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SageMath
E = EllipticCurve("dc1")
E.isogeny_class()
Elliptic curves in class 468270.dc
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
468270.dc1 | 468270dc2 | \([1, -1, 1, -23618, 969257]\) | \(30459021867/9245000\) | \(442208199015000\) | \([2]\) | \(2150400\) | \(1.5153\) | \(\Gamma_0(N)\)-optimal* |
468270.dc2 | 468270dc1 | \([1, -1, 1, -9098, -320119]\) | \(1740992427/68800\) | \(3290851713600\) | \([2]\) | \(1075200\) | \(1.1687\) | \(\Gamma_0(N)\)-optimal* |
Rank
sage: E.rank()
The elliptic curves in class 468270.dc have rank \(0\).
Complex multiplication
The elliptic curves in class 468270.dc do not have complex multiplication.Modular form 468270.2.a.dc
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.