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SageMath
E = EllipticCurve("dk1")
E.isogeny_class()
Elliptic curves in class 371280.dk
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 371280.dk1 | 371280dk3 | \([0, 1, 0, -96136, 7458164]\) | \(23989788887201929/7965841406250\) | \(32628086400000000\) | \([2]\) | \(3538944\) | \(1.8714\) | |
| 371280.dk2 | 371280dk2 | \([0, 1, 0, -39016, -2891980]\) | \(1603626125868649/53847202500\) | \(220558141440000\) | \([2, 2]\) | \(1769472\) | \(1.5248\) | |
| 371280.dk3 | 371280dk1 | \([0, 1, 0, -38696, -2942796]\) | \(1564491509212969/1856400\) | \(7603814400\) | \([2]\) | \(884736\) | \(1.1783\) | \(\Gamma_0(N)\)-optimal |
| 371280.dk4 | 371280dk4 | \([0, 1, 0, 12984, -9984780]\) | \(59095693799351/10558110940650\) | \(-43246022412902400\) | \([2]\) | \(3538944\) | \(1.8714\) |
Rank
sage: E.rank()
The elliptic curves in class 371280.dk have rank \(2\).
Complex multiplication
The elliptic curves in class 371280.dk do not have complex multiplication.Modular form 371280.2.a.dk
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
