Properties

Label 29400.bb
Number of curves $4$
Conductor $29400$
CM no
Rank $1$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("bb1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 29400.bb

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
29400.bb1 29400cp4 [0, -1, 0, -4577008, 3770470012] [2] 589824  
29400.bb2 29400cp3 [0, -1, 0, -804008, -202841988] [2] 589824  
29400.bb3 29400cp2 [0, -1, 0, -289508, 57495012] [2, 2] 294912  
29400.bb4 29400cp1 [0, -1, 0, 10617, 3472512] [2] 147456 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 29400.2.a.bb

sage: E.q_eigenform(10)
 
\(q - q^{3} + q^{9} - 2q^{13} + 6q^{17} + 4q^{19} + O(q^{20})\)  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 LMFDB numbering.

\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.