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SageMath
E = EllipticCurve("fk1")
E.isogeny_class()
Elliptic curves in class 106722.fk
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 106722.fk1 | 106722fq2 | \([1, -1, 1, -7525013, -8241406995]\) | \(-6329617441/279936\) | \(-2084139151390861133184\) | \([]\) | \(5597760\) | \(2.8557\) | |
| 106722.fk2 | 106722fq1 | \([1, -1, 1, -54473, 11298543]\) | \(-2401/6\) | \(-44670335034955014\) | \([]\) | \(799680\) | \(1.8827\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 106722.fk have rank \(0\).
Complex multiplication
The elliptic curves in class 106722.fk do not have complex multiplication.Modular form 106722.2.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.
\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
