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SageMath
E = EllipticCurve("fd1")
E.isogeny_class()
Elliptic curves in class 144150fd
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
144150.be2 | 144150fd1 | \([1, 1, 0, 2498100, -1063440000]\) | \(4173281/3600\) | \(-1487228746537743750000\) | \([2]\) | \(9142272\) | \(2.7502\) | \(\Gamma_0(N)\)-optimal |
144150.be1 | 144150fd2 | \([1, 1, 0, -12397400, -9419815500]\) | \(510082399/202500\) | \(83656616992748085937500\) | \([2]\) | \(18284544\) | \(3.0967\) |
Rank
sage: E.rank()
The elliptic curves in class 144150fd have rank \(0\).
Complex multiplication
The elliptic curves in class 144150fd do not have complex multiplication.Modular form 144150.2.a.fd
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.