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SageMath
E = EllipticCurve("n1")
E.isogeny_class()
Elliptic curves in class 92778.n
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
92778.n1 | 92778s2 | \([1, 1, 1, -3461549, 2477424941]\) | \(425547480243313/649446\) | \(7000518278557734\) | \([2]\) | \(2260992\) | \(2.3078\) | |
92778.n2 | 92778s1 | \([1, 1, 1, -214319, 39404657]\) | \(-100999381393/4062492\) | \(-43790476040339868\) | \([2]\) | \(1130496\) | \(1.9613\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 92778.n have rank \(0\).
Complex multiplication
The elliptic curves in class 92778.n do not have complex multiplication.Modular form 92778.2.a.n
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.