Properties

Label 283920.bp
Number of curves $8$
Conductor $283920$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("bp1")
 
E.isogeny_class()
 

Elliptic curves in class 283920.bp

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
283920.bp1 283920bp7 \([0, -1, 0, -108674990376, 13789346035420656]\) \(7179471593960193209684686321/49441793310\) \(977494396620176547840\) \([2]\) \(445906944\) \(4.5634\)  
283920.bp2 283920bp6 \([0, -1, 0, -6792191176, 215459944884976]\) \(1752803993935029634719121/4599740941532100\) \(90939682710550995226214400\) \([2, 2]\) \(222953472\) \(4.2168\)  
283920.bp3 283920bp8 \([0, -1, 0, -6708718696, 221013602702320]\) \(-1688971789881664420008241/89901485966373558750\) \(-1777407187254745459656821760000\) \([2]\) \(445906944\) \(4.5634\)  
283920.bp4 283920bp4 \([0, -1, 0, -1342279176, 18897685672176]\) \(13527956825588849127121/25701087819771000\) \(508126175224877222866944000\) \([2]\) \(148635648\) \(4.0141\)  
283920.bp5 283920bp3 \([0, -1, 0, -429733256, 3279608202480]\) \(443915739051786565201/21894701746029840\) \(432871601930455228336373760\) \([2]\) \(111476736\) \(3.8703\)  
283920.bp6 283920bp2 \([0, -1, 0, -111959176, 80679464176]\) \(7850236389974007121/4400862921000000\) \(87007742995861868544000000\) \([2, 2]\) \(74317824\) \(3.6675\)  
283920.bp7 283920bp1 \([0, -1, 0, -69560456, -222081315600]\) \(1882742462388824401/11650189824000\) \(230331355521808859136000\) \([2]\) \(37158912\) \(3.3209\) \(\Gamma_0(N)\)-optimal
283920.bp8 283920bp5 \([0, -1, 0, 439981304, 639684782320]\) \(476437916651992691759/284661685546875000\) \(-5627935071243576000000000000\) \([2]\) \(148635648\) \(4.0141\)  

Rank

sage: E.rank()
 

The elliptic curves in class 283920.bp have rank \(1\).

Complex multiplication

The elliptic curves in class 283920.bp do not have complex multiplication.

Modular form 283920.2.a.bp

sage: E.q_eigenform(10)
 
\(q - q^{3} - q^{5} + q^{7} + q^{9} + q^{15} + 6 q^{17} - 4 q^{19} + O(q^{20})\) 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.

\(\left(\begin{array}{rrrrrrrr} 1 & 2 & 4 & 3 & 4 & 6 & 12 & 12 \\ 2 & 1 & 2 & 6 & 2 & 3 & 6 & 6 \\ 4 & 2 & 1 & 12 & 4 & 6 & 12 & 3 \\ 3 & 6 & 12 & 1 & 12 & 2 & 4 & 4 \\ 4 & 2 & 4 & 12 & 1 & 6 & 3 & 12 \\ 6 & 3 & 6 & 2 & 6 & 1 & 2 & 2 \\ 12 & 6 & 12 & 4 & 3 & 2 & 1 & 4 \\ 12 & 6 & 3 & 4 & 12 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.