Properties

Label 3234.d
Number of curves 4
Conductor 3234
CM no
Rank 0
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("3234.d1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 3234.d

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
3234.d1 3234b3 [1, 1, 0, -3945, 93381] [2] 4320  
3234.d2 3234b4 [1, 1, 0, -1985, 188637] [2] 8640  
3234.d3 3234b1 [1, 1, 0, -270, -1728] [2] 1440 \(\Gamma_0(N)\)-optimal
3234.d4 3234b2 [1, 1, 0, 220, -6726] [2] 2880  

Rank

sage: E.rank()
 

The elliptic curves in class 3234.d have rank \(0\).

Modular form 3234.2.a.d

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

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.