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SageMath
E = EllipticCurve("o1")
E.isogeny_class()
Elliptic curves in class 357390o
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
357390.o2 | 357390o1 | \([1, -1, 0, 284220, -431763440]\) | \(10793861/348480\) | \(-81976202304156895680\) | \([2]\) | \(9338880\) | \(2.5011\) | \(\Gamma_0(N)\)-optimal |
357390.o1 | 357390o2 | \([1, -1, 0, -7123500, -6981669464]\) | \(169939405819/8784600\) | \(2066483433083955078600\) | \([2]\) | \(18677760\) | \(2.8476\) |
Rank
sage: E.rank()
The elliptic curves in class 357390o have rank \(2\).
Complex multiplication
The elliptic curves in class 357390o do not have complex multiplication.Modular form 357390.2.a.o
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.