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Properties

Label 11970.br
Number of curves $2$
Conductor $11970$
CM no
Rank $1$
Graph

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

Elliptic curves in class 11970.br

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
11970.br1 11970bk2 \([1, -1, 1, -57809432, 169193331739]\) \(1085496729895194829662267/56604800000000\) \(1114152278400000000\) \([2]\) \(798720\) \(2.9348\)  
11970.br2 11970bk1 \([1, -1, 1, -3619352, 2634701851]\) \(266394205833287968827/1913399541760000\) \(37661443180462080000\) \([2]\) \(399360\) \(2.5882\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 11970.br have rank \(1\).

Complex multiplication

The elliptic curves in class 11970.br do not have complex multiplication.

Modular form 11970.2.a.br

sage: E.q_eigenform(10)
 
\(q + q^{2} + q^{4} + q^{5} - q^{7} + q^{8} + q^{10} - 2 q^{11} - q^{14} + q^{16} - 4 q^{17} - q^{19} + O(q^{20})\) 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 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.