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SageMath
E = EllipticCurve("j1")
E.isogeny_class()
Elliptic curves in class 128673.j
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
128673.j1 | 128673e2 | \([0, 0, 1, -449094, 115902625]\) | \(-23100424192/14739\) | \(-6391216576671651\) | \([]\) | \(1161216\) | \(1.9737\) | |
128673.j2 | 128673e1 | \([0, 0, 1, 5046, 664600]\) | \(32768/459\) | \(-199034426263131\) | \([]\) | \(387072\) | \(1.4244\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 128673.j have rank \(2\).
Complex multiplication
The elliptic curves in class 128673.j do not have complex multiplication.Modular form 128673.2.a.j
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.