Properties

Label 29645.g
Number of curves $3$
Conductor $29645$
CM no
Rank $0$
Graph

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

Elliptic curves in class 29645.g

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
29645.g1 29645o3 \([0, -1, 1, -778675, -276403667]\) \(-250523582464/13671875\) \(-2849524727779296875\) \([]\) \(388800\) \(2.2994\)  
29645.g2 29645o1 \([0, -1, 1, -7905, 302763]\) \(-262144/35\) \(-7294783303115\) \([]\) \(43200\) \(1.2008\) \(\Gamma_0(N)\)-optimal
29645.g3 29645o2 \([0, -1, 1, 51385, -782244]\) \(71991296/42875\) \(-8936109546315875\) \([]\) \(129600\) \(1.7501\)  

Rank

sage: E.rank()
 

The elliptic curves in class 29645.g have rank \(0\).

Complex multiplication

The elliptic curves in class 29645.g do not have complex multiplication.

Modular form 29645.2.a.g

sage: E.q_eigenform(10)
 
\(q - q^{3} - 2q^{4} + q^{5} - 2q^{9} + 2q^{12} + 5q^{13} - q^{15} + 4q^{16} + 3q^{17} + 2q^{19} + O(q^{20})\)  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.

\(\left(\begin{array}{rrr} 1 & 9 & 3 \\ 9 & 1 & 3 \\ 3 & 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.