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SageMath
E = EllipticCurve("bt1")
E.isogeny_class()
Elliptic curves in class 81120bt
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
81120.bp2 | 81120bt1 | \([0, 1, 0, -93006, 9485100]\) | \(131096512/18225\) | \(12369088068667200\) | \([2]\) | \(838656\) | \(1.8143\) | \(\Gamma_0(N)\)-optimal |
81120.bp1 | 81120bt2 | \([0, 1, 0, -389601, -84179601]\) | \(150568768/16875\) | \(732982996661760000\) | \([2]\) | \(1677312\) | \(2.1609\) |
Rank
sage: E.rank()
The elliptic curves in class 81120bt have rank \(0\).
Complex multiplication
The elliptic curves in class 81120bt do not have complex multiplication.Modular form 81120.2.a.bt
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.