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SageMath
E = EllipticCurve("bo1")
E.isogeny_class()
Elliptic curves in class 14520bo
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 14520.z4 | 14520bo1 | \([0, 1, 0, 444, 1824]\) | \(21296/15\) | \(-6802794240\) | \([2]\) | \(11520\) | \(0.57520\) | \(\Gamma_0(N)\)-optimal |
| 14520.z3 | 14520bo2 | \([0, 1, 0, -1976, 13440]\) | \(470596/225\) | \(408167654400\) | \([2, 2]\) | \(23040\) | \(0.92178\) | |
| 14520.z2 | 14520bo3 | \([0, 1, 0, -16496, -811296]\) | \(136835858/1875\) | \(6802794240000\) | \([2]\) | \(46080\) | \(1.2684\) | |
| 14520.z1 | 14520bo4 | \([0, 1, 0, -26176, 1620320]\) | \(546718898/405\) | \(1469403555840\) | \([2]\) | \(46080\) | \(1.2684\) |
Rank
sage: E.rank()
The elliptic curves in class 14520bo have rank \(0\).
Complex multiplication
The elliptic curves in class 14520bo do not have complex multiplication.Modular form 14520.2.a.bo
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.
