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SageMath
E = EllipticCurve("g1")
E.isogeny_class()
Elliptic curves in class 485100g
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 485100.g2 | 485100g1 | \([0, 0, 0, -13818000, 19539852500]\) | \(34020720640/456533\) | \(3915506451849300000000\) | \([]\) | \(22394880\) | \(2.9501\) | \(\Gamma_0(N)\)-optimal |
| 485100.g1 | 485100g2 | \([0, 0, 0, -110838000, -439219217500]\) | \(17557957181440/443889677\) | \(3807069574823291700000000\) | \([]\) | \(67184640\) | \(3.4994\) |
Rank
sage: E.rank()
The elliptic curves in class 485100g have rank \(1\).
Complex multiplication
The elliptic curves in class 485100g do not have complex multiplication.Modular form 485100.2.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.
