Properties

Label 193600fw
Number of curves $2$
Conductor $193600$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("fw1")
 
E.isogeny_class()
 

Elliptic curves in class 193600fw

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
193600.r2 193600fw1 \([0, 1, 0, 5647, 258223]\) \(5488/11\) \(-39909726208000\) \([2]\) \(614400\) \(1.2943\) \(\Gamma_0(N)\)-optimal
193600.r1 193600fw2 \([0, 1, 0, -42753, 2726623]\) \(595508/121\) \(1756027953152000\) \([2]\) \(1228800\) \(1.6408\)  

Rank

sage: E.rank()
 

The elliptic curves in class 193600fw have rank \(1\).

Complex multiplication

The elliptic curves in class 193600fw do not have complex multiplication.

Modular form 193600.2.a.fw

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

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.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.