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SageMath
E = EllipticCurve("by1")
E.isogeny_class()
Elliptic curves in class 59290by
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
59290.x1 | 59290by1 | \([1, 1, 0, -2525877, 1547279749]\) | \(-584043889/1400\) | \(-4272116893636268600\) | \([]\) | \(1824768\) | \(2.4543\) | \(\Gamma_0(N)\)-optimal |
59290.x2 | 59290by2 | \([1, 1, 0, 4648213, 7801651411]\) | \(3639707951/10718750\) | \(-32708394966902681468750\) | \([]\) | \(5474304\) | \(3.0036\) |
Rank
sage: E.rank()
The elliptic curves in class 59290by have rank \(0\).
Complex multiplication
The elliptic curves in class 59290by do not have complex multiplication.Modular form 59290.2.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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.