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Properties

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

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

Elliptic curves in class 33150l

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
33150.a2 33150l1 \([1, 1, 0, -166285, 74540125]\) \(-4067963094761079821/16883900373270528\) \(-2110487546658816000\) \([2]\) \(746496\) \(2.2013\) \(\Gamma_0(N)\)-optimal
33150.a1 33150l2 \([1, 1, 0, -3865485, 2919224925]\) \(51100582610617794208781/87991789583872512\) \(10998973697984064000\) \([2]\) \(1492992\) \(2.5479\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 33150.2.a.l

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