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SageMath
E = EllipticCurve("bu1")
E.isogeny_class()
Elliptic curves in class 177744bu
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
177744.ba1 | 177744bu1 | \([0, -1, 0, -253122973, 1550168067553]\) | \(-47327266415721472000/1222082060283\) | \(-46313473081586047126272\) | \([]\) | \(25090560\) | \(3.4559\) | \(\Gamma_0(N)\)-optimal |
177744.ba2 | 177744bu2 | \([0, -1, 0, -78299053, 3638812064065]\) | \(-1400832679220224000/150124273180279587\) | \(-5689287741624715758105047808\) | \([]\) | \(75271680\) | \(4.0052\) |
Rank
sage: E.rank()
The elliptic curves in class 177744bu have rank \(0\).
Complex multiplication
The elliptic curves in class 177744bu do not have complex multiplication.Modular form 177744.2.a.bu
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.