Properties

Label 51984.br
Number of curves $4$
Conductor $51984$
CM no
Rank $0$
Graph

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

Elliptic curves in class 51984.br

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
51984.br1 51984cl3 \([0, 0, 0, -22250235, 40396752682]\) \(8671983378625/82308\) \(11562483630779154432\) \([2]\) \(2488320\) \(2.8202\)  
51984.br2 51984cl4 \([0, 0, 0, -21730395, 42374120074]\) \(-8078253774625/846825858\) \(-118960612835271330373632\) \([2]\) \(4976640\) \(3.1667\)  
51984.br3 51984cl1 \([0, 0, 0, -416955, -7915286]\) \(57066625/32832\) \(4612181836100272128\) \([2]\) \(829440\) \(2.2709\) \(\Gamma_0(N)\)-optimal
51984.br4 51984cl2 \([0, 0, 0, 1662405, -63226262]\) \(3616805375/2105352\) \(-295756160239929950208\) \([2]\) \(1658880\) \(2.6174\)  

Rank

sage: E.rank()
 

The elliptic curves in class 51984.br have rank \(0\).

Complex multiplication

The elliptic curves in class 51984.br do not have complex multiplication.

Modular form 51984.2.a.br

sage: E.q_eigenform(10)
 
\(q + 4 q^{7} + 4 q^{13} - 6 q^{17} + O(q^{20})\) 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.

\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.