88445bn3 \([0, 1, 1, -2323155, -1426494191]\) \(-250523582464/13671875\) \(-75672472610123046875\) \([]\) \(2052864\) \(2.5726\)  

Rank

sage: E.rank()
 

The elliptic curves in class 88445bn have rank \(2\).

Complex multiplication

The elliptic curves in class 88445bn do not have complex multiplication.

Modular form 88445.2.a.bn

sage: E.q_eigenform(10)
 
\(q + q^{3} - 2q^{4} + q^{5} - 2q^{9} - 3q^{11} - 2q^{12} + 5q^{13} + q^{15} + 4q^{16} - 3q^{17} + O(q^{20})\)  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 Cremona numbering.

\(\left(\begin{array}{rrr} 1 & 3 & 9 \\ 3 & 1 & 3 \\ 9 & 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.