Properties

Label 29400ct
Number of curves $2$
Conductor $29400$
CM no
Rank $1$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("ct1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 29400ct

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
29400.m1 29400ct1 [0, -1, 0, -3450008, 2467266012] [2] 645120 \(\Gamma_0(N)\)-optimal
29400.m2 29400ct2 [0, -1, 0, -3107008, 2976964012] [2] 1290240  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 29400.2.a.ct

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

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

Isogeny graph

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

The vertices are labelled with Cremona labels.