Properties

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

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Show commands: 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 j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
29624.g1 29624n4 \([0, 0, 0, -158171, -24212330]\) \(1443468546/7\) \(2122242504704\) \([2]\) \(101376\) \(1.5657\)  
29624.g2 29624n3 \([0, 0, 0, -31211, 1679046]\) \(11090466/2401\) \(727929179113472\) \([2]\) \(101376\) \(1.5657\)  
29624.g3 29624n2 \([0, 0, 0, -10051, -365010]\) \(740772/49\) \(7427848766464\) \([2, 2]\) \(50688\) \(1.2191\)  
29624.g4 29624n1 \([0, 0, 0, 529, -24334]\) \(432/7\) \(-265280313088\) \([2]\) \(25344\) \(0.87257\) \(\Gamma_0(N)\)-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)
 
\(q - 2q^{5} + q^{7} - 3q^{9} + 4q^{11} + 2q^{13} + 6q^{17} - 8q^{19} + O(q^{20})\)  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.