Properties

Label 388080.ik
Number of curves $4$
Conductor $388080$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("ik1")
 
E.isogeny_class()
 

Elliptic curves in class 388080.ik

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
388080.ik1 388080ik4 \([0, 0, 0, -54784107, -155572334694]\) \(1917114236485083/7117764500\) \(67512329775618545664000\) \([2]\) \(47775744\) \(3.2405\)  
388080.ik2 388080ik2 \([0, 0, 0, -3557547, 2415309274]\) \(382704614800227/27778076480\) \(361421614426026147840\) \([2]\) \(15925248\) \(2.6912\)  
388080.ik3 388080ik3 \([0, 0, 0, -1864107, -4655078694]\) \(-75526045083/943250000\) \(-8946770444688384000000\) \([2]\) \(23887872\) \(2.8939\)  
388080.ik4 388080ik1 \([0, 0, 0, 205653, 165668314]\) \(73929353373/954060800\) \(-12413321521555046400\) \([2]\) \(7962624\) \(2.3446\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 388080.ik have rank \(0\).

Complex multiplication

The elliptic curves in class 388080.ik do not have complex multiplication.

Modular form 388080.2.a.ik

sage: E.q_eigenform(10)
 
\(q + q^{5} - q^{11} - 2 q^{13} - 6 q^{17} - 4 q^{19} + O(q^{20})\) 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.

\(\left(\begin{array}{rrrr} 1 & 3 & 2 & 6 \\ 3 & 1 & 6 & 2 \\ 2 & 6 & 1 & 3 \\ 6 & 2 & 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.