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SageMath
E = EllipticCurve("k1")
E.isogeny_class()
Elliptic curves in class 46410.k
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 46410.k1 | 46410h4 | \([1, 1, 0, -6008, -119538]\) | \(23989788887201929/7965841406250\) | \(7965841406250\) | \([2]\) | \(147456\) | \(1.1783\) | |
| 46410.k2 | 46410h2 | \([1, 1, 0, -2438, 43968]\) | \(1603626125868649/53847202500\) | \(53847202500\) | \([2, 2]\) | \(73728\) | \(0.83168\) | |
| 46410.k3 | 46410h1 | \([1, 1, 0, -2418, 44772]\) | \(1564491509212969/1856400\) | \(1856400\) | \([2]\) | \(36864\) | \(0.48511\) | \(\Gamma_0(N)\)-optimal |
| 46410.k4 | 46410h3 | \([1, 1, 0, 812, 156418]\) | \(59095693799351/10558110940650\) | \(-10558110940650\) | \([2]\) | \(147456\) | \(1.1783\) |
Rank
sage: E.rank()
The elliptic curves in class 46410.k have rank \(1\).
Complex multiplication
The elliptic curves in class 46410.k do not have complex multiplication.Modular form 46410.2.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 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.
