Properties

Label 14784br
Number of curves $6$
Conductor $14784$
CM no
Rank $0$
Graph

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

Elliptic curves in class 14784br

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
14784.w4 14784br1 \([0, -1, 0, -2177, -38367]\) \(4354703137/1617\) \(423886848\) \([2]\) \(10240\) \(0.62279\) \(\Gamma_0(N)\)-optimal
14784.w3 14784br2 \([0, -1, 0, -2497, -26015]\) \(6570725617/2614689\) \(685425033216\) \([2, 2]\) \(20480\) \(0.96936\)  
14784.w2 14784br3 \([0, -1, 0, -18177, 930465]\) \(2533811507137/58110129\) \(15233221656576\) \([2, 2]\) \(40960\) \(1.3159\)  
14784.w6 14784br4 \([0, -1, 0, 8063, -197087]\) \(221115865823/190238433\) \(-49869863780352\) \([2]\) \(40960\) \(1.3159\)  
14784.w1 14784br5 \([0, -1, 0, -289217, 59962977]\) \(10206027697760497/5557167\) \(1456777986048\) \([2]\) \(81920\) \(1.6625\)  
14784.w5 14784br6 \([0, -1, 0, 1983, 2861793]\) \(3288008303/13504609503\) \(-3540152353554432\) \([2]\) \(81920\) \(1.6625\)  

Rank

sage: E.rank()
 

The elliptic curves in class 14784br have rank \(0\).

Complex multiplication

The elliptic curves in class 14784br do not have complex multiplication.

Modular form 14784.2.a.br

sage: E.q_eigenform(10)
 
\(q - q^{3} + 2 q^{5} - q^{7} + q^{9} - q^{11} - 6 q^{13} - 2 q^{15} + 2 q^{17} + 4 q^{19} + O(q^{20})\) 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 Cremona numbering.

\(\left(\begin{array}{rrrrrr} 1 & 2 & 4 & 4 & 8 & 8 \\ 2 & 1 & 2 & 2 & 4 & 4 \\ 4 & 2 & 1 & 4 & 2 & 2 \\ 4 & 2 & 4 & 1 & 8 & 8 \\ 8 & 4 & 2 & 8 & 1 & 4 \\ 8 & 4 & 2 & 8 & 4 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.