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SageMath
E = EllipticCurve("n1")
E.isogeny_class()
Elliptic curves in class 25230.n
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
25230.n1 | 25230k4 | \([1, 0, 1, -2716448, -1713479974]\) | \(3726830856733921/24967098180\) | \(14851012255160655780\) | \([2]\) | \(860160\) | \(2.5135\) | |
25230.n2 | 25230k2 | \([1, 0, 1, -277548, 11310106]\) | \(3975097468321/2207120400\) | \(1312846686174848400\) | \([2, 2]\) | \(430080\) | \(2.1670\) | |
25230.n3 | 25230k1 | \([1, 0, 1, -210268, 37037978]\) | \(1728432036001/3006720\) | \(1788467175717120\) | \([2]\) | \(215040\) | \(1.8204\) | \(\Gamma_0(N)\)-optimal |
25230.n4 | 25230k3 | \([1, 0, 1, 1084872, 89785498]\) | \(237395127814559/143224402500\) | \(-85193214743290702500\) | \([2]\) | \(860160\) | \(2.5135\) |
Rank
sage: E.rank()
The elliptic curves in class 25230.n have rank \(1\).
Complex multiplication
The elliptic curves in class 25230.n do not have complex multiplication.Modular form 25230.2.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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.