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SageMath
E = EllipticCurve("by1")
E.isogeny_class()
Elliptic curves in class 43120by
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
43120.f2 | 43120by1 | \([0, 1, 0, -8976, 331540]\) | \(-56933326423/1464100\) | \(-2056955084800\) | \([2]\) | \(86016\) | \(1.1461\) | \(\Gamma_0(N)\)-optimal |
43120.f1 | 43120by2 | \([0, 1, 0, -144496, 21093204]\) | \(237487154804983/151250\) | \(212495360000\) | \([2]\) | \(172032\) | \(1.4927\) |
Rank
sage: E.rank()
The elliptic curves in class 43120by have rank \(2\).
Complex multiplication
The elliptic curves in class 43120by do not have complex multiplication.Modular form 43120.2.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.