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SageMath
E = EllipticCurve("m1")
E.isogeny_class()
Elliptic curves in class 17424.m
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 17424.m1 | 17424v3 | \([0, 0, 0, -514371, -141972446]\) | \(5690357426/891\) | \(2356629422856192\) | \([2]\) | \(122880\) | \(1.9607\) | |
| 17424.m2 | 17424v2 | \([0, 0, 0, -35211, -1770230]\) | \(3650692/1089\) | \(1440162425078784\) | \([2, 2]\) | \(61440\) | \(1.6141\) | |
| 17424.m3 | 17424v1 | \([0, 0, 0, -13431, 577654]\) | \(810448/33\) | \(10910321402112\) | \([2]\) | \(30720\) | \(1.2675\) | \(\Gamma_0(N)\)-optimal |
| 17424.m4 | 17424v4 | \([0, 0, 0, 95469, -11832590]\) | \(36382894/43923\) | \(-116173102289688576\) | \([2]\) | \(122880\) | \(1.9607\) |
Rank
sage: E.rank()
The elliptic curves in class 17424.m have rank \(1\).
Complex multiplication
The elliptic curves in class 17424.m do not have complex multiplication.Modular form 17424.2.a.m
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
