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SageMath
E = EllipticCurve("kt1")
E.isogeny_class()
Elliptic curves in class 296450kt
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
296450.kt1 | 296450kt1 | \([1, -1, 1, -398355, 96872647]\) | \(-5154200289/20\) | \(-27127027812500\) | \([]\) | \(4032000\) | \(1.7908\) | \(\Gamma_0(N)\)-optimal |
296450.kt2 | 296450kt2 | \([1, -1, 1, 2777895, -918892103]\) | \(1747829720511/1280000000\) | \(-1736129780000000000000\) | \([]\) | \(28224000\) | \(2.7638\) |
Rank
sage: E.rank()
The elliptic curves in class 296450kt have rank \(0\).
Complex multiplication
The elliptic curves in class 296450kt do not have complex multiplication.Modular form 296450.2.a.kt
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.
\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.