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SageMath
E = EllipticCurve("s1")
E.isogeny_class()
Elliptic curves in class 46800.s
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
46800.s1 | 46800dm4 | \([0, 0, 0, -250275, -48190750]\) | \(37159393753/1053\) | \(49128768000000\) | \([2]\) | \(262144\) | \(1.7288\) | |
46800.s2 | 46800dm3 | \([0, 0, 0, -70275, 6493250]\) | \(822656953/85683\) | \(3997626048000000\) | \([2]\) | \(262144\) | \(1.7288\) | |
46800.s3 | 46800dm2 | \([0, 0, 0, -16275, -688750]\) | \(10218313/1521\) | \(70963776000000\) | \([2, 2]\) | \(131072\) | \(1.3822\) | |
46800.s4 | 46800dm1 | \([0, 0, 0, 1725, -58750]\) | \(12167/39\) | \(-1819584000000\) | \([2]\) | \(65536\) | \(1.0357\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 46800.s have rank \(1\).
Complex multiplication
The elliptic curves in class 46800.s do not have complex multiplication.Modular form 46800.2.a.s
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.