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SageMath
E = EllipticCurve("gp1")
E.isogeny_class()
Elliptic curves in class 235200.gp
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
235200.gp1 | 235200gp1 | \([0, -1, 0, -251533, -36642563]\) | \(2725888/675\) | \(435818955600000000\) | \([2]\) | \(2064384\) | \(2.0950\) | \(\Gamma_0(N)\)-optimal |
235200.gp2 | 235200gp2 | \([0, -1, 0, 605967, -233010063]\) | \(2382032/3645\) | \(-37654757763840000000\) | \([2]\) | \(4128768\) | \(2.4416\) |
Rank
sage: E.rank()
The elliptic curves in class 235200.gp have rank \(0\).
Complex multiplication
The elliptic curves in class 235200.gp do not have complex multiplication.Modular form 235200.2.a.gp
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.