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SageMath
sage: E = EllipticCurve("q1")
sage: E.isogeny_class()
Elliptic curves in class 221067.q
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 221067.q1 | 221067q1 | \([0, 0, 1, -68970, 10505250]\) | \(-28094464000/20657483\) | \(-26678477614662027\) | \([]\) | \(1209600\) | \(1.8513\) | \(\Gamma_0(N)\)-optimal |
| 221067.q2 | 221067q2 | \([0, 0, 1, 562650, -162148077]\) | \(15252992000000/17621717267\) | \(-22757883409104720723\) | \([]\) | \(3628800\) | \(2.4006\) |
Rank
sage: E.rank()
The elliptic curves in class 221067.q have rank \(0\).
Complex multiplication
The elliptic curves in class 221067.q do not have complex multiplication.Modular form 221067.2.a.q
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
