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SageMath
E = EllipticCurve("bt1")
E.isogeny_class()
Elliptic curves in class 42432bt
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 42432.v1 | 42432bt1 | \([0, -1, 0, -4037, -69483]\) | \(7107347955712/1996623837\) | \(2044542809088\) | \([2]\) | \(55296\) | \(1.0692\) | \(\Gamma_0(N)\)-optimal |
| 42432.v2 | 42432bt2 | \([0, -1, 0, 10543, -468975]\) | \(7909612346288/10289870721\) | \(-168589241892864\) | \([2]\) | \(110592\) | \(1.4158\) |
Rank
sage: E.rank()
The elliptic curves in class 42432bt have rank \(1\).
Complex multiplication
The elliptic curves in class 42432bt do not have complex multiplication.Modular form 42432.2.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.
