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SageMath
E = EllipticCurve("bb1")
E.isogeny_class()
Elliptic curves in class 54150.bb
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
54150.bb1 | 54150o2 | \([1, 0, 1, -6069501, 3442461148]\) | \(4904335099/1822500\) | \(9189036393784804687500\) | \([2]\) | \(3502080\) | \(2.9143\) | |
54150.bb2 | 54150o1 | \([1, 0, 1, -2640001, -1612621852]\) | \(403583419/10800\) | \(54453549000206250000\) | \([2]\) | \(1751040\) | \(2.5677\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 54150.bb have rank \(0\).
Complex multiplication
The elliptic curves in class 54150.bb do not have complex multiplication.Modular form 54150.2.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 LMFDB 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 LMFDB labels.