Properties

Label 11025.bd
Number of curves 4
Conductor 11025
CM no
Rank 1
Graph

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Show commands for: SageMath

sage: E = EllipticCurve("11025.bd1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 11025.bd

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
11025.bd1 11025x3 [1, -1, 0, -1240542, -531472509] [2] 147456  
11025.bd2 11025x2 [1, -1, 0, -82917, -7068384] [2, 2] 73728  
11025.bd3 11025x1 [1, -1, 0, -27792, 1696491] [2] 36864 \(\Gamma_0(N)\)-optimal
11025.bd4 11025x4 [1, -1, 0, 192708, -44277759] [2] 147456  

Rank

sage: E.rank()
 

The elliptic curves in class 11025.bd have rank \(1\).

Modular form 11025.2.a.bd

sage: E.q_eigenform(10)
 
\( q + q^{2} - q^{4} - 3q^{8} - 6q^{13} - q^{16} - 2q^{17} + 8q^{19} + O(q^{20}) \)

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 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.