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SageMath
E = EllipticCurve("q1")
E.isogeny_class()
Elliptic curves in class 165620.q
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 165620.q1 | 165620j2 | \([0, -1, 0, -2404250, 1416203125]\) | \(1000939264/15625\) | \(23992475898732250000\) | \([]\) | \(4245696\) | \(2.5196\) | |
| 165620.q2 | 165620j1 | \([0, -1, 0, -251190, -47447063]\) | \(1141504/25\) | \(38387961437971600\) | \([]\) | \(1415232\) | \(1.9703\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 165620.q have rank \(0\).
Complex multiplication
The elliptic curves in class 165620.q do not have complex multiplication.Modular form 165620.2.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.
