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SageMath
E = EllipticCurve("j1")
E.isogeny_class()
Elliptic curves in class 14883.j
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
14883.j1 | 14883j1 | \([0, 1, 1, -1250, -18595]\) | \(-122023936/9963\) | \(-17650062243\) | \([]\) | \(27000\) | \(0.71220\) | \(\Gamma_0(N)\)-optimal |
14883.j2 | 14883j2 | \([0, 1, 1, 2380, 1193825]\) | \(841232384/347568603\) | \(-615738981899283\) | \([]\) | \(135000\) | \(1.5169\) |
Rank
sage: E.rank()
The elliptic curves in class 14883.j have rank \(1\).
Complex multiplication
The elliptic curves in class 14883.j do not have complex multiplication.Modular form 14883.2.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.
\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.