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SageMath
E = EllipticCurve("d1")
E.isogeny_class()
Elliptic curves in class 424830d
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
424830.d2 | 424830d1 | \([1, 1, 0, -24868, -2013668]\) | \(-2942649737/1296540\) | \(-749412485101980\) | \([2]\) | \(2211840\) | \(1.5613\) | \(\Gamma_0(N)\)-optimal* |
424830.d1 | 424830d2 | \([1, 1, 0, -433038, -109852182]\) | \(15537040571177/1786050\) | \(1032353933558850\) | \([2]\) | \(4423680\) | \(1.9079\) | \(\Gamma_0(N)\)-optimal* |
Rank
sage: E.rank()
The elliptic curves in class 424830d have rank \(0\).
Complex multiplication
The elliptic curves in class 424830d do not have complex multiplication.Modular form 424830.2.a.d
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.