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SageMath
E = EllipticCurve("j1")
E.isogeny_class()
Elliptic curves in class 3920.j
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
3920.j1 | 3920bh2 | \([0, 1, 0, -933760, 346974900]\) | \(544737993463/20000\) | \(3305767485440000\) | \([2]\) | \(53760\) | \(2.0655\) | |
3920.j2 | 3920bh1 | \([0, 1, 0, -55680, 5928628]\) | \(-115501303/25600\) | \(-4231382381363200\) | \([2]\) | \(26880\) | \(1.7189\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 3920.j have rank \(0\).
Complex multiplication
The elliptic curves in class 3920.j do not have complex multiplication.Modular form 3920.2.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.