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SageMath
E = EllipticCurve("jb1")
E.isogeny_class()
Elliptic curves in class 242550jb
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 242550.jb4 | 242550jb1 | \([1, -1, 1, -1069655, 1557370847]\) | \(-100999381393/723148272\) | \(-969087846832701750000\) | \([2]\) | \(9437184\) | \(2.7101\) | \(\Gamma_0(N)\)-optimal |
| 242550.jb3 | 242550jb2 | \([1, -1, 1, -27750155, 56145673847]\) | \(1763535241378513/4612311396\) | \(6180938394984608062500\) | \([2, 2]\) | \(18874368\) | \(3.0566\) | |
| 242550.jb1 | 242550jb3 | \([1, -1, 1, -443723405, 3597741924347]\) | \(7209828390823479793/49509306\) | \(66347205140969156250\) | \([2]\) | \(37748736\) | \(3.4032\) | |
| 242550.jb2 | 242550jb4 | \([1, -1, 1, -38664905, 7880649347]\) | \(4770223741048753/2740574865798\) | \(3672632430462344211843750\) | \([2]\) | \(37748736\) | \(3.4032\) |
Rank
sage: E.rank()
The elliptic curves in class 242550jb have rank \(0\).
Complex multiplication
The elliptic curves in class 242550jb do not have complex multiplication.Modular form 242550.2.a.jb
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.
