Properties

Label 189618bb
Number of curves $2$
Conductor $189618$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("bb1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 189618bb

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
189618.q1 189618bb1 \([1, 0, 1, -33466, 2353496]\) \(858729462625/38148\) \(184133109732\) \([2]\) \(552960\) \(1.2389\) \(\Gamma_0(N)\)-optimal
189618.q2 189618bb2 \([1, 0, 1, -31776, 2602264]\) \(-735091890625/181908738\) \(-878038733757042\) \([2]\) \(1105920\) \(1.5855\)  

Rank

sage: E.rank()
 

The elliptic curves in class 189618bb have rank \(0\).

Complex multiplication

The elliptic curves in class 189618bb do not have complex multiplication.

Modular form 189618.2.a.bb

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

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

Isogeny graph

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

The vertices are labelled with Cremona labels.