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SageMath
E = EllipticCurve("gk1")
E.isogeny_class()
Elliptic curves in class 158400.gk
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
158400.gk1 | 158400ea2 | \([0, 0, 0, -68700, 6874000]\) | \(192143824/1815\) | \(338722560000000\) | \([2]\) | \(589824\) | \(1.6088\) | |
158400.gk2 | 158400ea1 | \([0, 0, 0, -1200, 259000]\) | \(-16384/2475\) | \(-28868400000000\) | \([2]\) | \(294912\) | \(1.2622\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 158400.gk have rank \(1\).
Complex multiplication
The elliptic curves in class 158400.gk do not have complex multiplication.Modular form 158400.2.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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.