Properties

Label 221760bs
Number of curves $4$
Conductor $221760$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("bs1")
 
E.isogeny_class()
 

Elliptic curves in class 221760bs

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
221760.iu4 221760bs1 \([0, 0, 0, 5748, 1370896]\) \(109902239/4312000\) \(-824036032512000\) \([2]\) \(884736\) \(1.5420\) \(\Gamma_0(N)\)-optimal
221760.iu2 221760bs2 \([0, 0, 0, -155532, 22595344]\) \(2177286259681/105875000\) \(20233027584000000\) \([2]\) \(1769472\) \(1.8885\)  
221760.iu3 221760bs3 \([0, 0, 0, -51852, -37497584]\) \(-80677568161/3131816380\) \(-598499430503546880\) \([2]\) \(2654208\) \(2.0913\)  
221760.iu1 221760bs4 \([0, 0, 0, -2027532, -1105155056]\) \(4823468134087681/30382271150\) \(5806142434403942400\) \([2]\) \(5308416\) \(2.4378\)  

Rank

sage: E.rank()
 

The elliptic curves in class 221760bs have rank \(1\).

Complex multiplication

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

Modular form 221760.2.a.bs

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