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SageMath
E = EllipticCurve("cp1")
E.isogeny_class()
Elliptic curves in class 363090cp
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
363090.cp1 | 363090cp1 | \([1, 0, 1, -3554, -80608]\) | \(42180533641/726180\) | \(85434350820\) | \([2]\) | \(491520\) | \(0.89476\) | \(\Gamma_0(N)\)-optimal |
363090.cp2 | 363090cp2 | \([1, 0, 1, -124, -228784]\) | \(-1771561/192178350\) | \(-22609590699150\) | \([2]\) | \(983040\) | \(1.2413\) |
Rank
sage: E.rank()
The elliptic curves in class 363090cp have rank \(1\).
Complex multiplication
The elliptic curves in class 363090cp do not have complex multiplication.Modular form 363090.2.a.cp
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.