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SageMath
E = EllipticCurve("s1")
E.isogeny_class()
Elliptic curves in class 205350.s
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
205350.s1 | 205350eg2 | \([1, 1, 0, -7029079875, -224100556621875]\) | \(511189448451769/7077888000\) | \(531790962914434756608000000000\) | \([]\) | \(531691776\) | \(4.5094\) | |
205350.s2 | 205350eg1 | \([1, 1, 0, -703786500, 7031988594000]\) | \(513108539209/12597120\) | \(946473662023005218670000000\) | \([]\) | \(177230592\) | \(3.9601\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 205350.s have rank \(1\).
Complex multiplication
The elliptic curves in class 205350.s do not have complex multiplication.Modular form 205350.2.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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.