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SageMath
sage: E = EllipticCurve("g1")
sage: E.isogeny_class()
Elliptic curves in class 23520.g
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 23520.g1 | 23520bd4 | \([0, -1, 0, -7856, -265404]\) | \(890277128/15\) | \(903544320\) | \([2]\) | \(24576\) | \(0.84876\) | |
| 23520.g2 | 23520bd3 | \([0, -1, 0, -1976, 30360]\) | \(14172488/1875\) | \(112943040000\) | \([2]\) | \(24576\) | \(0.84876\) | |
| 23520.g3 | 23520bd1 | \([0, -1, 0, -506, -3744]\) | \(1906624/225\) | \(1694145600\) | \([2, 2]\) | \(12288\) | \(0.50218\) | \(\Gamma_0(N)\)-optimal |
| 23520.g4 | 23520bd2 | \([0, -1, 0, 719, -20159]\) | \(85184/405\) | \(-195165573120\) | \([2]\) | \(24576\) | \(0.84876\) |
Rank
sage: E.rank()
The elliptic curves in class 23520.g have rank \(1\).
Complex multiplication
The elliptic curves in class 23520.g do not have complex multiplication.Modular form 23520.2.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.
