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SageMath
E = EllipticCurve("gx1")
E.isogeny_class()
Elliptic curves in class 381150.gx
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
381150.gx1 | 381150gx4 | \([1, -1, 0, -384771492, -2904742048334]\) | \(312196988566716625/25367712678\) | \(511899818288003296593750\) | \([2]\) | \(79626240\) | \(3.5945\) | |
381150.gx2 | 381150gx3 | \([1, -1, 0, -22406742, -51844371584]\) | \(-61653281712625/21875235228\) | \(-441424462676600186437500\) | \([2]\) | \(39813120\) | \(3.2480\) | |
381150.gx3 | 381150gx2 | \([1, -1, 0, -9883242, 6000585916]\) | \(5290763640625/2291573592\) | \(46242092073035541375000\) | \([2]\) | \(26542080\) | \(3.0452\) | |
381150.gx4 | 381150gx1 | \([1, -1, 0, 2095758, 693888916]\) | \(50447927375/39517632\) | \(-797433686542647000000\) | \([2]\) | \(13271040\) | \(2.6987\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 381150.gx have rank \(0\).
Complex multiplication
The elliptic curves in class 381150.gx do not have complex multiplication.Modular form 381150.2.a.gx
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.