Properties

Label 189618bq
Number of curves $6$
Conductor $189618$
CM no
Rank $1$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("bq1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 189618bq

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
189618.l5 189618bq1 \([1, 1, 0, -47999, 3045957]\) \(2533811507137/625016832\) \(3016836869849088\) \([2]\) \(1179648\) \(1.6807\) \(\Gamma_0(N)\)-optimal
189618.l4 189618bq2 \([1, 1, 0, -264319, -49865915]\) \(423108074414017/23284318464\) \(112388957920901376\) \([2, 2]\) \(2359296\) \(2.0273\)  
189618.l6 189618bq3 \([1, 1, 0, 181841, -200578763]\) \(137763859017023/3683199928848\) \(-17778102565362886032\) \([2]\) \(4718592\) \(2.3738\)  
189618.l2 189618bq4 \([1, 1, 0, -4171599, -3281186475]\) \(1663303207415737537/5483698704\) \(26468766257755536\) \([2, 2]\) \(4718592\) \(2.3738\)  
189618.l3 189618bq5 \([1, 1, 0, -4114139, -3375892047]\) \(-1595514095015181697/95635786040388\) \(-461615672781819161892\) \([2]\) \(9437184\) \(2.7204\)  
189618.l1 189618bq6 \([1, 1, 0, -66745539, -209912851143]\) \(6812873765474836663297/74052\) \(357434860068\) \([2]\) \(9437184\) \(2.7204\)  

Rank

sage: E.rank()
 

The elliptic curves in class 189618bq have rank \(1\).

Complex multiplication

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

Modular form 189618.2.a.bq

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

\(\left(\begin{array}{rrrrrr} 1 & 2 & 4 & 4 & 8 & 8 \\ 2 & 1 & 2 & 2 & 4 & 4 \\ 4 & 2 & 1 & 4 & 8 & 8 \\ 4 & 2 & 4 & 1 & 2 & 2 \\ 8 & 4 & 8 & 2 & 1 & 4 \\ 8 & 4 & 8 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.