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SageMath
E = EllipticCurve("by1")
E.isogeny_class()
Elliptic curves in class 22800by
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
22800.u2 | 22800by1 | \([0, -1, 0, 67, -2388]\) | \(131072/9747\) | \(-2436750000\) | \([2]\) | \(9216\) | \(0.48070\) | \(\Gamma_0(N)\)-optimal |
22800.u1 | 22800by2 | \([0, -1, 0, -2308, -40388]\) | \(340062928/13851\) | \(55404000000\) | \([2]\) | \(18432\) | \(0.82727\) |
Rank
sage: E.rank()
The elliptic curves in class 22800by have rank \(1\).
Complex multiplication
The elliptic curves in class 22800by do not have complex multiplication.Modular form 22800.2.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.