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SageMath
E = EllipticCurve("fk1")
E.isogeny_class()
Elliptic curves in class 61200.fk
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
61200.fk1 | 61200fq2 | \([0, 0, 0, -166296675, 825349009250]\) | \(10901014250685308569/1040774054400\) | \(48558354282086400000000\) | \([2]\) | \(9289728\) | \(3.3898\) | |
61200.fk2 | 61200fq1 | \([0, 0, 0, -9624675, 14884753250]\) | \(-2113364608155289/828431400960\) | \(-38651295443189760000000\) | \([2]\) | \(4644864\) | \(3.0432\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 61200.fk have rank \(0\).
Complex multiplication
The elliptic curves in class 61200.fk do not have complex multiplication.Modular form 61200.2.a.fk
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.