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Properties

Label 33150z
Number of curves $2$
Conductor $33150$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("z1")
 
E.isogeny_class()
 

Elliptic curves in class 33150z

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
33150.bb2 33150z1 \([1, 0, 1, -826, -12802]\) \(-99546915625/54454842\) \(-34034276250\) \([3]\) \(29376\) \(0.72452\) \(\Gamma_0(N)\)-optimal
33150.bb1 33150z2 \([1, 0, 1, -73951, -7746502]\) \(-71559517896165625/4598568\) \(-2874105000\) \([]\) \(88128\) \(1.2738\)  

Rank

sage: E.rank()
 

The elliptic curves in class 33150z have rank \(0\).

Complex multiplication

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

Modular form 33150.2.a.z

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

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.