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SageMath
E = EllipticCurve("g1")
E.isogeny_class()
Elliptic curves in class 115320.g
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 115320.g1 | 115320d4 | \([0, -1, 0, -207896, 36531276]\) | \(546718898/405\) | \(736131053168640\) | \([2]\) | \(983040\) | \(1.7864\) | |
| 115320.g2 | 115320d3 | \([0, -1, 0, -131016, -17992020]\) | \(136835858/1875\) | \(3408014135040000\) | \([2]\) | \(983040\) | \(1.7864\) | |
| 115320.g3 | 115320d2 | \([0, -1, 0, -15696, 320796]\) | \(470596/225\) | \(204480848102400\) | \([2, 2]\) | \(491520\) | \(1.4398\) | |
| 115320.g4 | 115320d1 | \([0, -1, 0, 3524, 36340]\) | \(21296/15\) | \(-3408014135040\) | \([2]\) | \(245760\) | \(1.0933\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 115320.g have rank \(0\).
Complex multiplication
The elliptic curves in class 115320.g do not have complex multiplication.Modular form 115320.2.a.g
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.
