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Properties

Label 33150.q
Number of curves $4$
Conductor $33150$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("q1")
 
E.isogeny_class()
 

Elliptic curves in class 33150.q

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
33150.q1 33150u4 \([1, 0, 1, -1714876, 864004148]\) \(35694515311673154481/10400566692750\) \(162508854574218750\) \([2]\) \(811008\) \(2.2819\)  
33150.q2 33150u3 \([1, 0, 1, -839376, -289037852]\) \(4185743240664514801/113629394531250\) \(1775459289550781250\) \([2]\) \(811008\) \(2.2819\)  
33150.q3 33150u2 \([1, 0, 1, -121126, 9754148]\) \(12577973014374481/4642947562500\) \(72546055664062500\) \([2, 2]\) \(405504\) \(1.9353\)  
33150.q4 33150u1 \([1, 0, 1, 23374, 1084148]\) \(90391899763439/84690294000\) \(-1323285843750000\) \([2]\) \(202752\) \(1.5888\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 33150.q have rank \(1\).

Complex multiplication

The elliptic curves in class 33150.q do not have complex multiplication.

Modular form 33150.2.a.q

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{3} + q^{4} - q^{6} - 4 q^{7} - q^{8} + q^{9} + 4 q^{11} + q^{12} + q^{13} + 4 q^{14} + q^{16} - q^{17} - q^{18} + 4 q^{19} + O(q^{20})\) Copy content Toggle raw display

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.