Properties

Label 8820.b
Number of curves $4$
Conductor $8820$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("b1")
 
E.isogeny_class()
 

Elliptic curves in class 8820.b

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
8820.b1 8820s3 \([0, 0, 0, -132888, -17221687]\) \(189123395584/16078125\) \(22063334627250000\) \([2]\) \(82944\) \(1.8775\)  
8820.b2 8820s1 \([0, 0, 0, -27048, 1707797]\) \(1594753024/4725\) \(6483918747600\) \([2]\) \(27648\) \(1.3282\) \(\Gamma_0(N)\)-optimal
8820.b3 8820s2 \([0, 0, 0, -16023, 3112382]\) \(-20720464/178605\) \(-3921474058548480\) \([2]\) \(55296\) \(1.6747\)  
8820.b4 8820s4 \([0, 0, 0, 142737, -79347562]\) \(14647977776/132355125\) \(-2906005930424352000\) \([2]\) \(165888\) \(2.2240\)  

Rank

sage: E.rank()
 

The elliptic curves in class 8820.b have rank \(0\).

Complex multiplication

The elliptic curves in class 8820.b do not have complex multiplication.

Modular form 8820.2.a.b

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

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.