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SageMath
E = EllipticCurve("gl1")
E.isogeny_class()
Elliptic curves in class 259920.gl
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
259920.gl1 | 259920gl2 | \([0, 0, 0, -103891107, 406717670306]\) | \(882774443450089/2166000000\) | \(304275885020504064000000\) | \([2]\) | \(46448640\) | \(3.3842\) | |
259920.gl2 | 259920gl1 | \([0, 0, 0, -4081827, 11133569954]\) | \(-53540005609/350208000\) | \(-49196606251736236032000\) | \([2]\) | \(23224320\) | \(3.0376\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 259920.gl have rank \(1\).
Complex multiplication
The elliptic curves in class 259920.gl do not have complex multiplication.Modular form 259920.2.a.gl
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.