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SageMath
E = EllipticCurve("lq1")
E.isogeny_class()
Elliptic curves in class 242550lq
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 242550.lq3 | 242550lq1 | \([1, -1, 1, -10926005, -9578254003]\) | \(107639597521009/32699842560\) | \(43820916463779840000000\) | \([2]\) | \(23592960\) | \(3.0495\) | \(\Gamma_0(N)\)-optimal |
| 242550.lq2 | 242550lq2 | \([1, -1, 1, -67374005, 205488625997]\) | \(25238585142450289/995844326400\) | \(1334526640549779600000000\) | \([2, 2]\) | \(47185920\) | \(3.3961\) | |
| 242550.lq1 | 242550lq3 | \([1, -1, 1, -1067562005, 13425973609997]\) | \(100407751863770656369/166028940000\) | \(222494658711589687500000\) | \([2]\) | \(94371840\) | \(3.7427\) | |
| 242550.lq4 | 242550lq4 | \([1, -1, 1, 29645995, 748606585997]\) | \(2150235484224911/181905111732960\) | \(-243770247240743235127500000\) | \([2]\) | \(94371840\) | \(3.7427\) |
Rank
sage: E.rank()
The elliptic curves in class 242550lq have rank \(1\).
Complex multiplication
The elliptic curves in class 242550lq do not have complex multiplication.Modular form 242550.2.a.lq
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 Cremona numbering.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
