Properties

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

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Show commands: SageMath
E = EllipticCurve("gd1")
 
E.isogeny_class()
 

Elliptic curves in class 193600gd

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
193600.s2 193600gd1 \([0, 1, 0, 15327, -235457]\) \(34295/22\) \(-255422247731200\) \([]\) \(829440\) \(1.4534\) \(\Gamma_0(N)\)-optimal
193600.s1 193600gd2 \([0, 1, 0, -178273, 33489663]\) \(-53969305/10648\) \(-123624367901900800\) \([]\) \(2488320\) \(2.0027\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 193600.2.a.gd

sage: E.q_eigenform(10)
 
\(q - 2 q^{3} - 4 q^{7} + q^{9} - 5 q^{13} - 7 q^{19} + O(q^{20})\) 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.