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SageMath
E = EllipticCurve("cg1")
E.isogeny_class()
Elliptic curves in class 173280cg
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 173280.bh3 | 173280cg1 | \([0, -1, 0, -10950, 428400]\) | \(48228544/2025\) | \(6097146177600\) | \([2, 2]\) | \(460800\) | \(1.2180\) | \(\Gamma_0(N)\)-optimal |
| 173280.bh1 | 173280cg2 | \([0, -1, 0, -173400, 27849960]\) | \(23937672968/45\) | \(1083937098240\) | \([2]\) | \(921600\) | \(1.5645\) | |
| 173280.bh4 | 173280cg3 | \([0, -1, 0, 5295, 1575297]\) | \(85184/5625\) | \(-1083937098240000\) | \([2]\) | \(921600\) | \(1.5645\) | |
| 173280.bh2 | 173280cg4 | \([0, -1, 0, -29000, -1326060]\) | \(111980168/32805\) | \(790190144616960\) | \([2]\) | \(921600\) | \(1.5645\) |
Rank
sage: E.rank()
The elliptic curves in class 173280cg have rank \(1\).
Complex multiplication
The elliptic curves in class 173280cg do not have complex multiplication.Modular form 173280.2.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.
