Properties

Label 81144.bd
Number of curves $2$
Conductor $81144$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("bd1")
 
E.isogeny_class()
 

Elliptic curves in class 81144.bd

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
81144.bd1 81144bi2 \([0, 0, 0, -7483035, 1148735126]\) \(263822189935250/149429406721\) \(26247128223316990445568\) \([2]\) \(4423680\) \(2.9918\)  
81144.bd2 81144bi1 \([0, 0, 0, 1848525, 142792958]\) \(7953970437500/4703287687\) \(-413063926641717378048\) \([2]\) \(2211840\) \(2.6452\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 81144.bd have rank \(0\).

Complex multiplication

The elliptic curves in class 81144.bd do not have complex multiplication.

Modular form 81144.2.a.bd

sage: E.q_eigenform(10)
 
\(q - 6 q^{17} - 6 q^{19} + O(q^{20})\) 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.