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SageMath
E = EllipticCurve("g1")
E.isogeny_class()
Elliptic curves in class 14400.g
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
14400.g1 | 14400eh3 | \([0, 0, 0, -96300, -11502000]\) | \(132304644/5\) | \(3732480000000\) | \([2]\) | \(49152\) | \(1.4984\) | |
14400.g2 | 14400eh2 | \([0, 0, 0, -6300, -162000]\) | \(148176/25\) | \(4665600000000\) | \([2, 2]\) | \(24576\) | \(1.1518\) | |
14400.g3 | 14400eh1 | \([0, 0, 0, -1800, 27000]\) | \(55296/5\) | \(58320000000\) | \([2]\) | \(12288\) | \(0.80524\) | \(\Gamma_0(N)\)-optimal |
14400.g4 | 14400eh4 | \([0, 0, 0, 11700, -918000]\) | \(237276/625\) | \(-466560000000000\) | \([2]\) | \(49152\) | \(1.4984\) |
Rank
sage: E.rank()
The elliptic curves in class 14400.g have rank \(1\).
Complex multiplication
The elliptic curves in class 14400.g do not have complex multiplication.Modular form 14400.2.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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.