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SageMath
E = EllipticCurve("du1")
E.isogeny_class()
Elliptic curves in class 72450.du
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
72450.du1 | 72450dy1 | \([1, -1, 1, -55130, -4742503]\) | \(1626794704081/83462400\) | \(950688900000000\) | \([2]\) | \(589824\) | \(1.6319\) | \(\Gamma_0(N)\)-optimal |
72450.du2 | 72450dy2 | \([1, -1, 1, 34870, -18782503]\) | \(411664745519/13605414480\) | \(-154974174311250000\) | \([2]\) | \(1179648\) | \(1.9785\) |
Rank
sage: E.rank()
The elliptic curves in class 72450.du have rank \(0\).
Complex multiplication
The elliptic curves in class 72450.du do not have complex multiplication.Modular form 72450.2.a.du
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.