Properties

Label 11025.g
Number of curves 6
Conductor 11025
CM no
Rank 1
Graph

Related objects

Downloads

Learn more about

Show commands for: SageMath

sage: E = EllipticCurve("11025.g1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 11025.g

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
11025.g1 11025ba5 [1, -1, 1, -8643830, -9779383078] [2] 196608  
11025.g2 11025ba3 [1, -1, 1, -540455, -152573578] [2, 2] 98304  
11025.g3 11025ba4 [1, -1, 1, -430205, 108057422] [2] 98304  
11025.g4 11025ba6 [1, -1, 1, -375080, -247829578] [2] 196608  
11025.g5 11025ba2 [1, -1, 1, -44330, -759328] [2, 2] 49152  
11025.g6 11025ba1 [1, -1, 1, 10795, -97828] [2] 24576 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Modular form 11025.2.a.g

sage: E.q_eigenform(10)
 
\( q - q^{2} - q^{4} + 3q^{8} - 4q^{11} - 2q^{13} - q^{16} + 6q^{17} - 4q^{19} + O(q^{20}) \)

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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.