Properties

Label 29400.j
Number of curves $4$
Conductor $29400$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("j1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 29400.j

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
29400.j1 29400q4 [0, -1, 0, -559008, -160505988] [2] 294912  
29400.j2 29400q3 [0, -1, 0, -412008, 101154012] [2] 294912  
29400.j3 29400q2 [0, -1, 0, -44508, -1010988] [2, 2] 147456  
29400.j4 29400q1 [0, -1, 0, 10617, -128988] [2] 73728 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 29400.2.a.j

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