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SageMath
E = EllipticCurve("g1")
E.isogeny_class()
Elliptic curves in class 202005g
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 202005.f2 | 202005g1 | \([0, 0, 1, 9642372, 1751267758]\) | \(1503484706816/890163675\) | \(-58701096345555291573675\) | \([]\) | \(17233920\) | \(3.0582\) | \(\Gamma_0(N)\)-optimal |
| 202005.f1 | 202005g2 | \([0, 0, 1, -121256868, -567657153761]\) | \(-2989967081734144/380653171875\) | \(-25101853899481567584421875\) | \([]\) | \(51701760\) | \(3.6076\) |
Rank
sage: E.rank()
The elliptic curves in class 202005g have rank \(1\).
Complex multiplication
The elliptic curves in class 202005g do not have complex multiplication.Modular form 202005.2.a.g
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
