Properties

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

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Show commands: SageMath
E = EllipticCurve("gl1")
 
E.isogeny_class()
 

Elliptic curves in class 193600gl

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
193600.bx2 193600gl1 \([0, 1, 0, 4767, 49663]\) \(24167/16\) \(-7929856000000\) \([]\) \(331776\) \(1.1639\) \(\Gamma_0(N)\)-optimal
193600.bx1 193600gl2 \([0, 1, 0, -83233, 9465663]\) \(-128667913/4096\) \(-2030043136000000\) \([]\) \(995328\) \(1.7132\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 193600.2.a.gl

sage: E.q_eigenform(10)
 
\(q - 2 q^{3} + 2 q^{7} + q^{9} - 5 q^{13} + 3 q^{17} + 2 q^{19} + O(q^{20})\) 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.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.