Properties

Label 195195.br
Number of curves $4$
Conductor $195195$
CM no
Rank $0$
Graph

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

Elliptic curves in class 195195.br

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
195195.br1 195195bw3 \([1, 1, 0, -148892, 22051359]\) \(75627935783569/396165\) \(1912212787485\) \([2]\) \(884736\) \(1.5526\)  
195195.br2 195195bw2 \([1, 1, 0, -9467, 328944]\) \(19443408769/1334025\) \(6439083876225\) \([2, 2]\) \(442368\) \(1.2060\)  
195195.br3 195195bw1 \([1, 1, 0, -1862, -25449]\) \(148035889/31185\) \(150524038665\) \([2]\) \(221184\) \(0.85947\) \(\Gamma_0(N)\)-optimal
195195.br4 195195bw4 \([1, 1, 0, 8278, 1439781]\) \(12994449551/192163125\) \(-927534701218125\) \([2]\) \(884736\) \(1.5526\)  

Rank

sage: E.rank()
 

The elliptic curves in class 195195.br have rank \(0\).

Complex multiplication

The elliptic curves in class 195195.br do not have complex multiplication.

Modular form 195195.2.a.br

sage: E.q_eigenform(10)
 
\(q + q^{2} - q^{3} - q^{4} + q^{5} - q^{6} + q^{7} - 3 q^{8} + q^{9} + q^{10} + q^{11} + q^{12} + q^{14} - q^{15} - q^{16} + 6 q^{17} + q^{18} - 4 q^{19} + O(q^{20})\) 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.

\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.