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SageMath
E = EllipticCurve("gm1")
E.isogeny_class()
Elliptic curves in class 405720gm
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 405720.gm1 | 405720gm1 | \([0, 0, 0, -38367, -796446]\) | \(10536048/5635\) | \(3340514938763520\) | \([2]\) | \(2211840\) | \(1.6700\) | \(\Gamma_0(N)\)-optimal |
| 405720.gm2 | 405720gm2 | \([0, 0, 0, 146853, -6241914]\) | \(147704148/92575\) | \(-219519553118745600\) | \([2]\) | \(4423680\) | \(2.0166\) |
Rank
sage: E.rank()
The elliptic curves in class 405720gm have rank \(0\).
Complex multiplication
The elliptic curves in class 405720gm do not have complex multiplication.Modular form 405720.2.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 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.
