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SageMath
E = EllipticCurve("j1")
E.isogeny_class()
Elliptic curves in class 73283j
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
73283.a2 | 73283j1 | \([1, 0, 0, -3437, -81872]\) | \(-95443993/5887\) | \(-276959101447\) | \([2]\) | \(85536\) | \(0.95001\) | \(\Gamma_0(N)\)-optimal |
73283.a1 | 73283j2 | \([1, 0, 0, -55782, -5075585]\) | \(408023180713/1421\) | \(66852196901\) | \([2]\) | \(171072\) | \(1.2966\) |
Rank
sage: E.rank()
The elliptic curves in class 73283j have rank \(0\).
Complex multiplication
The elliptic curves in class 73283j do not have complex multiplication.Modular form 73283.2.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 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.