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SageMath
E = EllipticCurve("gp1")
E.isogeny_class()
Elliptic curves in class 162240gp
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
162240.ga2 | 162240gp1 | \([0, 1, 0, -576, 4590]\) | \(150568768/16875\) | \(2372760000\) | \([2]\) | \(129024\) | \(0.53181\) | \(\Gamma_0(N)\)-optimal |
162240.ga1 | 162240gp2 | \([0, 1, 0, -2201, -35385]\) | \(131096512/18225\) | \(164005171200\) | \([2]\) | \(258048\) | \(0.87839\) |
Rank
sage: E.rank()
The elliptic curves in class 162240gp have rank \(1\).
Complex multiplication
The elliptic curves in class 162240gp do not have complex multiplication.Modular form 162240.2.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 Cremona 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 Cremona labels.