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SageMath
E = EllipticCurve("by1")
E.isogeny_class()
Elliptic curves in class 17424by
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 17424.l2 | 17424by1 | \([0, 0, 0, 2904, 33275]\) | \(131072/99\) | \(-2045685262896\) | \([2]\) | \(23040\) | \(1.0504\) | \(\Gamma_0(N)\)-optimal |
| 17424.l1 | 17424by2 | \([0, 0, 0, -13431, 284834]\) | \(810448/363\) | \(120013535423232\) | \([2]\) | \(46080\) | \(1.3970\) |
Rank
sage: E.rank()
The elliptic curves in class 17424by have rank \(0\).
Complex multiplication
The elliptic curves in class 17424by do not have complex multiplication.Modular form 17424.2.a.by
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
