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SageMath
E = EllipticCurve("io1")
E.isogeny_class()
Elliptic curves in class 270480io
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
270480.io1 | 270480io1 | \([0, 1, 0, -225328280, 818367518100]\) | \(2625564132023811051529/918925030195200000\) | \(442821062153974107340800000\) | \([2]\) | \(82944000\) | \(3.8144\) | \(\Gamma_0(N)\)-optimal |
270480.io2 | 270480io2 | \([0, 1, 0, 673825640, 5720914351508]\) | \(70213095586874240921591/69970703040000000000\) | \(-33718203359039324160000000000\) | \([2]\) | \(165888000\) | \(4.1609\) |
Rank
sage: E.rank()
The elliptic curves in class 270480io have rank \(0\).
Complex multiplication
The elliptic curves in class 270480io do not have complex multiplication.Modular form 270480.2.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.