Properties

Label 189630o
Number of curves $2$
Conductor $189630$
CM no
Rank $1$
Graph

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

Elliptic curves in class 189630o

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
189630.et2 189630o1 \([1, -1, 1, -16547, 554019]\) \(5841725401/1857600\) \(159319146369600\) \([2]\) \(829440\) \(1.4290\) \(\Gamma_0(N)\)-optimal
189630.et1 189630o2 \([1, -1, 1, -104747, -12605421]\) \(1481933914201/53916840\) \(4624238223377640\) \([2]\) \(1658880\) \(1.7756\)  

Rank

sage: E.rank()
 

The elliptic curves in class 189630o have rank \(1\).

Complex multiplication

The elliptic curves in class 189630o do not have complex multiplication.

Modular form 189630.2.a.o

sage: E.q_eigenform(10)
 
\(q + q^{2} + q^{4} + q^{5} + q^{8} + q^{10} + 2q^{11} + 2q^{13} + q^{16} - 4q^{17} + 6q^{19} + O(q^{20})\)  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.