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SageMath
E = EllipticCurve("cg1")
E.isogeny_class()
Elliptic curves in class 31200cg
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 31200.cj3 | 31200cg1 | \([0, 1, 0, -2158, 25688]\) | \(1111934656/342225\) | \(342225000000\) | \([2, 2]\) | \(36864\) | \(0.91789\) | \(\Gamma_0(N)\)-optimal |
| 31200.cj4 | 31200cg2 | \([0, 1, 0, 5967, 180063]\) | \(367061696/426465\) | \(-27293760000000\) | \([4]\) | \(73728\) | \(1.2645\) | |
| 31200.cj2 | 31200cg3 | \([0, 1, 0, -13408, -581812]\) | \(33324076232/1285245\) | \(10281960000000\) | \([2]\) | \(73728\) | \(1.2645\) | |
| 31200.cj1 | 31200cg4 | \([0, 1, 0, -31408, 2131688]\) | \(428320044872/73125\) | \(585000000000\) | \([2]\) | \(73728\) | \(1.2645\) |
Rank
sage: E.rank()
The elliptic curves in class 31200cg have rank \(0\).
Complex multiplication
The elliptic curves in class 31200cg do not have complex multiplication.Modular form 31200.2.a.cg
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 2 & 2 \\ 2 & 1 & 4 & 4 \\ 2 & 4 & 1 & 4 \\ 2 & 4 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
