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SageMath
E = EllipticCurve("do1")
E.isogeny_class()
Elliptic curves in class 465290do
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 465290.do2 | 465290do1 | \([1, 1, 1, -2635686, 1577311139]\) | \(83890194895342081/3958384640000\) | \(95545782376540160000\) | \([2]\) | \(22937600\) | \(2.5946\) | \(\Gamma_0(N)\)-optimal |
| 465290.do1 | 465290do2 | \([1, 1, 1, -7259686, -5477063261]\) | \(1753007192038126081/478174101507200\) | \(11541960369143043996800\) | \([2]\) | \(45875200\) | \(2.9411\) |
Rank
sage: E.rank()
The elliptic curves in class 465290do have rank \(0\).
Complex multiplication
The elliptic curves in class 465290do do not have complex multiplication.Modular form 465290.2.a.do
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.
