Properties

Label 1638.c
Number of curves $4$
Conductor $1638$
CM no
Rank $0$
Graph

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

Elliptic curves in class 1638.c

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
1638.c1 1638e3 \([1, -1, 0, -532203, -149255515]\) \(22868021811807457713/8953460393696\) \(6527072627004384\) \([2]\) \(23040\) \(1.9993\)  
1638.c2 1638e4 \([1, -1, 0, -281643, 56492261]\) \(3389174547561866673/74853681183008\) \(54568333582412832\) \([2]\) \(23040\) \(1.9993\)  
1638.c3 1638e2 \([1, -1, 0, -38283, -1573435]\) \(8511781274893233/3440817243136\) \(2508355770246144\) \([2, 2]\) \(11520\) \(1.6527\)  
1638.c4 1638e1 \([1, -1, 0, 7797, -181819]\) \(71903073502287/60782804992\) \(-44310664839168\) \([2]\) \(5760\) \(1.3062\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 1638.c have rank \(0\).

Complex multiplication

The elliptic curves in class 1638.c do not have complex multiplication.

Modular form 1638.2.a.c

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

\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.