Properties

Label 133584.dd
Number of curves 2
Conductor 133584
CM no
Rank 0
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("133584.dd1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 133584.dd

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
133584.dd1 133584v2 [0, 1, 0, -2396808, -1417918284] [2] 2457600  
133584.dd2 133584v1 [0, 1, 0, -44568, -52678188] [2] 1228800 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 133584.dd have rank \(0\).

Modular form 133584.2.a.dd

sage: E.q_eigenform(10)
 
\( q + q^{3} - 2q^{7} + q^{9} - 2q^{13} + 2q^{19} + O(q^{20}) \)

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.

\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.