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SageMath
E = EllipticCurve("bh1")
E.isogeny_class()
Elliptic curves in class 19110bh
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 19110.bg3 | 19110bh1 | \([1, 0, 1, -663, -6422]\) | \(273359449/9360\) | \(1101194640\) | \([2]\) | \(12288\) | \(0.50684\) | \(\Gamma_0(N)\)-optimal |
| 19110.bg2 | 19110bh2 | \([1, 0, 1, -1643, 16706]\) | \(4165509529/1368900\) | \(161049716100\) | \([2, 2]\) | \(24576\) | \(0.85341\) | |
| 19110.bg1 | 19110bh3 | \([1, 0, 1, -23693, 1401446]\) | \(12501706118329/2570490\) | \(302415578010\) | \([2]\) | \(49152\) | \(1.2000\) | |
| 19110.bg4 | 19110bh4 | \([1, 0, 1, 4727, 116078]\) | \(99317171591/106616250\) | \(-12543295196250\) | \([2]\) | \(49152\) | \(1.2000\) |
Rank
sage: E.rank()
The elliptic curves in class 19110bh have rank \(1\).
Complex multiplication
The elliptic curves in class 19110bh do not have complex multiplication.Modular form 19110.2.a.bh
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.
