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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: SageMath
E = EllipticCurve("s1")
 
E.isogeny_class()
 

Elliptic curves in class 4018.s

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
4018.s1 4018s2 \([1, -1, 1, -470954322, 3933954127513]\) \(98191033604529537629349729/10906239337336\) \(1283108151798243064\) \([]\) \(1185408\) \(3.3437\)  
4018.s2 4018s1 \([1, -1, 1, -948282, -326942087]\) \(801581275315909089/70810888830976\) \(8330830260075495424\) \([]\) \(169344\) \(2.3707\) \(\Gamma_0(N)\)-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)
 
\(q + q^{2} + 3 q^{3} + q^{4} + q^{5} + 3 q^{6} + q^{8} + 6 q^{9} + q^{10} - 2 q^{11} + 3 q^{12} + 3 q^{15} + q^{16} + 3 q^{17} + 6 q^{18} + 8 q^{19} + O(q^{20})\) 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 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.