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SageMath
E = EllipticCurve("lh1")
E.isogeny_class()
Elliptic curves in class 346800.lh
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 346800.lh1 | 346800lh3 | \([0, 1, 0, -756142008, 8002647515988]\) | \(30949975477232209/478125000\) | \(738609611400000000000000\) | \([2]\) | \(127401984\) | \(3.7150\) | |
| 346800.lh2 | 346800lh2 | \([0, 1, 0, -48670008, 117164603988]\) | \(8253429989329/936360000\) | \(1446493062965760000000000\) | \([2, 2]\) | \(63700992\) | \(3.3684\) | |
| 346800.lh3 | 346800lh1 | \([0, 1, 0, -11678008, -13417156012]\) | \(114013572049/15667200\) | \(24202759746355200000000\) | \([2]\) | \(31850496\) | \(3.0219\) | \(\Gamma_0(N)\)-optimal |
| 346800.lh4 | 346800lh4 | \([0, 1, 0, 66929992, 589506203988]\) | \(21464092074671/109596256200\) | \(-169304780554827379200000000\) | \([2]\) | \(127401984\) | \(3.7150\) |
Rank
sage: E.rank()
The elliptic curves in class 346800.lh have rank \(1\).
Complex multiplication
The elliptic curves in class 346800.lh do not have complex multiplication.Modular form 346800.2.a.lh
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
