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Properties

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

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Show commands: SageMath
E = EllipticCurve("j1")
 
E.isogeny_class()
 

Elliptic curves in class 33150j

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
33150.k1 33150j1 \([1, 1, 0, -44225, -1300875]\) \(612241204436497/308834353152\) \(4825536768000000\) \([2]\) \(229376\) \(1.7020\) \(\Gamma_0(N)\)-optimal
33150.k2 33150j2 \([1, 1, 0, 163775, -9828875]\) \(31091549545392623/20700995942016\) \(-323453061594000000\) \([2]\) \(458752\) \(2.0486\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 33150.2.a.j

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

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

Isogeny graph

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

The vertices are labelled with Cremona labels.