Properties

Label 159450.d
Number of curves $2$
Conductor $159450$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("d1")
 
E.isogeny_class()
 

Elliptic curves in class 159450.d

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
159450.d1 159450t1 \([1, 1, 0, -28609650, 58891576500]\) \(-165745346665991446425889/10662541623558144\) \(-166602212868096000000\) \([]\) \(13829760\) \(2.9377\) \(\Gamma_0(N)\)-optimal
159450.d2 159450t2 \([1, 1, 0, 196741350, -1692770188500]\) \(53900230693869615719525471/110424476261224735356024\) \(-1725382441581636489937875000\) \([]\) \(96808320\) \(3.9107\)  

Rank

sage: E.rank()
 

The elliptic curves in class 159450.d have rank \(0\).

Complex multiplication

The elliptic curves in class 159450.d do not have complex multiplication.

Modular form 159450.2.a.d

sage: E.q_eigenform(10)
 
\(q - q^{2} - q^{3} + q^{4} + q^{6} - q^{7} - q^{8} + q^{9} - 2 q^{11} - q^{12} + q^{14} + q^{16} + 3 q^{17} - q^{18} - 8 q^{19} + O(q^{20})\) 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.

\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.