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SageMath
E = EllipticCurve("j1")
E.isogeny_class()
Elliptic curves in class 95830.j
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 95830.j1 | 95830e4 | \([1, -1, 0, -366464, -85291930]\) | \(2121328796049/120050\) | \(308015455400450\) | \([2]\) | \(774144\) | \(1.8444\) | |
| 95830.j2 | 95830e3 | \([1, -1, 0, -120044, 14990058]\) | \(74565301329/5468750\) | \(14031316299218750\) | \([2]\) | \(774144\) | \(1.8444\) | |
| 95830.j3 | 95830e2 | \([1, -1, 0, -24214, -1166880]\) | \(611960049/122500\) | \(314301485102500\) | \([2, 2]\) | \(387072\) | \(1.4979\) | |
| 95830.j4 | 95830e1 | \([1, -1, 0, 3166, -110012]\) | \(1367631/2800\) | \(-7184033945200\) | \([2]\) | \(193536\) | \(1.1513\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 95830.j have rank \(0\).
Complex multiplication
The elliptic curves in class 95830.j do not have complex multiplication.Modular form 95830.2.a.j
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.
\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
