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SageMath
E = EllipticCurve("n1")
E.isogeny_class()
Elliptic curves in class 8280.n
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
8280.n1 | 8280q2 | \([0, 0, 0, -1347, 18414]\) | \(9776035692/359375\) | \(9936000000\) | \([2]\) | \(4608\) | \(0.68765\) | |
8280.n2 | 8280q1 | \([0, 0, 0, 33, 1026]\) | \(574992/66125\) | \(-457056000\) | \([2]\) | \(2304\) | \(0.34107\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 8280.n have rank \(1\).
Complex multiplication
The elliptic curves in class 8280.n do not have complex multiplication.Modular form 8280.2.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.