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SageMath
E = EllipticCurve("gk1")
E.isogeny_class()
Elliptic curves in class 338800.gk
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 338800.gk1 | 338800gk1 | \([0, 1, 0, -170408, -27188812]\) | \(-584043889/1400\) | \(-1311833600000000\) | \([]\) | \(1990656\) | \(1.7802\) | \(\Gamma_0(N)\)-optimal |
| 338800.gk2 | 338800gk2 | \([0, 1, 0, 313592, -136572812]\) | \(3639707951/10718750\) | \(-10043726000000000000\) | \([]\) | \(5971968\) | \(2.3295\) |
Rank
sage: E.rank()
The elliptic curves in class 338800.gk have rank \(2\).
Complex multiplication
The elliptic curves in class 338800.gk do not have complex multiplication.Modular form 338800.2.a.gk
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
