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SageMath
E = EllipticCurve("dh1")
E.isogeny_class()
Elliptic curves in class 289800dh
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 289800.dh1 | 289800dh1 | \([0, 0, 0, -10575, -384750]\) | \(44851536/4025\) | \(11736900000000\) | \([2]\) | \(491520\) | \(1.2475\) | \(\Gamma_0(N)\)-optimal |
| 289800.dh2 | 289800dh2 | \([0, 0, 0, 11925, -1802250]\) | \(16078716/129605\) | \(-1511712720000000\) | \([2]\) | \(983040\) | \(1.5941\) |
Rank
sage: E.rank()
The elliptic curves in class 289800dh have rank \(0\).
Complex multiplication
The elliptic curves in class 289800dh do not have complex multiplication.Modular form 289800.2.a.dh
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.
