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SageMath
E = EllipticCurve("s1")
E.isogeny_class()
Elliptic curves in class 450840.s
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
450840.s1 | 450840s2 | \([0, -1, 0, -179897678420, -29368756943723100]\) | \(21208997008348807455199568/61790625\) | \(1875870465580144800000\) | \([2]\) | \(1027768320\) | \(4.6786\) | \(\Gamma_0(N)\)-optimal* |
450840.s2 | 450840s1 | \([0, -1, 0, -11243600295, -458884411110600]\) | \(-82847542748407455193088/141410419921875\) | \(-268312982609347534218750000\) | \([2]\) | \(513884160\) | \(4.3321\) | \(\Gamma_0(N)\)-optimal* |
Rank
sage: E.rank()
The elliptic curves in class 450840.s have rank \(0\).
Complex multiplication
The elliptic curves in class 450840.s do not have complex multiplication.Modular form 450840.2.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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.