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SageMath
E = EllipticCurve("io1")
E.isogeny_class()
Elliptic curves in class 346560io
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
346560.io2 | 346560io1 | \([0, 1, 0, -54606785, 7851023775]\) | \(212883113611/122880000\) | \(10394498315867526266880000\) | \([2]\) | \(112066560\) | \(3.4898\) | \(\Gamma_0(N)\)-optimal |
346560.io1 | 346560io2 | \([0, 1, 0, -616496065, 5876559797663]\) | \(306331959547531/900000000\) | \(76131579461920358400000000\) | \([2]\) | \(224133120\) | \(3.8364\) |
Rank
sage: E.rank()
The elliptic curves in class 346560io have rank \(1\).
Complex multiplication
The elliptic curves in class 346560io do not have complex multiplication.Modular form 346560.2.a.io
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.