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SageMath
E = EllipticCurve("q1")
E.isogeny_class()
Elliptic curves in class 242550.q
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 242550.q1 | 242550q2 | \([1, -1, 0, -2585592, -1599602684]\) | \(1426487591593/2156\) | \(2889246201187500\) | \([2]\) | \(4718592\) | \(2.2347\) | |
| 242550.q2 | 242550q1 | \([1, -1, 0, -160092, -25453184]\) | \(-338608873/13552\) | \(-18160976121750000\) | \([2]\) | \(2359296\) | \(1.8881\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 242550.q have rank \(1\).
Complex multiplication
The elliptic curves in class 242550.q do not have complex multiplication.Modular form 242550.2.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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
