Properties

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

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Show commands for: SageMath
sage: E = EllipticCurve("193600.bb1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 193600.bb

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
193600.bb1 193600l2 [0, 1, 0, -13713, 606703] [2] 327680  
193600.bb2 193600l1 [0, 1, 0, -1613, -10397] [2] 163840 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 193600.bb have rank \(2\).

Modular form 193600.2.a.bb

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

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.