Properties

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

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Show commands: SageMath
sage: E = EllipticCurve("br1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 15600.br

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
15600.br1 15600cg2 \([0, 1, 0, -53808, 4787028]\) \(-168256703745625/30371328\) \(-3110023987200\) \([]\) \(46656\) \(1.4009\)  
15600.br2 15600cg1 \([0, 1, 0, 192, 22068]\) \(7604375/2047032\) \(-209616076800\) \([]\) \(15552\) \(0.85155\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 15600.2.a.br

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

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.