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SageMath
E = EllipticCurve("bk1")
E.isogeny_class()
Elliptic curves in class 9600.bk
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
9600.bk1 | 9600r1 | \([0, 1, 0, -883, -10387]\) | \(19056256/27\) | \(108000000\) | \([2]\) | \(3840\) | \(0.44462\) | \(\Gamma_0(N)\)-optimal |
9600.bk2 | 9600r2 | \([0, 1, 0, -633, -16137]\) | \(-219488/729\) | \(-93312000000\) | \([2]\) | \(7680\) | \(0.79119\) |
Rank
sage: E.rank()
The elliptic curves in class 9600.bk have rank \(0\).
Complex multiplication
The elliptic curves in class 9600.bk do not have complex multiplication.Modular form 9600.2.a.bk
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.