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SageMath
sage: E = EllipticCurve("21780.q1")
sage: E.isogeny_class()
Elliptic curves in class 21780.q
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | Torsion structure | Modular degree | Optimality |
|---|---|---|---|---|---|
| 21780.q1 | 21780y3 | [0, 0, 0, -45012, -3674891] | [2] | 51840 | |
| 21780.q2 | 21780y4 | [0, 0, 0, -39567, -4597274] | [2] | 103680 | |
| 21780.q3 | 21780y1 | [0, 0, 0, -1452, 14641] | [2] | 17280 | \(\Gamma_0(N)\)-optimal |
| 21780.q4 | 21780y2 | [0, 0, 0, 3993, 98494] | [2] | 34560 |
Rank
sage: E.rank()
The elliptic curves in class 21780.q have rank \(1\).
Modular form 21780.2.a.q
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
