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SageMath
E = EllipticCurve("fk1")
E.isogeny_class()
Elliptic curves in class 87120.fk
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 87120.fk1 | 87120bs2 | \([0, 0, 0, -3207567, 2211116974]\) | \(14692827276345584/6075\) | \(1509009004800\) | \([2]\) | \(737280\) | \(2.1189\) | |
| 87120.fk2 | 87120bs1 | \([0, 0, 0, -200442, 34559899]\) | \(-57367289145344/36905625\) | \(-572951856510000\) | \([2]\) | \(368640\) | \(1.7723\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 87120.fk have rank \(1\).
Complex multiplication
The elliptic curves in class 87120.fk do not have complex multiplication.Modular form 87120.2.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.
