Properties

Label 126960.cx
Number of curves $4$
Conductor $126960$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("cx1")
 
E.isogeny_class()
 

Elliptic curves in class 126960.cx

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
126960.cx1 126960r4 \([0, 1, 0, -558800, 158032500]\) \(63649751618/1164375\) \(353012302344960000\) \([4]\) \(1622016\) \(2.1620\)  
126960.cx2 126960r2 \([0, 1, 0, -72120, -3739932]\) \(273671716/119025\) \(18042851008742400\) \([2, 2]\) \(811008\) \(1.8154\)  
126960.cx3 126960r1 \([0, 1, 0, -61540, -5894020]\) \(680136784/345\) \(13074529716480\) \([2]\) \(405504\) \(1.4688\) \(\Gamma_0(N)\)-optimal
126960.cx4 126960r3 \([0, 1, 0, 245280, -27481452]\) \(5382838942/4197615\) \(-1272622424483297280\) \([2]\) \(1622016\) \(2.1620\)  

Rank

sage: E.rank()
 

The elliptic curves in class 126960.cx have rank \(0\).

Complex multiplication

The elliptic curves in class 126960.cx do not have complex multiplication.

Modular form 126960.2.a.cx

sage: E.q_eigenform(10)
 
\(q + q^{3} + q^{5} + q^{9} + 4 q^{11} + 2 q^{13} + q^{15} - 2 q^{17} + O(q^{20})\) 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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.