Properties

Label 11025.p
Number of curves 8
Conductor 11025
CM no
Rank 1
Graph

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Show commands for: SageMath

sage: E = EllipticCurve("11025.p1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 11025.p

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
11025.p1 11025z7 [1, -1, 1, -23814230, -44724460728] [2] 294912  
11025.p2 11025z5 [1, -1, 1, -1488605, -698328228] [2, 2] 147456  
11025.p3 11025z8 [1, -1, 1, -1212980, -965133228] [2] 294912  
11025.p4 11025z4 [1, -1, 1, -882230, 319169022] [2] 73728  
11025.p5 11025z3 [1, -1, 1, -110480, -6509478] [2, 2] 73728  
11025.p6 11025z2 [1, -1, 1, -55355, 4956522] [2, 2] 36864  
11025.p7 11025z1 [1, -1, 1, -230, 215772] [2] 18432 \(\Gamma_0(N)\)-optimal
11025.p8 11025z6 [1, -1, 1, 385645, -49176228] [2] 147456  

Rank

sage: E.rank()
 

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

Modular form 11025.2.a.p

sage: E.q_eigenform(10)
 
\( q - q^{2} - q^{4} + 3q^{8} + 4q^{11} - 2q^{13} - q^{16} - 2q^{17} - 4q^{19} + O(q^{20}) \)

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 LMFDB numbering.

\(\left(\begin{array}{rrrrrrrr} 1 & 2 & 4 & 16 & 4 & 8 & 16 & 8 \\ 2 & 1 & 2 & 8 & 2 & 4 & 8 & 4 \\ 4 & 2 & 1 & 16 & 4 & 8 & 16 & 8 \\ 16 & 8 & 16 & 1 & 4 & 2 & 4 & 8 \\ 4 & 2 & 4 & 4 & 1 & 2 & 4 & 2 \\ 8 & 4 & 8 & 2 & 2 & 1 & 2 & 4 \\ 16 & 8 & 16 & 4 & 4 & 2 & 1 & 8 \\ 8 & 4 & 8 & 8 & 2 & 4 & 8 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.