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SageMath
E = EllipticCurve("n1")
E.isogeny_class()
Elliptic curves in class 450800n
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
450800.n2 | 450800n1 | \([0, 1, 0, -34708, 3186588]\) | \(-9826000/3703\) | \(-1742616988000000\) | \([2]\) | \(2211840\) | \(1.6343\) | \(\Gamma_0(N)\)-optimal* |
450800.n1 | 450800n2 | \([0, 1, 0, -598208, 177871588]\) | \(12576878500/1127\) | \(2121446768000000\) | \([2]\) | \(4423680\) | \(1.9809\) | \(\Gamma_0(N)\)-optimal* |
Rank
sage: E.rank()
The elliptic curves in class 450800n have rank \(1\).
Complex multiplication
The elliptic curves in class 450800n do not have complex multiplication.Modular form 450800.2.a.n
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.