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SageMath
E = EllipticCurve("bt1")
E.isogeny_class()
Elliptic curves in class 84150.bt
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 84150.bt1 | 84150cn1 | \([1, -1, 0, -1913292, -1018146884]\) | \(68001744211490809/1022422500\) | \(11646031289062500\) | \([2]\) | \(1548288\) | \(2.2194\) | \(\Gamma_0(N)\)-optimal |
| 84150.bt2 | 84150cn2 | \([1, -1, 0, -1857042, -1080865634]\) | \(-62178675647294809/8362782148050\) | \(-95257315405132031250\) | \([2]\) | \(3096576\) | \(2.5660\) |
Rank
sage: E.rank()
The elliptic curves in class 84150.bt have rank \(0\).
Complex multiplication
The elliptic curves in class 84150.bt do not have complex multiplication.Modular form 84150.2.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 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.
