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SageMath
E = EllipticCurve("gm1")
E.isogeny_class()
Elliptic curves in class 58800.gm
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
58800.gm1 | 58800ei1 | \([0, 1, 0, -34708, 1814588]\) | \(78608/21\) | \(1235314500000000\) | \([2]\) | \(245760\) | \(1.6042\) | \(\Gamma_0(N)\)-optimal |
58800.gm2 | 58800ei2 | \([0, 1, 0, 87792, 11859588]\) | \(318028/441\) | \(-103766418000000000\) | \([2]\) | \(491520\) | \(1.9507\) |
Rank
sage: E.rank()
The elliptic curves in class 58800.gm have rank \(0\).
Complex multiplication
The elliptic curves in class 58800.gm do not have complex multiplication.Modular form 58800.2.a.gm
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.