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SageMath
E = EllipticCurve("bb1")
E.isogeny_class()
Elliptic curves in class 22080bb
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
22080.ce2 | 22080bb1 | \([0, 1, 0, -801, -16065]\) | \(-217081801/285660\) | \(-74884055040\) | \([2]\) | \(27648\) | \(0.77950\) | \(\Gamma_0(N)\)-optimal |
22080.ce1 | 22080bb2 | \([0, 1, 0, -15521, -749121]\) | \(1577505447721/838350\) | \(219768422400\) | \([2]\) | \(55296\) | \(1.1261\) |
Rank
sage: E.rank()
The elliptic curves in class 22080bb have rank \(0\).
Complex multiplication
The elliptic curves in class 22080bb do not have complex multiplication.Modular form 22080.2.a.bb
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.