Properties

Label 47040.bk
Number of curves $4$
Conductor $47040$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("bk1")
 
E.isogeny_class()
 

Elliptic curves in class 47040.bk

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
47040.bk1 47040m4 \([0, -1, 0, -1171361, -487569375]\) \(5763259856089/5670\) \(174868353515520\) \([2]\) \(589824\) \(2.0263\)  
47040.bk2 47040m2 \([0, -1, 0, -73761, -7479135]\) \(1439069689/44100\) \(1360087194009600\) \([2, 2]\) \(294912\) \(1.6797\)  
47040.bk3 47040m1 \([0, -1, 0, -11041, 285601]\) \(4826809/1680\) \(51812845486080\) \([2]\) \(147456\) \(1.3331\) \(\Gamma_0(N)\)-optimal
47040.bk4 47040m3 \([0, -1, 0, 20319, -25335519]\) \(30080231/9003750\) \(-277684468776960000\) \([2]\) \(589824\) \(2.0263\)  

Rank

sage: E.rank()
 

The elliptic curves in class 47040.bk have rank \(0\).

Complex multiplication

The elliptic curves in class 47040.bk do not have complex multiplication.

Modular form 47040.2.a.bk

sage: E.q_eigenform(10)
 
\(q - q^{3} - q^{5} + q^{9} + 4 q^{11} - 2 q^{13} + q^{15} + 6 q^{17} + O(q^{20})\) 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 LMFDB 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 LMFDB labels.