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SageMath
E = EllipticCurve("fd1")
E.isogeny_class()
Elliptic curves in class 206400.fd
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
206400.fd1 | 206400fg2 | \([0, -1, 0, -44033, 3179937]\) | \(2305199161/277350\) | \(1136025600000000\) | \([2]\) | \(1032192\) | \(1.6196\) | |
206400.fd2 | 206400fg1 | \([0, -1, 0, 3967, 251937]\) | \(1685159/7740\) | \(-31703040000000\) | \([2]\) | \(516096\) | \(1.2730\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 206400.fd have rank \(0\).
Complex multiplication
The elliptic curves in class 206400.fd do not have complex multiplication.Modular form 206400.2.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 LMFDB 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 LMFDB labels.