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SageMath
E = EllipticCurve("s1")
E.isogeny_class()
Elliptic curves in class 283920.s
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
283920.s1 | 283920s1 | \([0, -1, 0, -2461541, -1485658695]\) | \(-225596176962617344/15946875\) | \(-116597426400000\) | \([]\) | \(3525120\) | \(2.1521\) | \(\Gamma_0(N)\)-optimal |
283920.s2 | 283920s2 | \([0, -1, 0, -2218181, -1791294519]\) | \(-165082666931912704/94207763671875\) | \(-688810992187500000000\) | \([]\) | \(10575360\) | \(2.7015\) |
Rank
sage: E.rank()
The elliptic curves in class 283920.s have rank \(0\).
Complex multiplication
The elliptic curves in class 283920.s do not have complex multiplication.Modular form 283920.2.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.