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SageMath
E = EllipticCurve("j1")
E.isogeny_class()
Elliptic curves in class 9744j
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
9744.h2 | 9744j1 | \([0, -1, 0, -897, -9540]\) | \(4994190819328/276357501\) | \(4421720016\) | \([2]\) | \(6912\) | \(0.60616\) | \(\Gamma_0(N)\)-optimal |
9744.h1 | 9744j2 | \([0, -1, 0, -2612, 39852]\) | \(7701397204048/1892605743\) | \(484507070208\) | \([2]\) | \(13824\) | \(0.95273\) |
Rank
sage: E.rank()
The elliptic curves in class 9744j have rank \(0\).
Complex multiplication
The elliptic curves in class 9744j do not have complex multiplication.Modular form 9744.2.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 Cremona 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 Cremona labels.