Properties

Label 119658bw
Number of curves $4$
Conductor $119658$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("bw1")
 
E.isogeny_class()
 

Elliptic curves in class 119658bw

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
119658.bu4 119658bw1 \([1, 0, 1, -1116540, -391720262]\) \(1308451928740468777/194033737531392\) \(22827875186830737408\) \([2]\) \(4423680\) \(2.4391\) \(\Gamma_0(N)\)-optimal
119658.bu2 119658bw2 \([1, 0, 1, -17172860, -27392027974]\) \(4760617885089919932457/133756441657344\) \(15736311604544864256\) \([2, 2]\) \(8847360\) \(2.7857\)  
119658.bu3 119658bw3 \([1, 0, 1, -16482940, -29693601094]\) \(-4209586785160189454377/801182513521564416\) \(-94258321533298531977984\) \([2]\) \(17694720\) \(3.1323\)  
119658.bu1 119658bw4 \([1, 0, 1, -274763900, -1753045923142]\) \(19499096390516434897995817/15393430272\) \(1811021678070528\) \([2]\) \(17694720\) \(3.1323\)  

Rank

sage: E.rank()
 

The elliptic curves in class 119658bw have rank \(1\).

Complex multiplication

The elliptic curves in class 119658bw do not have complex multiplication.

Modular form 119658.2.a.bw

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{3} + q^{4} + 2 q^{5} - q^{6} - q^{8} + q^{9} - 2 q^{10} + q^{11} + q^{12} - 6 q^{13} + 2 q^{15} + q^{16} + 2 q^{17} - q^{18} + O(q^{20})\) Copy content 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.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.