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SageMath
E = EllipticCurve("g1")
E.isogeny_class()
Elliptic curves in class 21780g
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 21780.f2 | 21780g1 | \([0, 0, 0, -5808, 9317]\) | \(1048576/605\) | \(12501409939920\) | \([2]\) | \(34560\) | \(1.2026\) | \(\Gamma_0(N)\)-optimal |
| 21780.f1 | 21780g2 | \([0, 0, 0, -65703, 6465998]\) | \(94875856/275\) | \(90919345017600\) | \([2]\) | \(69120\) | \(1.5492\) |
Rank
sage: E.rank()
The elliptic curves in class 21780g have rank \(0\).
Complex multiplication
The elliptic curves in class 21780g do not have complex multiplication.Modular form 21780.2.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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
