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SageMath
E = EllipticCurve("q1")
E.isogeny_class()
Elliptic curves in class 350064q
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
350064.q2 | 350064q1 | \([0, 0, 0, -4566, -132325]\) | \(-902576293888/126190779\) | \(-1471889246256\) | \([2]\) | \(475136\) | \(1.0662\) | \(\Gamma_0(N)\)-optimal |
350064.q1 | 350064q2 | \([0, 0, 0, -75351, -7961146]\) | \(253526452425808/4091373\) | \(763548394752\) | \([2]\) | \(950272\) | \(1.4128\) |
Rank
sage: E.rank()
The elliptic curves in class 350064q have rank \(0\).
Complex multiplication
The elliptic curves in class 350064q do not have complex multiplication.Modular form 350064.2.a.q
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.