Properties

Label 193600m
Number of curves $2$
Conductor $193600$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("193600.bh1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 193600m

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
193600.bh2 193600m1 [0, 1, 0, -12833, -293537] [] 552960 \(\Gamma_0(N)\)-optimal
193600.bh1 193600m2 [0, 1, 0, -892833, -325013537] [] 1658880  

Rank

sage: E.rank()
 

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

Modular form 193600.2.a.bh

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

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 Cremona numbering.

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.