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Properties

Label 150590o
Number of curves $2$
Conductor $150590$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("o1")
 
E.isogeny_class()
 

Elliptic curves in class 150590o

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
150590.c2 150590o1 \([1, 1, 0, 13662, -2475308]\) \(109902239/1100000\) \(-2822299049900000\) \([]\) \(1033200\) \(1.6458\) \(\Gamma_0(N)\)-optimal
150590.c1 150590o2 \([1, 1, 0, -8131888, -8928943978]\) \(-23178622194826561/1610510\) \(-4132128038958590\) \([]\) \(5166000\) \(2.4505\)  

Rank

sage: E.rank()
 

The elliptic curves in class 150590o have rank \(0\).

Complex multiplication

The elliptic curves in class 150590o do not have complex multiplication.

Modular form 150590.2.a.o

sage: E.q_eigenform(10)
 
\(q - q^{2} - q^{3} + q^{4} - q^{5} + q^{6} + 3 q^{7} - q^{8} - 2 q^{9} + q^{10} + q^{11} - q^{12} + 6 q^{13} - 3 q^{14} + q^{15} + q^{16} + 7 q^{17} + 2 q^{18} - 5 q^{19} + O(q^{20})\) 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.