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SageMath
E = EllipticCurve("fd1")
E.isogeny_class()
Elliptic curves in class 243360.fd
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
243360.fd1 | 243360fd2 | \([0, 0, 0, -5187, -117286]\) | \(18821096/3645\) | \(2988994245120\) | \([2]\) | \(516096\) | \(1.1108\) | |
243360.fd2 | 243360fd1 | \([0, 0, 0, 663, -10816]\) | \(314432/675\) | \(-69189681600\) | \([2]\) | \(258048\) | \(0.76426\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 243360.fd have rank \(0\).
Complex multiplication
The elliptic curves in class 243360.fd do not have complex multiplication.Modular form 243360.2.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.