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SageMath
sage: E = EllipticCurve("16830.l1")
sage: E.isogeny_class()
Elliptic curves in class 16830.l
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | Torsion structure | Modular degree | Optimality |
|---|---|---|---|---|---|
| 16830.l1 | 16830t5 | [1, -1, 0, -2629260, 1641423766] | [2] | 393216 | |
| 16830.l2 | 16830t3 | [1, -1, 0, -179010, 20828416] | [2, 2] | 196608 | |
| 16830.l3 | 16830t2 | [1, -1, 0, -66510, -6329084] | [2, 2] | 98304 | |
| 16830.l4 | 16830t1 | [1, -1, 0, -65790, -6478700] | [2] | 49152 | \(\Gamma_0(N)\)-optimal |
| 16830.l5 | 16830t4 | [1, -1, 0, 34470, -23919800] | [2] | 196608 | |
| 16830.l6 | 16830t6 | [1, -1, 0, 471240, 136963066] | [2] | 393216 |
Rank
sage: E.rank()
The elliptic curves in class 16830.l have rank \(1\).
Modular form 16830.2.a.l
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.
\(\left(\begin{array}{rrrrrr} 1 & 2 & 4 & 8 & 8 & 4 \\ 2 & 1 & 2 & 4 & 4 & 2 \\ 4 & 2 & 1 & 2 & 2 & 4 \\ 8 & 4 & 2 & 1 & 4 & 8 \\ 8 & 4 & 2 & 4 & 1 & 8 \\ 4 & 2 & 4 & 8 & 8 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
