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SageMath
E = EllipticCurve("n1")
E.isogeny_class()
Elliptic curves in class 4704.n
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
4704.n1 | 4704e2 | \([0, -1, 0, -14177, -373743]\) | \(1906624/729\) | \(120495224844288\) | \([2]\) | \(10752\) | \(1.4011\) | |
4704.n2 | 4704e1 | \([0, -1, 0, -12462, -531180]\) | \(82881856/27\) | \(69731032896\) | \([2]\) | \(5376\) | \(1.0545\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 4704.n have rank \(0\).
Complex multiplication
The elliptic curves in class 4704.n do not have complex multiplication.Modular form 4704.2.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.