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SageMath
E = EllipticCurve("dc1")
E.isogeny_class()
Elliptic curves in class 20800.dc
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 20800.dc1 | 20800v3 | \([0, 1, 0, -735233, -242898337]\) | \(-10730978619193/6656\) | \(-27262976000000\) | \([]\) | \(124416\) | \(1.8988\) | |
| 20800.dc2 | 20800v2 | \([0, 1, 0, -7233, -474337]\) | \(-10218313/17576\) | \(-71991296000000\) | \([]\) | \(41472\) | \(1.3495\) | |
| 20800.dc3 | 20800v1 | \([0, 1, 0, 767, 13663]\) | \(12167/26\) | \(-106496000000\) | \([]\) | \(13824\) | \(0.80021\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 20800.dc have rank \(0\).
Complex multiplication
The elliptic curves in class 20800.dc do not have complex multiplication.Modular form 20800.2.a.dc
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.
\(\left(\begin{array}{rrr} 1 & 3 & 9 \\ 3 & 1 & 3 \\ 9 & 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
