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SageMath
E = EllipticCurve("db1")
E.isogeny_class()
Elliptic curves in class 62160db
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
62160.cz4 | 62160db1 | \([0, 1, 0, 1280, -13900]\) | \(56578878719/54390000\) | \(-222781440000\) | \([2]\) | \(61440\) | \(0.86454\) | \(\Gamma_0(N)\)-optimal |
62160.cz3 | 62160db2 | \([0, 1, 0, -6720, -132300]\) | \(8194759433281/2958272100\) | \(12117082521600\) | \([2, 2]\) | \(122880\) | \(1.2111\) | |
62160.cz2 | 62160db3 | \([0, 1, 0, -45920, 3677940]\) | \(2614441086442081/74385450090\) | \(304682803568640\) | \([4]\) | \(245760\) | \(1.5577\) | |
62160.cz1 | 62160db4 | \([0, 1, 0, -95520, -11392140]\) | \(23531588875176481/6398929110\) | \(26210013634560\) | \([2]\) | \(245760\) | \(1.5577\) |
Rank
sage: E.rank()
The elliptic curves in class 62160db have rank \(0\).
Complex multiplication
The elliptic curves in class 62160db do not have complex multiplication.Modular form 62160.2.a.db
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 Cremona 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 Cremona labels.