Properties

Label 19600.br
Number of curves $3$
Conductor $19600$
CM no
Rank $1$
Graph

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

Elliptic curves in class 19600.br

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
19600.br1 19600ci3 \([0, -1, 0, -2574133, -1662031363]\) \(-250523582464/13671875\) \(-102942875000000000000\) \([]\) \(497664\) \(2.5983\)  
19600.br2 19600ci1 \([0, -1, 0, -26133, 1812637]\) \(-262144/35\) \(-263533760000000\) \([]\) \(55296\) \(1.4997\) \(\Gamma_0(N)\)-optimal
19600.br3 19600ci2 \([0, -1, 0, 169867, -4655363]\) \(71991296/42875\) \(-322828856000000000\) \([]\) \(165888\) \(2.0490\)  

Rank

sage: E.rank()
 

The elliptic curves in class 19600.br have rank \(1\).

Complex multiplication

The elliptic curves in class 19600.br do not have complex multiplication.

Modular form 19600.2.a.br

sage: E.q_eigenform(10)
 
\(q - q^{3} - 2q^{9} + 3q^{11} + 5q^{13} + 3q^{17} + 2q^{19} + O(q^{20})\)  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.

\(\left(\begin{array}{rrr} 1 & 9 & 3 \\ 9 & 1 & 3 \\ 3 & 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.