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SageMath
E = EllipticCurve("n1")
E.isogeny_class()
Elliptic curves in class 33150.n
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
33150.n1 | 33150q4 | \([1, 0, 1, -1915501, 1018505648]\) | \(49745123032831462081/97939634471640\) | \(1530306788619375000\) | \([2]\) | \(1105920\) | \(2.3774\) | |
33150.n2 | 33150q3 | \([1, 0, 1, -1605501, -779074352]\) | \(29291056630578924481/175463302795560\) | \(2741614106180625000\) | \([2]\) | \(1105920\) | \(2.3774\) | |
33150.n3 | 33150q2 | \([1, 0, 1, -160501, 4115648]\) | \(29263955267177281/16463793153600\) | \(257246768025000000\) | \([2, 2]\) | \(552960\) | \(2.0308\) | |
33150.n4 | 33150q1 | \([1, 0, 1, 39499, 515648]\) | \(436192097814719/259683840000\) | \(-4057560000000000\) | \([2]\) | \(276480\) | \(1.6843\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 33150.n have rank \(1\).
Complex multiplication
The elliptic curves in class 33150.n do not have complex multiplication.Modular form 33150.2.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.
\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.