Properties

Label 119952.bp
Number of curves $4$
Conductor $119952$
CM no
Rank $0$
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Show commands: SageMath
sage: E = EllipticCurve("bp1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 119952.bp

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
119952.bp1 119952bk4 \([0, 0, 0, -79983034131, -8706526495316174]\) \(322159999717985454060440834/4250799\) \(746648660747630592\) \([2]\) \(106168320\) \(4.4133\)  
119952.bp2 119952bk3 \([0, 0, 0, -5011799331, -135304372441406]\) \(79260902459030376659234/842751810121431609\) \(148028526018239955088831875072\) \([2]\) \(106168320\) \(4.4133\)  
119952.bp3 119952bk2 \([0, 0, 0, -4998939771, -136039468613510]\) \(157304700372188331121828/18069292138401\) \(1586926690228683686421504\) \([2, 2]\) \(53084160\) \(4.0667\)  
119952.bp4 119952bk1 \([0, 0, 0, -311630151, -2137094698970]\) \(-152435594466395827792/1646846627220711\) \(-36158373657255268692999936\) \([2]\) \(26542080\) \(3.7201\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 119952.bp have rank \(0\).

Complex multiplication

The elliptic curves in class 119952.bp do not have complex multiplication.

Modular form 119952.2.a.bp

sage: E.q_eigenform(10)
 
\(q - 2q^{5} - 2q^{13} + q^{17} + O(q^{20})\)  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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.