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Properties

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

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Show commands: SageMath
E = EllipticCurve("cg1")
 
E.isogeny_class()
 

Elliptic curves in class 33150cg

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
33150.cl3 33150cg1 \([1, 0, 0, -14688, 682992]\) \(22428153804601/35802000\) \(559406250000\) \([4]\) \(129024\) \(1.1518\) \(\Gamma_0(N)\)-optimal
33150.cl2 33150cg2 \([1, 0, 0, -19188, 228492]\) \(50002789171321/27473062500\) \(429266601562500\) \([2, 2]\) \(258048\) \(1.4984\)  
33150.cl4 33150cg3 \([1, 0, 0, 74562, 1822242]\) \(2933972022568679/1789082460750\) \(-27954413449218750\) \([2]\) \(516096\) \(1.8450\)  
33150.cl1 33150cg4 \([1, 0, 0, -184938, -30435258]\) \(44769506062996441/323730468750\) \(5058288574218750\) \([2]\) \(516096\) \(1.8450\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 33150.2.a.cg

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

\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.