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SageMath
E = EllipticCurve("gx1")
E.isogeny_class()
Elliptic curves in class 141120.gx
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 141120.gx1 | 141120en5 | \([0, 0, 0, -18487308, 30594892048]\) | \(62161150998242/1607445\) | \(18070152461791395840\) | \([2]\) | \(6291456\) | \(2.8018\) | |
| 141120.gx2 | 141120en3 | \([0, 0, 0, -1200108, 439100368]\) | \(34008619684/4862025\) | \(27328316994684518400\) | \([2, 2]\) | \(3145728\) | \(2.4552\) | |
| 141120.gx3 | 141120en2 | \([0, 0, 0, -318108, -62228432]\) | \(2533446736/275625\) | \(387306079856640000\) | \([2, 2]\) | \(1572864\) | \(2.1086\) | |
| 141120.gx4 | 141120en1 | \([0, 0, 0, -309288, -66204488]\) | \(37256083456/525\) | \(46107866649600\) | \([2]\) | \(786432\) | \(1.7620\) | \(\Gamma_0(N)\)-optimal |
| 141120.gx5 | 141120en4 | \([0, 0, 0, 422772, -309089648]\) | \(1486779836/8203125\) | \(-46107866649600000000\) | \([2]\) | \(3145728\) | \(2.4552\) | |
| 141120.gx6 | 141120en6 | \([0, 0, 0, 1975092, 2368351888]\) | \(75798394558/259416045\) | \(-2916235071299445719040\) | \([2]\) | \(6291456\) | \(2.8018\) |
Rank
sage: E.rank()
The elliptic curves in class 141120.gx have rank \(0\).
Complex multiplication
The elliptic curves in class 141120.gx do not have complex multiplication.Modular form 141120.2.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.
\(\left(\begin{array}{rrrrrr} 1 & 2 & 4 & 8 & 8 & 4 \\ 2 & 1 & 2 & 4 & 4 & 2 \\ 4 & 2 & 1 & 2 & 2 & 4 \\ 8 & 4 & 2 & 1 & 4 & 8 \\ 8 & 4 & 2 & 4 & 1 & 8 \\ 4 & 2 & 4 & 8 & 8 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
