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SageMath
E = EllipticCurve("s1")
E.isogeny_class()
Elliptic curves in class 95550s
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
95550.v1 | 95550s1 | \([1, 1, 0, -281775, -13966875]\) | \(1345938541921/733824000\) | \(1348963434000000000\) | \([2]\) | \(2211840\) | \(2.1696\) | \(\Gamma_0(N)\)-optimal |
95550.v2 | 95550s2 | \([1, 1, 0, 1090225, -108634875]\) | \(77958456780959/47911500000\) | \(-88074063492187500000\) | \([2]\) | \(4423680\) | \(2.5162\) |
Rank
sage: E.rank()
The elliptic curves in class 95550s have rank \(2\).
Complex multiplication
The elliptic curves in class 95550s do not have complex multiplication.Modular form 95550.2.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 Cremona 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 Cremona labels.