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Properties

Label 33150.l
Number of curves $8$
Conductor $33150$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("l1")
 
E.isogeny_class()
 

Elliptic curves in class 33150.l

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
33150.l1 33150b8 \([1, 1, 0, -164775000150, -25744606186158000]\) \(31664865542564944883878115208137569/103216295812500\) \(1612754622070312500\) \([2]\) \(79626240\) \(4.5789\)  
33150.l2 33150b6 \([1, 1, 0, -10298437650, -402262678345500]\) \(7730680381889320597382223137569/441370202660156250000\) \(6896409416564941406250000\) \([2, 2]\) \(39813120\) \(4.2323\)  
33150.l3 33150b7 \([1, 1, 0, -10279763150, -403794192765000]\) \(-7688701694683937879808871873249/58423707246780395507812500\) \(-912870425730943679809570312500\) \([2]\) \(79626240\) \(4.5789\)  
33150.l4 33150b5 \([1, 1, 0, -2034331650, -35313074887500]\) \(59589391972023341137821784609/8834417507562311995200\) \(138037773555661124925000000\) \([2]\) \(26542080\) \(4.0296\)  
33150.l5 33150b3 \([1, 1, 0, -644819650, -6261614367500]\) \(1897660325010178513043539489/14258428094958372000000\) \(222787938983724562500000000\) \([2]\) \(19906560\) \(3.8858\)  
33150.l6 33150b2 \([1, 1, 0, -138931650, -443401087500]\) \(18980483520595353274840609/5549773448629762560000\) \(86715210134840040000000000\) \([2, 2]\) \(13271040\) \(3.6830\)  
33150.l7 33150b1 \([1, 1, 0, -52403650, 140576384500]\) \(1018563973439611524445729/42904970360310988800\) \(670390161879859200000000\) \([2]\) \(6635520\) \(3.3365\) \(\Gamma_0(N)\)-optimal
33150.l8 33150b4 \([1, 1, 0, 372020350, -2946554935500]\) \(364421318680576777174674911/450962301637624725000000\) \(-7046285963087886328125000000\) \([2]\) \(26542080\) \(4.0296\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 33150.2.a.l

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

\(\left(\begin{array}{rrrrrrrr} 1 & 2 & 4 & 3 & 4 & 6 & 12 & 12 \\ 2 & 1 & 2 & 6 & 2 & 3 & 6 & 6 \\ 4 & 2 & 1 & 12 & 4 & 6 & 12 & 3 \\ 3 & 6 & 12 & 1 & 12 & 2 & 4 & 4 \\ 4 & 2 & 4 & 12 & 1 & 6 & 3 & 12 \\ 6 & 3 & 6 & 2 & 6 & 1 & 2 & 2 \\ 12 & 6 & 12 & 4 & 3 & 2 & 1 & 4 \\ 12 & 6 & 3 & 4 & 12 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.