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SageMath
E = EllipticCurve("j1")
E.isogeny_class()
Elliptic curves in class 29040j
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 29040.bb4 | 29040j1 | \([0, -1, 0, 444, -1824]\) | \(21296/15\) | \(-6802794240\) | \([2]\) | \(23040\) | \(0.57520\) | \(\Gamma_0(N)\)-optimal |
| 29040.bb3 | 29040j2 | \([0, -1, 0, -1976, -13440]\) | \(470596/225\) | \(408167654400\) | \([2, 2]\) | \(46080\) | \(0.92178\) | |
| 29040.bb2 | 29040j3 | \([0, -1, 0, -16496, 811296]\) | \(136835858/1875\) | \(6802794240000\) | \([2]\) | \(92160\) | \(1.2684\) | |
| 29040.bb1 | 29040j4 | \([0, -1, 0, -26176, -1620320]\) | \(546718898/405\) | \(1469403555840\) | \([2]\) | \(92160\) | \(1.2684\) |
Rank
sage: E.rank()
The elliptic curves in class 29040j have rank \(0\).
Complex multiplication
The elliptic curves in class 29040j do not have complex multiplication.Modular form 29040.2.a.j
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.
