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Properties

Label 33150.s
Number of curves $2$
Conductor $33150$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("s1")
 
E.isogeny_class()
 

Elliptic curves in class 33150.s

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
33150.s1 33150bd1 \([1, 0, 1, -3731, -87442]\) \(45932714112797/344208384\) \(43026048000\) \([2]\) \(34560\) \(0.87061\) \(\Gamma_0(N)\)-optimal
33150.s2 33150bd2 \([1, 0, 1, -1331, -197842]\) \(-2083908933917/133914988896\) \(-16739373612000\) \([2]\) \(69120\) \(1.2172\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 33150.2.a.s

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

\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)

Isogeny graph

sage: E.isogeny_graph().plot(edge_labels=True)
 

The vertices are labelled with LMFDB labels.