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SageMath
E = EllipticCurve("bd1")
E.isogeny_class()
Elliptic curves in class 105966bd
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
105966.bb2 | 105966bd1 | \([1, -1, 0, -10229661, 9101174917]\) | \(11194326053/3096576\) | \(32748487961824570392576\) | \([2]\) | \(13095936\) | \(3.0277\) | \(\Gamma_0(N)\)-optimal |
105966.bb1 | 105966bd2 | \([1, -1, 0, -150710301, 712094393605]\) | \(35796701971493/4572288\) | \(48355189256131592220288\) | \([2]\) | \(26191872\) | \(3.3743\) |
Rank
sage: E.rank()
The elliptic curves in class 105966bd have rank \(0\).
Complex multiplication
The elliptic curves in class 105966bd do not have complex multiplication.Modular form 105966.2.a.bd
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.