Properties

Label 193600.w
Number of curves 2
Conductor 193600
CM no
Rank 0
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("193600.w1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 193600.w

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
193600.w1 193600j2 [0, 1, 0, -1068833, -342965537] [2] 6144000  
193600.w2 193600j1 [0, 1, 0, 141167, -31995537] [2] 3072000 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 193600.w have rank \(0\).

Modular form 193600.2.a.w

sage: E.q_eigenform(10)
 
\( q - 2q^{3} - 4q^{7} + q^{9} + 6q^{13} + 2q^{17} - 4q^{19} + O(q^{20}) \)

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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.