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SageMath
E = EllipticCurve("cg1")
E.isogeny_class()
Elliptic curves in class 8400cg
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 8400.co3 | 8400cg1 | \([0, 1, 0, -1008, -12012]\) | \(1771561/105\) | \(6720000000\) | \([2]\) | \(6144\) | \(0.63876\) | \(\Gamma_0(N)\)-optimal |
| 8400.co2 | 8400cg2 | \([0, 1, 0, -3008, 47988]\) | \(47045881/11025\) | \(705600000000\) | \([2, 2]\) | \(12288\) | \(0.98533\) | |
| 8400.co1 | 8400cg3 | \([0, 1, 0, -45008, 3659988]\) | \(157551496201/13125\) | \(840000000000\) | \([2]\) | \(24576\) | \(1.3319\) | |
| 8400.co4 | 8400cg4 | \([0, 1, 0, 6992, 307988]\) | \(590589719/972405\) | \(-62233920000000\) | \([4]\) | \(24576\) | \(1.3319\) |
Rank
sage: E.rank()
The elliptic curves in class 8400cg have rank \(0\).
Complex multiplication
The elliptic curves in class 8400cg do not have complex multiplication.Modular form 8400.2.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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
