Properties

Label 29400br
Number of curves $6$
Conductor $29400$
CM no
Rank $1$
Graph

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

Elliptic curves in class 29400br

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
29400.eo5 29400br1 \([0, 1, 0, -18783, -4082562]\) \(-24918016/229635\) \(-6754082028750000\) \([4]\) \(147456\) \(1.7199\) \(\Gamma_0(N)\)-optimal
29400.eo4 29400br2 \([0, 1, 0, -514908, -142005312]\) \(32082281296/99225\) \(46694888100000000\) \([2, 2]\) \(294912\) \(2.0664\)  
29400.eo3 29400br3 \([0, 1, 0, -735408, -8823312]\) \(23366901604/13505625\) \(25422772410000000000\) \([2, 2]\) \(589824\) \(2.4130\)  
29400.eo1 29400br4 \([0, 1, 0, -8232408, -9094305312]\) \(32779037733124/315\) \(592950960000000\) \([2]\) \(589824\) \(2.4130\)  
29400.eo6 29400br5 \([0, 1, 0, 2939592, -67623312]\) \(746185003198/432360075\) \(-1627735374837600000000\) \([2]\) \(1179648\) \(2.7596\)  
29400.eo2 29400br6 \([0, 1, 0, -7938408, 8577152688]\) \(14695548366242/57421875\) \(216180037500000000000\) \([2]\) \(1179648\) \(2.7596\)  

Rank

sage: E.rank()
 

The elliptic curves in class 29400br have rank \(1\).

Complex multiplication

The elliptic curves in class 29400br do not have complex multiplication.

Modular form 29400.2.a.br

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