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SageMath
E = EllipticCurve("ck1")
E.isogeny_class()
Elliptic curves in class 16830ck
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
16830.cd2 | 16830ck1 | \([1, -1, 1, 238, -1299]\) | \(2053225511/2098140\) | \(-1529544060\) | \([2]\) | \(8192\) | \(0.44919\) | \(\Gamma_0(N)\)-optimal |
16830.cd1 | 16830ck2 | \([1, -1, 1, -1292, -11091]\) | \(326940373369/112003650\) | \(81650660850\) | \([2]\) | \(16384\) | \(0.79576\) |
Rank
sage: E.rank()
The elliptic curves in class 16830ck have rank \(0\).
Complex multiplication
The elliptic curves in class 16830ck do not have complex multiplication.Modular form 16830.2.a.ck
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.