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Properties

Label 120666.bs
Number of curves $2$
Conductor $120666$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("bs1")
 
E.isogeny_class()
 

Elliptic curves in class 120666.bs

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
120666.bs1 120666bi2 \([1, 1, 1, -64477, 6273899]\) \(6141556990297/1019592\) \(4921375841928\) \([2]\) \(414720\) \(1.4434\)  
120666.bs2 120666bi1 \([1, 1, 1, -3637, 116891]\) \(-1102302937/616896\) \(-2977639164864\) \([2]\) \(207360\) \(1.0968\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 120666.bs have rank \(1\).

Complex multiplication

The elliptic curves in class 120666.bs do not have complex multiplication.

Modular form 120666.2.a.bs

sage: E.q_eigenform(10)
 
\(q + q^{2} - q^{3} + q^{4} + 2 q^{5} - q^{6} - q^{7} + q^{8} + q^{9} + 2 q^{10} + 2 q^{11} - q^{12} - q^{14} - 2 q^{15} + q^{16} + q^{17} + q^{18} + 2 q^{19} + O(q^{20})\) 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.