Properties

Label 29624.g
Number of curves $4$
Conductor $29624$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("g1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 29624.g

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
29624.g1 29624n4 [0, 0, 0, -158171, -24212330] [2] 101376  
29624.g2 29624n3 [0, 0, 0, -31211, 1679046] [2] 101376  
29624.g3 29624n2 [0, 0, 0, -10051, -365010] [2, 2] 50688  
29624.g4 29624n1 [0, 0, 0, 529, -24334] [2] 25344 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 29624.g have rank \(0\).

Complex multiplication

The elliptic curves in class 29624.g do not have complex multiplication.

Modular form 29624.2.a.g

sage: E.q_eigenform(10)
 
\( q - 2q^{5} + q^{7} - 3q^{9} + 4q^{11} + 2q^{13} + 6q^{17} - 8q^{19} + O(q^{20}) \)

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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.