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SageMath
E = EllipticCurve("bj1")
E.isogeny_class()
Elliptic curves in class 11466.bj
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
11466.bj1 | 11466cd3 | \([1, -1, 1, -202649, -35062023]\) | \(-10730978619193/6656\) | \(-570859301376\) | \([]\) | \(68040\) | \(1.5766\) | |
11466.bj2 | 11466cd2 | \([1, -1, 1, -1994, -67791]\) | \(-10218313/17576\) | \(-1507425342696\) | \([]\) | \(22680\) | \(1.0273\) | |
11466.bj3 | 11466cd1 | \([1, -1, 1, 211, 1887]\) | \(12167/26\) | \(-2229919146\) | \([]\) | \(7560\) | \(0.47804\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 11466.bj have rank \(0\).
Complex multiplication
The elliptic curves in class 11466.bj do not have complex multiplication.Modular form 11466.2.a.bj
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.
\(\left(\begin{array}{rrr} 1 & 3 & 9 \\ 3 & 1 & 3 \\ 9 & 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.