Properties

Label 15600.q
Number of curves $2$
Conductor $15600$
CM no
Rank $0$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("q1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 15600.q

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
15600.q1 15600h1 \([0, -1, 0, -16283, -745938]\) \(1909913257984/129730653\) \(32432663250000\) \([2]\) \(38400\) \(1.3411\) \(\Gamma_0(N)\)-optimal
15600.q2 15600h2 \([0, -1, 0, 14092, -3236688]\) \(77366117936/1172914587\) \(-4691658348000000\) \([2]\) \(76800\) \(1.6877\)  

Rank

sage: E.rank()
 

The elliptic curves in class 15600.q have rank \(0\).

Complex multiplication

The elliptic curves in class 15600.q do not have complex multiplication.

Modular form 15600.2.a.q

sage: E.q_eigenform(10)
 
\(q - q^{3} + q^{9} + 2q^{11} + q^{13} - 2q^{17} - 8q^{19} + O(q^{20})\)  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 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.