Properties

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

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Show commands for: SageMath
sage: E = EllipticCurve("b1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 189618.b

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
189618.b1 189618bj2 \([1, 1, 0, -187270086, 703054931220]\) \(150476552140919246594353/42832838728685592576\) \(206745931471168176416169984\) \([2]\) \(70087680\) \(3.7561\)  
189618.b2 189618bj1 \([1, 1, 0, -69592006, -214810557164]\) \(7722211175253055152433/340131399900069888\) \(1641749302220256436027392\) \([2]\) \(35043840\) \(3.4096\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 189618.2.a.b

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