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SageMath
E = EllipticCurve("j1")
E.isogeny_class()
Elliptic curves in class 1290.j
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
1290.j1 | 1290k2 | \([1, 1, 1, -165776, -26048527]\) | \(503835593418244309249/898614000000\) | \(898614000000\) | \([2]\) | \(10080\) | \(1.5520\) | |
1290.j2 | 1290k1 | \([1, 1, 1, -10256, -418831]\) | \(-119305480789133569/5200091136000\) | \(-5200091136000\) | \([2]\) | \(5040\) | \(1.2054\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 1290.j have rank \(0\).
Complex multiplication
The elliptic curves in class 1290.j do not have complex multiplication.Modular form 1290.2.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.