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Properties

Label 158950ct
Number of curves $2$
Conductor $158950$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("ct1")
 
E.isogeny_class()
 

Elliptic curves in class 158950ct

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
158950.r2 158950ct1 \([1, 1, 0, 72100, -30050000]\) \(109902239/1100000\) \(-414864467187500000\) \([]\) \(2112000\) \(2.0617\) \(\Gamma_0(N)\)-optimal
158950.r1 158950ct2 \([1, 1, 0, -42916650, -108232733750]\) \(-23178622194826561/1610510\) \(-607403066409218750\) \([]\) \(10560000\) \(2.8664\)  

Rank

sage: E.rank()
 

The elliptic curves in class 158950ct have rank \(1\).

Complex multiplication

The elliptic curves in class 158950ct do not have complex multiplication.

Modular form 158950.2.a.ct

sage: E.q_eigenform(10)
 
\(q - q^{2} - q^{3} + q^{4} + q^{6} + 3 q^{7} - q^{8} - 2 q^{9} - q^{11} - q^{12} + 6 q^{13} - 3 q^{14} + q^{16} + 2 q^{18} + 5 q^{19} + O(q^{20})\) 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 Cremona numbering.

\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.