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SageMath
E = EllipticCurve("i1")
E.isogeny_class()
Elliptic curves in class 142296i
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
142296.cu4 | 142296i1 | \([0, 1, 0, -43479, 22626162]\) | \(-2725888/64827\) | \(-216182362144473648\) | \([2]\) | \(1658880\) | \(2.0069\) | \(\Gamma_0(N)\)-optimal |
142296.cu3 | 142296i2 | \([0, 1, 0, -1496084, 700702176]\) | \(6940769488/35721\) | \(1905934294824747264\) | \([2, 2]\) | \(3317760\) | \(2.3535\) | |
142296.cu1 | 142296i3 | \([0, 1, 0, -23907704, 44986063296]\) | \(7080974546692/189\) | \(40337233752904704\) | \([2]\) | \(6635520\) | \(2.7001\) | |
142296.cu2 | 142296i4 | \([0, 1, 0, -2326144, -164552368]\) | \(6522128932/3720087\) | \(793957771958423288832\) | \([2]\) | \(6635520\) | \(2.7001\) |
Rank
sage: E.rank()
The elliptic curves in class 142296i have rank \(1\).
Complex multiplication
The elliptic curves in class 142296i do not have complex multiplication.Modular form 142296.2.a.i
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.