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SageMath
E = EllipticCurve("n1")
E.isogeny_class()
Elliptic curves in class 106560.n
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
106560.n1 | 106560fh1 | \([0, 0, 0, -276528, -55967848]\) | \(3132662187311104/151723125\) | \(113260705920000\) | \([2]\) | \(688128\) | \(1.7694\) | \(\Gamma_0(N)\)-optimal |
106560.n2 | 106560fh2 | \([0, 0, 0, -261948, -62132272]\) | \(-166426126492624/43316015625\) | \(-517363718400000000\) | \([2]\) | \(1376256\) | \(2.1160\) |
Rank
sage: E.rank()
The elliptic curves in class 106560.n have rank \(0\).
Complex multiplication
The elliptic curves in class 106560.n do not have complex multiplication.Modular form 106560.2.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.