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SageMath
E = EllipticCurve("ck1")
E.isogeny_class()
Elliptic curves in class 217800.ck
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
217800.ck1 | 217800fh1 | \([0, 0, 0, -1543575, 738130250]\) | \(104795188976/1875\) | \(7277242500000000\) | \([2]\) | \(2949120\) | \(2.1706\) | \(\Gamma_0(N)\)-optimal |
217800.ck2 | 217800fh2 | \([0, 0, 0, -1494075, 787679750]\) | \(-23758298924/3515625\) | \(-54579318750000000000\) | \([2]\) | \(5898240\) | \(2.5171\) |
Rank
sage: E.rank()
The elliptic curves in class 217800.ck have rank \(0\).
Complex multiplication
The elliptic curves in class 217800.ck do not have complex multiplication.Modular form 217800.2.a.ck
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.