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SageMath
E = EllipticCurve("s1")
E.isogeny_class()
Elliptic curves in class 54208.s
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
54208.s1 | 54208cn2 | \([0, 1, 0, -40817, 2372335]\) | \(194672/49\) | \(1892998133497856\) | \([2]\) | \(304128\) | \(1.6413\) | |
54208.s2 | 54208cn1 | \([0, 1, 0, -14197, -625077]\) | \(131072/7\) | \(16901769049088\) | \([2]\) | \(152064\) | \(1.2947\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 54208.s have rank \(1\).
Complex multiplication
The elliptic curves in class 54208.s do not have complex multiplication.Modular form 54208.2.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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.