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SageMath
E = EllipticCurve("ni1")
E.isogeny_class()
Elliptic curves in class 273600ni
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
273600.ni2 | 273600ni1 | \([0, 0, 0, -1418700, 713626000]\) | \(-105756712489/12476160\) | \(-37253614141440000000\) | \([2]\) | \(7077888\) | \(2.4912\) | \(\Gamma_0(N)\)-optimal |
273600.ni1 | 273600ni2 | \([0, 0, 0, -23306700, 43307674000]\) | \(468898230633769/5540400\) | \(16543545753600000000\) | \([2]\) | \(14155776\) | \(2.8377\) |
Rank
sage: E.rank()
The elliptic curves in class 273600ni have rank \(1\).
Complex multiplication
The elliptic curves in class 273600ni do not have complex multiplication.Modular form 273600.2.a.ni
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.