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SageMath
E = EllipticCurve("fg1")
E.isogeny_class()
Elliptic curves in class 76230.fg
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 76230.fg1 | 76230fe4 | \([1, -1, 1, -291512, -60504551]\) | \(2121328796049/120050\) | \(155040729678450\) | \([2]\) | \(655360\) | \(1.7872\) | |
| 76230.fg2 | 76230fe3 | \([1, -1, 1, -95492, 10637641]\) | \(74565301329/5468750\) | \(7062715455468750\) | \([2]\) | \(655360\) | \(1.7872\) | |
| 76230.fg3 | 76230fe2 | \([1, -1, 1, -19262, -827351]\) | \(611960049/122500\) | \(158204826202500\) | \([2, 2]\) | \(327680\) | \(1.4407\) | |
| 76230.fg4 | 76230fe1 | \([1, -1, 1, 2518, -78119]\) | \(1367631/2800\) | \(-3616110313200\) | \([2]\) | \(163840\) | \(1.0941\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 76230.fg have rank \(0\).
Complex multiplication
The elliptic curves in class 76230.fg do not have complex multiplication.Modular form 76230.2.a.fg
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.
