Properties

Label 111600.br
Number of curves $2$
Conductor $111600$
CM no
Rank $0$
Graph

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

Elliptic curves in class 111600.br

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
111600.br1 111600fe2 \([0, 0, 0, -7245075, -2630024750]\) \(901456690969801/457629750000\) \(21351173616000000000000\) \([2]\) \(8847360\) \(2.9771\)  
111600.br2 111600fe1 \([0, 0, 0, 1682925, -317672750]\) \(11298232190519/7472736000\) \(-348647970816000000000\) \([2]\) \(4423680\) \(2.6305\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 111600.br have rank \(0\).

Complex multiplication

The elliptic curves in class 111600.br do not have complex multiplication.

Modular form 111600.2.a.br

sage: E.q_eigenform(10)
 
\(q - 2 q^{7} - 4 q^{11} + 4 q^{13} + 2 q^{17} + 8 q^{19} + O(q^{20})\) 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.