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SageMath
E = EllipticCurve("x1")
E.isogeny_class()
Elliptic curves in class 17424.x
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
17424.x1 | 17424f2 | \([0, 0, 0, -81675, 8409258]\) | \(1687500/121\) | \(4320487275236352\) | \([2]\) | \(92160\) | \(1.7470\) | |
17424.x2 | 17424f1 | \([0, 0, 0, -16335, -646866]\) | \(54000/11\) | \(98192892619008\) | \([2]\) | \(46080\) | \(1.4004\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 17424.x have rank \(0\).
Complex multiplication
The elliptic curves in class 17424.x do not have complex multiplication.Modular form 17424.2.a.x
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.