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SageMath
E = EllipticCurve("e1")
E.isogeny_class()
Elliptic curves in class 14079.e
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
14079.e1 | 14079d4 | \([1, 0, 0, -25097, 1528188]\) | \(37159393753/1053\) | \(49539312693\) | \([2]\) | \(28800\) | \(1.1539\) | |
14079.e2 | 14079d3 | \([1, 0, 0, -7047, -206778]\) | \(822656953/85683\) | \(4031032221723\) | \([2]\) | \(28800\) | \(1.1539\) | |
14079.e3 | 14079d2 | \([1, 0, 0, -1632, 21735]\) | \(10218313/1521\) | \(71556785001\) | \([2, 2]\) | \(14400\) | \(0.80728\) | |
14079.e4 | 14079d1 | \([1, 0, 0, 173, 1880]\) | \(12167/39\) | \(-1834789359\) | \([2]\) | \(7200\) | \(0.46071\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 14079.e have rank \(1\).
Complex multiplication
The elliptic curves in class 14079.e do not have complex multiplication.Modular form 14079.2.a.e
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.
\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.