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SageMath
E = EllipticCurve("cy1")
E.isogeny_class()
Elliptic curves in class 21168cy
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 21168.bu3 | 21168cy1 | \([0, 0, 0, 8085, 172186]\) | \(4492125/3584\) | \(-46631560937472\) | \([]\) | \(41472\) | \(1.3107\) | \(\Gamma_0(N)\)-optimal |
| 21168.bu2 | 21168cy2 | \([0, 0, 0, -85995, -12428262]\) | \(-7414875/2744\) | \(-26026968566366208\) | \([]\) | \(124416\) | \(1.8600\) | |
| 21168.bu1 | 21168cy3 | \([0, 0, 0, -7494795, -7897465926]\) | \(-545407363875/14\) | \(-1195115903557632\) | \([]\) | \(373248\) | \(2.4093\) |
Rank
sage: E.rank()
The elliptic curves in class 21168cy have rank \(0\).
Complex multiplication
The elliptic curves in class 21168cy do not have complex multiplication.Modular form 21168.2.a.cy
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.
\(\left(\begin{array}{rrr} 1 & 3 & 9 \\ 3 & 1 & 3 \\ 9 & 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
