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SageMath
E = EllipticCurve("co1")
E.isogeny_class()
Elliptic curves in class 16830.co
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
16830.co1 | 16830cs1 | \([1, -1, 1, -76532, -8129869]\) | \(68001744211490809/1022422500\) | \(745346002500\) | \([2]\) | \(64512\) | \(1.4147\) | \(\Gamma_0(N)\)-optimal |
16830.co2 | 16830cs2 | \([1, -1, 1, -74282, -8632069]\) | \(-62178675647294809/8362782148050\) | \(-6096468185928450\) | \([2]\) | \(129024\) | \(1.7613\) |
Rank
sage: E.rank()
The elliptic curves in class 16830.co have rank \(1\).
Complex multiplication
The elliptic curves in class 16830.co do not have complex multiplication.Modular form 16830.2.a.co
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.