Properties

Label 29400.x
Number of curves $2$
Conductor $29400$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("x1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 29400.x

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
29400.x1 29400e2 [0, -1, 0, -157208, -21267588] [2] 258048  
29400.x2 29400e1 [0, -1, 0, 14292, -1716588] [2] 129024 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 29400.x have rank \(0\).

Complex multiplication

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

Modular form 29400.2.a.x

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

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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.