Properties

Label 29040ce
Number of curves $4$
Conductor $29040$
CM no
Rank $1$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("ce1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 29040ce

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
29040.v4 29040ce1 \([0, -1, 0, 26459, -6095384]\) \(72268906496/606436875\) \(-17189438667390000\) \([2]\) \(138240\) \(1.7966\) \(\Gamma_0(N)\)-optimal
29040.v3 29040ce2 \([0, -1, 0, -381916, -83523284]\) \(13584145739344/1195803675\) \(542320423497388800\) \([2]\) \(276480\) \(2.1432\)  
29040.v2 29040ce3 \([0, -1, 0, -1890181, -1000400300]\) \(-26348629355659264/24169921875\) \(-685095855468750000\) \([2]\) \(414720\) \(2.3459\)  
29040.v1 29040ce4 \([0, -1, 0, -30249556, -64026275300]\) \(6749703004355978704/5671875\) \(2572306572000000\) \([2]\) \(829440\) \(2.6925\)  

Rank

sage: E.rank()
 

The elliptic curves in class 29040ce have rank \(1\).

Complex multiplication

The elliptic curves in class 29040ce do not have complex multiplication.

Modular form 29040.2.a.ce

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

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

Isogeny graph

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

The vertices are labelled with Cremona labels.