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SageMath
E = EllipticCurve("gx1")
E.isogeny_class()
Elliptic curves in class 212160.gx
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
212160.gx1 | 212160r3 | \([0, 1, 0, -249985, 48024575]\) | \(26362547147244676/244298925\) | \(16010374348800\) | \([2]\) | \(1179648\) | \(1.6974\) | |
212160.gx2 | 212160r2 | \([0, 1, 0, -15985, 709775]\) | \(27572037674704/2472575625\) | \(40510679040000\) | \([2, 2]\) | \(589824\) | \(1.3508\) | |
212160.gx3 | 212160r1 | \([0, 1, 0, -3485, -67725]\) | \(4572531595264/776953125\) | \(795600000000\) | \([2]\) | \(294912\) | \(1.0042\) | \(\Gamma_0(N)\)-optimal |
212160.gx4 | 212160r4 | \([0, 1, 0, 18015, 3354975]\) | \(9865576607324/79640206425\) | \(-5219300568268800\) | \([2]\) | \(1179648\) | \(1.6974\) |
Rank
sage: E.rank()
The elliptic curves in class 212160.gx have rank \(1\).
Complex multiplication
The elliptic curves in class 212160.gx do not have complex multiplication.Modular form 212160.2.a.gx
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.