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SageMath
E = EllipticCurve("ii1")
E.isogeny_class()
Elliptic curves in class 308550ii
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
308550.ii2 | 308550ii1 | \([1, 0, 0, -605063, 154924617]\) | \(885012508801/137332800\) | \(3801459882825000000\) | \([2]\) | \(6635520\) | \(2.2884\) | \(\Gamma_0(N)\)-optimal |
308550.ii1 | 308550ii2 | \([1, 0, 0, -2662063, -1521530383]\) | \(75370704203521/7497765000\) | \(207542938455703125000\) | \([2]\) | \(13271040\) | \(2.6350\) |
Rank
sage: E.rank()
The elliptic curves in class 308550ii have rank \(1\).
Complex multiplication
The elliptic curves in class 308550ii do not have complex multiplication.Modular form 308550.2.a.ii
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.