Properties

Label 84966bd
Number of curves $2$
Conductor $84966$
CM no
Rank $0$
Graph

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

Elliptic curves in class 84966bd

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
84966.b2 84966bd1 \([1, 1, 0, -205629, -151712931]\) \(-68921/672\) \(-9375572695101011616\) \([]\) \(2611200\) \(2.3227\) \(\Gamma_0(N)\)-optimal
84966.b1 84966bd2 \([1, 1, 0, -12242479, 23138628871]\) \(-14544652121/8168202\) \(-113960672082246240005706\) \([]\) \(13056000\) \(3.1274\)  

Rank

sage: E.rank()
 

The elliptic curves in class 84966bd have rank \(0\).

Complex multiplication

The elliptic curves in class 84966bd do not have complex multiplication.

Modular form 84966.2.a.bd

sage: E.q_eigenform(10)
 
\(q - q^{2} - q^{3} + q^{4} - 3 q^{5} + q^{6} - q^{8} + q^{9} + 3 q^{10} - 5 q^{11} - q^{12} + q^{13} + 3 q^{15} + q^{16} - q^{18} + O(q^{20})\) 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.