Properties

Label 215985bp
Number of curves 4
Conductor 215985
CM no
Rank 0
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("215985.bu1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 215985bp

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
215985.bu4 215985bp1 [1, 0, 1, 1691, -44893] [2] 368640 \(\Gamma_0(N)\)-optimal
215985.bu3 215985bp2 [1, 0, 1, -13434, -492593] [2, 2] 737280  
215985.bu2 215985bp3 [1, 0, 1, -64859, 5904677] [2] 1474560  
215985.bu1 215985bp4 [1, 0, 1, -204009, -35482163] [2] 1474560  

Rank

sage: E.rank()
 

The elliptic curves in class 215985bp have rank \(0\).

Modular form 215985.2.a.bu

sage: E.q_eigenform(10)
 
\( q + q^{2} + q^{3} - q^{4} - q^{5} + q^{6} - q^{7} - 3q^{8} + q^{9} - q^{10} - q^{12} + 6q^{13} - q^{14} - q^{15} - q^{16} + q^{17} + q^{18} - 4q^{19} + O(q^{20}) \)

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.