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SageMath
E = EllipticCurve("bd1")
E.isogeny_class()
Elliptic curves in class 8400.bd
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
8400.bd1 | 8400bt1 | \([0, -1, 0, -2728, -53648]\) | \(4386781853/27216\) | \(13934592000\) | \([2]\) | \(7680\) | \(0.78449\) | \(\Gamma_0(N)\)-optimal |
8400.bd2 | 8400bt2 | \([0, -1, 0, -1128, -117648]\) | \(-310288733/11573604\) | \(-5925685248000\) | \([2]\) | \(15360\) | \(1.1311\) |
Rank
sage: E.rank()
The elliptic curves in class 8400.bd have rank \(0\).
Complex multiplication
The elliptic curves in class 8400.bd do not have complex multiplication.Modular form 8400.2.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 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.