Properties

Label 33462.t
Number of curves 4
Conductor 33462
CM no
Rank 0
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("33462.t1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 33462.t

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
33462.t1 33462q3 [1, -1, 0, -122472, 16464384] [2] 207360  
33462.t2 33462q4 [1, -1, 0, -61632, 32781672] [2] 414720  
33462.t3 33462q1 [1, -1, 0, -8397, -277263] [2] 69120 \(\Gamma_0(N)\)-optimal
33462.t4 33462q2 [1, -1, 0, 6813, -1180737] [2] 138240  

Rank

sage: E.rank()
 

The elliptic curves in class 33462.t have rank \(0\).

Modular form 33462.2.a.t

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

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.

\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.