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SageMath
E = EllipticCurve("u1")
E.isogeny_class()
Elliptic curves in class 11550u
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
11550.v2 | 11550u1 | \([1, 0, 1, -10126, 611648]\) | \(-7347774183121/6119866368\) | \(-95622912000000\) | \([2]\) | \(53760\) | \(1.3805\) | \(\Gamma_0(N)\)-optimal |
11550.v1 | 11550u2 | \([1, 0, 1, -186126, 30883648]\) | \(45637459887836881/13417633152\) | \(209650518000000\) | \([2]\) | \(107520\) | \(1.7270\) |
Rank
sage: E.rank()
The elliptic curves in class 11550u have rank \(0\).
Complex multiplication
The elliptic curves in class 11550u do not have complex multiplication.Modular form 11550.2.a.u
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.