Properties

Label 9660.d
Number of curves $2$
Conductor $9660$
CM no
Rank $1$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("d1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 9660.d

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
9660.d1 9660e2 \([0, 1, 0, -379541, -91405305]\) \(-23618971583050153984/391556092921875\) \(-100238359788000000\) \([]\) \(116640\) \(2.0617\)  
9660.d2 9660e1 \([0, 1, 0, 17899, -600201]\) \(2477112820760576/2053567248075\) \(-525713215507200\) \([3]\) \(38880\) \(1.5124\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 9660.d have rank \(1\).

Complex multiplication

The elliptic curves in class 9660.d do not have complex multiplication.

Modular form 9660.2.a.d

sage: E.q_eigenform(10)
 
\(q + q^{3} - q^{5} + q^{7} + q^{9} - 3 q^{11} - 4 q^{13} - q^{15} + 6 q^{17} - q^{19} + O(q^{20})\)  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 LMFDB numbering.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.