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SageMath
E = EllipticCurve("bk1")
E.isogeny_class()
Elliptic curves in class 92400bk
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
92400.ck1 | 92400bk1 | \([0, -1, 0, -4443, -112518]\) | \(4850878539776/130977\) | \(261954000\) | \([2]\) | \(66560\) | \(0.71963\) | \(\Gamma_0(N)\)-optimal |
92400.ck2 | 92400bk2 | \([0, -1, 0, -4268, -121968]\) | \(-268750151696/50014503\) | \(-1600464096000\) | \([2]\) | \(133120\) | \(1.0662\) |
Rank
sage: E.rank()
The elliptic curves in class 92400bk have rank \(1\).
Complex multiplication
The elliptic curves in class 92400bk do not have complex multiplication.Modular form 92400.2.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 Cremona 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 Cremona labels.