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SageMath
E = EllipticCurve("k1")
E.isogeny_class()
Elliptic curves in class 16830.k
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
16830.k1 | 16830i2 | \([1, -1, 0, -46185, 3831821]\) | \(553529221679043/11190080\) | \(220254344640\) | \([2]\) | \(46080\) | \(1.2967\) | |
16830.k2 | 16830i1 | \([1, -1, 0, -2985, 56141]\) | \(149467669443/19148800\) | \(376905830400\) | \([2]\) | \(23040\) | \(0.95013\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 16830.k have rank \(1\).
Complex multiplication
The elliptic curves in class 16830.k do not have complex multiplication.Modular form 16830.2.a.k
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.