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SageMath
E = EllipticCurve("bo1")
E.isogeny_class()
Elliptic curves in class 6960.bo
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
6960.bo1 | 6960bk1 | \([0, 1, 0, -28160, -1793100]\) | \(602944222256641/13363200000\) | \(54735667200000\) | \([2]\) | \(26880\) | \(1.4238\) | \(\Gamma_0(N)\)-optimal |
6960.bo2 | 6960bk2 | \([0, 1, 0, 2560, -5467212]\) | \(452807907839/3153750000000\) | \(-12917760000000000\) | \([2]\) | \(53760\) | \(1.7704\) |
Rank
sage: E.rank()
The elliptic curves in class 6960.bo have rank \(0\).
Complex multiplication
The elliptic curves in class 6960.bo do not have complex multiplication.Modular form 6960.2.a.bo
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.