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SageMath
E = EllipticCurve("bk1")
E.isogeny_class()
Elliptic curves in class 22736.bk
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
22736.bk1 | 22736j2 | \([0, -1, 0, -1752648, 893633168]\) | \(2471097448795250/98942809\) | \(23839790153811968\) | \([2]\) | \(294912\) | \(2.2254\) | |
22736.bk2 | 22736j1 | \([0, -1, 0, -104288, 15386960]\) | \(-1041220466500/242597383\) | \(-29226331660868608\) | \([2]\) | \(147456\) | \(1.8789\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 22736.bk have rank \(0\).
Complex multiplication
The elliptic curves in class 22736.bk do not have complex multiplication.Modular form 22736.2.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.