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SageMath
E = EllipticCurve("g1")
E.isogeny_class()
Elliptic curves in class 5577.g
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 5577.g1 | 5577g4 | \([1, 0, 1, -1160020, 480793679]\) | \(35765103905346817/1287\) | \(6212103183\) | \([2]\) | \(43008\) | \(1.8236\) | |
| 5577.g2 | 5577g5 | \([1, 0, 1, -508525, -135200167]\) | \(3013001140430737/108679952667\) | \(524577373652649603\) | \([2]\) | \(86016\) | \(2.1701\) | |
| 5577.g3 | 5577g3 | \([1, 0, 1, -80110, 5834051]\) | \(11779205551777/3763454409\) | \(18165475612450881\) | \([2, 2]\) | \(43008\) | \(1.8236\) | |
| 5577.g4 | 5577g2 | \([1, 0, 1, -72505, 7507151]\) | \(8732907467857/1656369\) | \(7994976796521\) | \([2, 2]\) | \(21504\) | \(1.4770\) | |
| 5577.g5 | 5577g1 | \([1, 0, 1, -4060, 142469]\) | \(-1532808577/938223\) | \(-4528623220407\) | \([2]\) | \(10752\) | \(1.1304\) | \(\Gamma_0(N)\)-optimal |
| 5577.g6 | 5577g6 | \([1, 0, 1, 226625, 39820289]\) | \(266679605718863/296110251723\) | \(-1429267628008841907\) | \([2]\) | \(86016\) | \(2.1701\) |
Rank
sage: E.rank()
The elliptic curves in class 5577.g have rank \(1\).
Complex multiplication
The elliptic curves in class 5577.g do not have complex multiplication.Modular form 5577.2.a.g
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.
\(\left(\begin{array}{rrrrrr} 1 & 8 & 4 & 2 & 4 & 8 \\ 8 & 1 & 2 & 4 & 8 & 4 \\ 4 & 2 & 1 & 2 & 4 & 2 \\ 2 & 4 & 2 & 1 & 2 & 4 \\ 4 & 8 & 4 & 2 & 1 & 8 \\ 8 & 4 & 2 & 4 & 8 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
