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Properties

Label 10766b
Number of curves $2$
Conductor $10766$
CM no
Rank $1$
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Show commands: SageMath
E = EllipticCurve("b1")
 
E.isogeny_class()
 

Elliptic curves in class 10766b

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
10766.d2 10766b1 \([1, 1, 0, 70, -364]\) \(37092620375/88195072\) \(-88195072\) \([2]\) \(2520\) \(0.20855\) \(\Gamma_0(N)\)-optimal
10766.d1 10766b2 \([1, 1, 0, -570, -4588]\) \(20537058291625/3709016192\) \(3709016192\) \([2]\) \(5040\) \(0.55512\)  

Rank

sage: E.rank()
 

The elliptic curves in class 10766b have rank \(1\).

Complex multiplication

The elliptic curves in class 10766b do not have complex multiplication.

Modular form 10766.2.a.b

sage: E.q_eigenform(10)
 
\(q - q^{2} + 2 q^{3} + q^{4} - 2 q^{6} - q^{7} - q^{8} + q^{9} + 2 q^{11} + 2 q^{12} + 2 q^{13} + q^{14} + q^{16} - 2 q^{17} - q^{18} + 2 q^{19} + O(q^{20})\) 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 Cremona 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 Cremona labels.