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SageMath
E = EllipticCurve("s1")
E.isogeny_class()
Elliptic curves in class 28611.s
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
28611.s1 | 28611b2 | \([1, -1, 0, -43404, -3450511]\) | \(19034163/121\) | \(57487072245867\) | \([2]\) | \(122880\) | \(1.4772\) | |
28611.s2 | 28611b1 | \([1, -1, 0, -4389, 21824]\) | \(19683/11\) | \(5226097476897\) | \([2]\) | \(61440\) | \(1.1306\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 28611.s have rank \(1\).
Complex multiplication
The elliptic curves in class 28611.s do not have complex multiplication.Modular form 28611.2.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.