Properties

Label 663.c
Number of curves $2$
Conductor $663$
CM no
Rank $0$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("c1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 663.c

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
663.c1 663a2 \([1, 1, 0, -327, -900]\) \(3885442650361/1996623837\) \(1996623837\) \([2]\) \(576\) \(0.47674\)  
663.c2 663a1 \([1, 1, 0, -262, -1745]\) \(2000852317801/2094417\) \(2094417\) \([2]\) \(288\) \(0.13017\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 663.c have rank \(0\).

Complex multiplication

The elliptic curves in class 663.c do not have complex multiplication.

Modular form 663.2.a.c

sage: E.q_eigenform(10)
 
\(q + q^{2} - q^{3} - q^{4} - 4q^{5} - q^{6} + 2q^{7} - 3q^{8} + q^{9} - 4q^{10} + 6q^{11} + q^{12} - q^{13} + 2q^{14} + 4q^{15} - q^{16} + q^{17} + q^{18} + 4q^{19} + O(q^{20})\)  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.

\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.