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Properties

Label 18150o
Number of curves $2$
Conductor $18150$
CM no
Rank $0$
Graph

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

Elliptic curves in class 18150o

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
18150.w2 18150o1 \([1, 1, 0, -21375, 253125]\) \(571305535801/314928000\) \(595410750000000\) \([]\) \(145152\) \(1.5256\) \(\Gamma_0(N)\)-optimal
18150.w1 18150o2 \([1, 1, 0, -1320750, 583672500]\) \(134766108430924201/283115520\) \(535265280000000\) \([]\) \(435456\) \(2.0749\)  

Rank

sage: E.rank()
 

The elliptic curves in class 18150o have rank \(0\).

Complex multiplication

The elliptic curves in class 18150o do not have complex multiplication.

Modular form 18150.2.a.o

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

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

Isogeny graph

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

The vertices are labelled with Cremona labels.