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SageMath
E = EllipticCurve("bkd1")
E.isogeny_class()
Elliptic curves in class 705600.bkd
sage: E.isogeny_class().curves
LMFDB label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height |
---|---|---|---|---|---|---|
705600.bkd1 | \([0, 0, 0, -266700, -37926000]\) | \(55306341/15625\) | \(592704000000000000\) | \([2]\) | \(9437184\) | \(2.1172\) |
705600.bkd2 | \([0, 0, 0, -98700, 11466000]\) | \(2803221/125\) | \(4741632000000000\) | \([2]\) | \(4718592\) | \(1.7706\) |
Rank
sage: E.rank()
The elliptic curves in class 705600.bkd have rank \(1\).
Complex multiplication
The elliptic curves in class 705600.bkd do not have complex multiplication.Modular form 705600.2.a.bkd
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.