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SageMath
E = EllipticCurve("n1")
E.isogeny_class()
Elliptic curves in class 10350.n
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
10350.n1 | 10350o3 | \([1, -1, 0, -2394792, -1422683384]\) | \(133345896593725369/340006815000\) | \(3872890127109375000\) | \([2]\) | \(368640\) | \(2.4432\) | |
10350.n2 | 10350o2 | \([1, -1, 0, -207792, -3320384]\) | \(87109155423289/49979073600\) | \(569292885225000000\) | \([2, 2]\) | \(184320\) | \(2.0966\) | |
10350.n3 | 10350o1 | \([1, -1, 0, -135792, 19215616]\) | \(24310870577209/114462720\) | \(1303801920000000\) | \([2]\) | \(92160\) | \(1.7500\) | \(\Gamma_0(N)\)-optimal |
10350.n4 | 10350o4 | \([1, -1, 0, 827208, -27125384]\) | \(5495662324535111/3207841648920\) | \(-36539321282229375000\) | \([2]\) | \(368640\) | \(2.4432\) |
Rank
sage: E.rank()
The elliptic curves in class 10350.n have rank \(1\).
Complex multiplication
The elliptic curves in class 10350.n do not have complex multiplication.Modular form 10350.2.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.