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SageMath
E = EllipticCurve("dv1")
E.isogeny_class()
Elliptic curves in class 72450dv
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
72450.di2 | 72450dv1 | \([1, -1, 1, -2052005, -1083780003]\) | \(83890194895342081/3958384640000\) | \(45088475040000000000\) | \([2]\) | \(2580480\) | \(2.5320\) | \(\Gamma_0(N)\)-optimal |
72450.di1 | 72450dv2 | \([1, -1, 1, -5652005, 3761819997]\) | \(1753007192038126081/478174101507200\) | \(5446701874980450000000\) | \([2]\) | \(5160960\) | \(2.8786\) |
Rank
sage: E.rank()
The elliptic curves in class 72450dv have rank \(0\).
Complex multiplication
The elliptic curves in class 72450dv do not have complex multiplication.Modular form 72450.2.a.dv
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.