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Properties

Label 4018.s
Number of curves $2$
Conductor $4018$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("s1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 4018.s

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
4018.s1 4018s2 [1, -1, 1, -470954322, 3933954127513] [] 1185408  
4018.s2 4018s1 [1, -1, 1, -948282, -326942087] [] 169344 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 4018.s have rank \(0\).

Complex multiplication

The elliptic curves in class 4018.s do not have complex multiplication.

Modular form 4018.2.a.s

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

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.

\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.