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SageMath
E = EllipticCurve("j1")
E.isogeny_class()
Elliptic curves in class 141120.j
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
141120.j1 | 141120cu2 | \([0, 0, 0, -2417268, 1446548992]\) | \(4446542056384/25725\) | \(9037141863321600\) | \([2]\) | \(2949120\) | \(2.2520\) | |
141120.j2 | 141120cu1 | \([0, 0, 0, -148323, 23466688]\) | \(-65743598656/5294205\) | \(-29060059304243520\) | \([2]\) | \(1474560\) | \(1.9055\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 141120.j have rank \(2\).
Complex multiplication
The elliptic curves in class 141120.j do not have complex multiplication.Modular form 141120.2.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.