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SageMath
E = EllipticCurve("x1")
E.isogeny_class()
Elliptic curves in class 92442x
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
92442.n4 | 92442x1 | \([1, 0, 0, -641724110, 6256980453636]\) | \(29225959703644585098026815619041/166525600515144466563072\) | \(166525600515144466563072\) | \([10]\) | \(53760000\) | \(3.6470\) | \(\Gamma_0(N)\)-optimal |
92442.n3 | 92442x2 | \([1, 0, 0, -653356750, 6018360109316]\) | \(30844295769861594410348211372001/2202100653928823895428923392\) | \(2202100653928823895428923392\) | \([10]\) | \(107520000\) | \(3.9936\) | |
92442.n2 | 92442x3 | \([1, 0, 0, -4848854030, -126568786842684]\) | \(12607850284985940451480268863665121/375761672147788784506617095232\) | \(375761672147788784506617095232\) | \([2]\) | \(268800000\) | \(4.4517\) | |
92442.n1 | 92442x4 | \([1, 0, 0, -77018028070, -8226909050266324]\) | \(50524368854438581121704407622653206881/46954775434734002946337674552\) | \(46954775434734002946337674552\) | \([2]\) | \(537600000\) | \(4.7983\) |
Rank
sage: E.rank()
The elliptic curves in class 92442x have rank \(0\).
Complex multiplication
The elliptic curves in class 92442x do not have complex multiplication.Modular form 92442.2.a.x
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 5 & 10 \\ 2 & 1 & 10 & 5 \\ 5 & 10 & 1 & 2 \\ 10 & 5 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.