Properties

Label 161874.g
Number of curves $6$
Conductor $161874$
CM no
Rank $0$
Graph

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

Elliptic curves in class 161874.g

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
161874.g1 161874bp6 \([1, -1, 0, -132089283, -584285278581]\) \(2361739090258884097/5202\) \(561390284347362\) \([2]\) \(12976128\) \(2.9641\)  
161874.g2 161874bp4 \([1, -1, 0, -8255673, -9127693575]\) \(576615941610337/27060804\) \(2920352259174977124\) \([2, 2]\) \(6488064\) \(2.6176\)  
161874.g3 161874bp5 \([1, -1, 0, -7827183, -10117762569]\) \(-491411892194497/125563633938\) \(-13550596724364070242978\) \([2]\) \(12976128\) \(2.9641\)  
161874.g4 161874bp2 \([1, -1, 0, -542853, -126832635]\) \(163936758817/30338064\) \(3274028138313815184\) \([2, 2]\) \(3244032\) \(2.2710\)  
161874.g5 161874bp1 \([1, -1, 0, -161973, 23310261]\) \(4354703137/352512\) \(38042447504009472\) \([2]\) \(1622016\) \(1.9244\) \(\Gamma_0(N)\)-optimal
161874.g6 161874bp3 \([1, -1, 0, 1075887, -739687599]\) \(1276229915423/2927177028\) \(-315895567874660903268\) \([2]\) \(6488064\) \(2.6176\)  

Rank

sage: E.rank()
 

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

Complex multiplication

The elliptic curves in class 161874.g do not have complex multiplication.

Modular form 161874.2.a.g

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

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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.