Properties

Label 161874bp
Number of curves 6
Conductor 161874
CM no
Rank 0
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("161874.g1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 161874bp

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
161874.g5 161874bp1 [1, -1, 0, -161973, 23310261] [2] 1622016 \(\Gamma_0(N)\)-optimal
161874.g4 161874bp2 [1, -1, 0, -542853, -126832635] [2, 2] 3244032  
161874.g6 161874bp3 [1, -1, 0, 1075887, -739687599] [2] 6488064  
161874.g2 161874bp4 [1, -1, 0, -8255673, -9127693575] [2, 2] 6488064  
161874.g3 161874bp5 [1, -1, 0, -7827183, -10117762569] [2] 12976128  
161874.g1 161874bp6 [1, -1, 0, -132089283, -584285278581] [2] 12976128  

Rank

sage: E.rank()
 

The elliptic curves in class 161874bp have rank \(0\).

Modular form 161874.2.a.g

sage: E.q_eigenform(10)
 
\( q - q^{2} + q^{4} - 2q^{5} - q^{8} + 2q^{10} - 4q^{11} - 2q^{13} + q^{16} + q^{17} - 4q^{19} + O(q^{20}) \)

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.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.