Properties

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

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Show commands for: SageMath

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

Elliptic curves in class 11025ba

sage: E.isogeny_class().curves
LMFDB label Cremona label Weierstrass coefficients Torsion order Modular degree Optimality
11025.g6 11025ba1 [1, -1, 1, 10795, -97828] 2 24576 \(\Gamma_0(N)\)-optimal
11025.g5 11025ba2 [1, -1, 1, -44330, -759328] 4 49152  
11025.g2 11025ba3 [1, -1, 1, -540455, -152573578] 4 98304  
11025.g3 11025ba4 [1, -1, 1, -430205, 108057422] 2 98304  
11025.g1 11025ba5 [1, -1, 1, -8643830, -9779383078] 2 196608  
11025.g4 11025ba6 [1, -1, 1, -375080, -247829578] 2 196608  

Rank

sage: E.rank()

The elliptic curves in class 11025ba 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 Cremona numbering.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.