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SageMath
E = EllipticCurve("o1")
E.isogeny_class()
Elliptic curves in class 249090o
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
249090.o1 | 249090o1 | \([1, 1, 0, -256546462, -1581704816396]\) | \(5786812293313543219/16560000000\) | \(5343708275220240000000\) | \([2]\) | \(66393600\) | \(3.4000\) | \(\Gamma_0(N)\)-optimal |
249090.o2 | 249090o2 | \([1, 1, 0, -253254142, -1624272538604]\) | \(-5566868688930446899/309960937500000\) | \(-100020581323295507812500000\) | \([2]\) | \(132787200\) | \(3.7465\) |
Rank
sage: E.rank()
The elliptic curves in class 249090o have rank \(1\).
Complex multiplication
The elliptic curves in class 249090o do not have complex multiplication.Modular form 249090.2.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.