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SageMath
E = EllipticCurve("co1")
E.isogeny_class()
Elliptic curves in class 176890co
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
176890.k2 | 176890co1 | \([1, 0, 1, -1256288, 637266606]\) | \(-115501303/25600\) | \(-48600857416774835200\) | \([2]\) | \(7338240\) | \(2.4980\) | \(\Gamma_0(N)\)-optimal |
176890.k1 | 176890co2 | \([1, 0, 1, -21067968, 37217552558]\) | \(544737993463/20000\) | \(37969419856855340000\) | \([2]\) | \(14676480\) | \(2.8446\) |
Rank
sage: E.rank()
The elliptic curves in class 176890co have rank \(0\).
Complex multiplication
The elliptic curves in class 176890co do not have complex multiplication.Modular form 176890.2.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 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.