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SageMath
E = EllipticCurve("h1")
E.isogeny_class()
Elliptic curves in class 179520h
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 179520.gu4 | 179520h1 | \([0, 1, 0, -1198625, -505494177]\) | \(726497538898787209/1038579300\) | \(272257332019200\) | \([2]\) | \(2211840\) | \(2.0411\) | \(\Gamma_0(N)\)-optimal |
| 179520.gu3 | 179520h2 | \([0, 1, 0, -1209505, -495861025]\) | \(746461053445307689/27443694341250\) | \(7194199809392640000\) | \([2]\) | \(4423680\) | \(2.3877\) | |
| 179520.gu2 | 179520h3 | \([0, 1, 0, -1525985, -208080225]\) | \(1499114720492202169/796539777000000\) | \(208808123301888000000\) | \([2]\) | \(6635520\) | \(2.5904\) | |
| 179520.gu1 | 179520h4 | \([0, 1, 0, -14103265, 20224968863]\) | \(1183430669265454849849/10449720703125000\) | \(2739331584000000000000\) | \([2]\) | \(13271040\) | \(2.9370\) |
Rank
sage: E.rank()
The elliptic curves in class 179520h have rank \(1\).
Complex multiplication
The elliptic curves in class 179520h do not have complex multiplication.Modular form 179520.2.a.h
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
