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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)
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.