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SageMath
E = EllipticCurve("fk1")
E.isogeny_class()
Elliptic curves in class 176400.fk
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 176400.fk1 | 176400hl2 | \([0, 0, 0, -160935600, -786457154000]\) | \(-1713910976512/1594323\) | \(-428813188302276288000000\) | \([]\) | \(22364160\) | \(3.4575\) | |
| 176400.fk2 | 176400hl1 | \([0, 0, 0, -411600, 110446000]\) | \(-28672/3\) | \(-806887666368000000\) | \([]\) | \(1720320\) | \(2.1750\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 176400.fk have rank \(1\).
Complex multiplication
The elliptic curves in class 176400.fk do not have complex multiplication.Modular form 176400.2.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.
\(\left(\begin{array}{rr} 1 & 13 \\ 13 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
