Properties

Label 15600.bq
Number of curves $2$
Conductor $15600$
CM no
Rank $1$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("bq1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 15600.bq

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
15600.bq1 15600cy2 \([0, 1, 0, -145568, 19649268]\) \(666276475992821/58199166792\) \(29797973397504000\) \([2]\) \(147456\) \(1.9017\)  
15600.bq2 15600cy1 \([0, 1, 0, -142368, 20628468]\) \(623295446073461/5458752\) \(2794881024000\) \([2]\) \(73728\) \(1.5551\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 15600.bq have rank \(1\).

Complex multiplication

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

Modular form 15600.2.a.bq

sage: E.q_eigenform(10)
 
\(q + q^{3} - 4q^{7} + q^{9} - 2q^{11} + q^{13} + 4q^{17} - 2q^{19} + O(q^{20})\)  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.