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SageMath
E = EllipticCurve("bt1")
E.isogeny_class()
Elliptic curves in class 20800.bt
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
20800.bt1 | 20800dn2 | \([0, 0, 0, -940, -10800]\) | \(5606442/169\) | \(2768896000\) | \([2]\) | \(10240\) | \(0.58823\) | |
20800.bt2 | 20800dn1 | \([0, 0, 0, -140, 400]\) | \(37044/13\) | \(106496000\) | \([2]\) | \(5120\) | \(0.24165\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 20800.bt have rank \(1\).
Complex multiplication
The elliptic curves in class 20800.bt do not have complex multiplication.Modular form 20800.2.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.