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SageMath
E = EllipticCurve("n1")
E.isogeny_class()
Elliptic curves in class 4410.n
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
4410.n1 | 4410q1 | \([1, -1, 0, -6624, -77652]\) | \(1092727/540\) | \(15885600931620\) | \([2]\) | \(10752\) | \(1.2261\) | \(\Gamma_0(N)\)-optimal |
4410.n2 | 4410q2 | \([1, -1, 0, 24246, -614790]\) | \(53582633/36450\) | \(-1072278062884350\) | \([2]\) | \(21504\) | \(1.5727\) |
Rank
sage: E.rank()
The elliptic curves in class 4410.n have rank \(0\).
Complex multiplication
The elliptic curves in class 4410.n do not have complex multiplication.Modular form 4410.2.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.