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Properties

Label 33635.j
Number of curves $3$
Conductor $33635$
CM no
Rank $1$
Graph

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

Elliptic curves in class 33635.j

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
33635.j1 33635b3 \([0, -1, 1, -126211, 18095692]\) \(-250523582464/13671875\) \(-12133839388671875\) \([]\) \(181440\) \(1.8445\)  
33635.j2 33635b1 \([0, -1, 1, -1281, -19158]\) \(-262144/35\) \(-31062628835\) \([]\) \(20160\) \(0.74584\) \(\Gamma_0(N)\)-optimal
33635.j3 33635b2 \([0, -1, 1, 8329, 47151]\) \(71991296/42875\) \(-38051720322875\) \([]\) \(60480\) \(1.2951\)  

Rank

sage: E.rank()
 

The elliptic curves in class 33635.j have rank \(1\).

Complex multiplication

The elliptic curves in class 33635.j do not have complex multiplication.

Modular form 33635.2.a.j

sage: E.q_eigenform(10)
 
\(q - q^{3} - 2 q^{4} - q^{5} + q^{7} - 2 q^{9} + 3 q^{11} + 2 q^{12} - 5 q^{13} + q^{15} + 4 q^{16} - 3 q^{17} + 2 q^{19} + O(q^{20})\) 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 LMFDB numbering.

\(\left(\begin{array}{rrr} 1 & 9 & 3 \\ 9 & 1 & 3 \\ 3 & 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.