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SageMath
E = EllipticCurve("fj1")
E.isogeny_class()
Elliptic curves in class 446400.fj
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
446400.fj1 | 446400fj2 | \([0, 0, 0, -9518700, -11303534000]\) | \(31942518433489/27900\) | \(83308953600000000\) | \([2]\) | \(11796480\) | \(2.5472\) | \(\Gamma_0(N)\)-optimal* |
446400.fj2 | 446400fj1 | \([0, 0, 0, -590700, -179246000]\) | \(-7633736209/230640\) | \(-688687349760000000\) | \([2]\) | \(5898240\) | \(2.2006\) | \(\Gamma_0(N)\)-optimal* |
Rank
sage: E.rank()
The elliptic curves in class 446400.fj have rank \(0\).
Complex multiplication
The elliptic curves in class 446400.fj do not have complex multiplication.Modular form 446400.2.a.fj
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.