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SageMath
E = EllipticCurve("n1")
E.isogeny_class()
Elliptic curves in class 14784.n
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
14784.n1 | 14784bx2 | \([0, -1, 0, -6753, 205569]\) | \(129938649625/7072758\) | \(1854081073152\) | \([2]\) | \(24576\) | \(1.1099\) | |
14784.n2 | 14784bx1 | \([0, -1, 0, 287, 12673]\) | \(9938375/274428\) | \(-71939653632\) | \([2]\) | \(12288\) | \(0.76336\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 14784.n have rank \(1\).
Complex multiplication
The elliptic curves in class 14784.n do not have complex multiplication.Modular form 14784.2.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.