Properties

Label 221760hj
Number of curves $4$
Conductor $221760$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("hj1")
 
E.isogeny_class()
 

Elliptic curves in class 221760hj

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
221760.l3 221760hj1 \([0, 0, 0, -16908, -4021232]\) \(-75526045083/943250000\) \(-6676217856000000\) \([2]\) \(1327104\) \(1.7182\) \(\Gamma_0(N)\)-optimal
221760.l2 221760hj2 \([0, 0, 0, -496908, -134389232]\) \(1917114236485083/7117764500\) \(50378739941376000\) \([2]\) \(2654208\) \(2.0648\)  
221760.l4 221760hj3 \([0, 0, 0, 151092, 104327568]\) \(73929353373/954060800\) \(-4922744170453401600\) \([2]\) \(3981312\) \(2.2675\)  
221760.l1 221760hj4 \([0, 0, 0, -2613708, 1521011088]\) \(382704614800227/27778076480\) \(143328773237857320960\) \([2]\) \(7962624\) \(2.6141\)  

Rank

sage: E.rank()
 

The elliptic curves in class 221760hj have rank \(0\).

Complex multiplication

The elliptic curves in class 221760hj do not have complex multiplication.

Modular form 221760.2.a.hj

sage: E.q_eigenform(10)
 
\(q - q^{5} - q^{7} - q^{11} - 2 q^{13} - 6 q^{17} - 4 q^{19} + O(q^{20})\) 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 Cremona numbering.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.