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SageMath
E = EllipticCurve("k1")
E.isogeny_class()
Elliptic curves in class 40560k
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 40560.bf4 | 40560k1 | \([0, -1, 0, 620, 2560]\) | \(21296/15\) | \(-18534946560\) | \([2]\) | \(30720\) | \(0.65873\) | \(\Gamma_0(N)\)-optimal |
| 40560.bf3 | 40560k2 | \([0, -1, 0, -2760, 24192]\) | \(470596/225\) | \(1112096793600\) | \([2, 2]\) | \(61440\) | \(1.0053\) | |
| 40560.bf2 | 40560k3 | \([0, -1, 0, -23040, -1322400]\) | \(136835858/1875\) | \(18534946560000\) | \([2]\) | \(122880\) | \(1.3519\) | |
| 40560.bf1 | 40560k4 | \([0, -1, 0, -36560, 2701152]\) | \(546718898/405\) | \(4003548456960\) | \([2]\) | \(122880\) | \(1.3519\) |
Rank
sage: E.rank()
The elliptic curves in class 40560k have rank \(0\).
Complex multiplication
The elliptic curves in class 40560k do not have complex multiplication.Modular form 40560.2.a.k
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.
