Properties

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

Related objects

Downloads

Learn more

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

Elliptic curves in class 189618.o

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
189618.o1 189618y2 \([1, 0, 1, -30762, 2073970]\) \(666940371553/37026\) \(178717430034\) \([2]\) \(414720\) \(1.2245\)  
189618.o2 189618y1 \([1, 0, 1, -2032, 28394]\) \(192100033/38148\) \(184133109732\) \([2]\) \(207360\) \(0.87789\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 189618.2.a.o

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.