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SageMath
E = EllipticCurve("ga1")
E.isogeny_class()
Elliptic curves in class 485100.ga
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 485100.ga1 | 485100ga1 | \([0, 0, 0, -151200, -14718375]\) | \(226492416/75625\) | \(127641179531250000\) | \([2]\) | \(4423680\) | \(1.9849\) | \(\Gamma_0(N)\)-optimal |
| 485100.ga2 | 485100ga2 | \([0, 0, 0, 439425, -101540250]\) | \(347482224/366025\) | \(-9884532942900000000\) | \([2]\) | \(8847360\) | \(2.3315\) |
Rank
sage: E.rank()
The elliptic curves in class 485100.ga have rank \(2\).
Complex multiplication
The elliptic curves in class 485100.ga do not have complex multiplication.Modular form 485100.2.a.ga
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.
