↑

Properties

Label 29575.p
Number of curves $2$
Conductor $29575$
CM no
Rank $1$
Graph

Related objects

Downloads

Learn more

Show commands: SageMath
E = EllipticCurve("p1")
 
E.isogeny_class()
 

Elliptic curves in class 29575.p

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
29575.p1 29575v2 \([1, 0, 1, -1755576, 253349423]\) \(63473450669/33787663\) \(318528507533919921875\) \([2]\) \(1128960\) \(2.6256\)  
29575.p2 29575v1 \([1, 0, 1, -1016201, -391385577]\) \(12310389629/107653\) \(1014883729056640625\) \([2]\) \(564480\) \(2.2790\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 29575.p have rank \(1\).

Complex multiplication

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

Modular form 29575.2.a.p

sage: E.q_eigenform(10)
 
\(q + q^{2} - 2 q^{3} - q^{4} - 2 q^{6} + q^{7} - 3 q^{8} + q^{9} - 6 q^{11} + 2 q^{12} + q^{14} - q^{16} - 2 q^{17} + q^{18} + O(q^{20})\) Copy content 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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.