Properties

Label 29575h
Number of curves $3$
Conductor $29575$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("h1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 29575h

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
29575.k2 29575h1 \([0, -1, 1, -5633, 182418]\) \(-262144/35\) \(-2639661171875\) \([]\) \(32832\) \(1.1160\) \(\Gamma_0(N)\)-optimal
29575.k3 29575h2 \([0, -1, 1, 36617, -472457]\) \(71991296/42875\) \(-3233584935546875\) \([]\) \(98496\) \(1.6653\)  
29575.k1 29575h3 \([0, -1, 1, -554883, -166240332]\) \(-250523582464/13671875\) \(-1031117645263671875\) \([]\) \(295488\) \(2.2147\)  

Rank

sage: E.rank()
 

The elliptic curves in class 29575h have rank \(0\).

Complex multiplication

The elliptic curves in class 29575h do not have complex multiplication.

Modular form 29575.2.a.h

sage: E.q_eigenform(10)
 
\(q - q^{3} - 2q^{4} + q^{7} - 2q^{9} + 3q^{11} + 2q^{12} + 4q^{16} - 3q^{17} - 2q^{19} + O(q^{20})\)  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 Cremona numbering.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.