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SageMath
E = EllipticCurve("j1")
E.isogeny_class()
Elliptic curves in class 44880.j
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 44880.j1 | 44880bj1 | \([0, -1, 0, -136056, -19270800]\) | \(68001744211490809/1022422500\) | \(4187842560000\) | \([2]\) | \(193536\) | \(1.5585\) | \(\Gamma_0(N)\)-optimal |
| 44880.j2 | 44880bj2 | \([0, -1, 0, -132056, -20461200]\) | \(-62178675647294809/8362782148050\) | \(-34253955678412800\) | \([2]\) | \(387072\) | \(1.9051\) |
Rank
sage: E.rank()
The elliptic curves in class 44880.j have rank \(0\).
Complex multiplication
The elliptic curves in class 44880.j do not have complex multiplication.Modular form 44880.2.a.j
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.
