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Properties

Label 9555.b
Number of curves $8$
Conductor $9555$
CM no
Rank $0$
Graph

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

Elliptic curves in class 9555.b

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
9555.b1 9555e7 \([1, 1, 1, -6370001, 6185446448]\) \(242970740812818720001/24375\) \(2867694375\) \([2]\) \(147456\) \(2.1624\)  
9555.b2 9555e5 \([1, 1, 1, -398126, 96522698]\) \(59319456301170001/594140625\) \(69900050390625\) \([2, 2]\) \(73728\) \(1.8158\)  
9555.b3 9555e8 \([1, 1, 1, -388571, 101388104]\) \(-55150149867714721/5950927734375\) \(-700120697021484375\) \([2]\) \(147456\) \(2.1624\)  
9555.b4 9555e3 \([1, 1, 1, -25481, 1423694]\) \(15551989015681/1445900625\) \(170108762630625\) \([2, 2]\) \(36864\) \(1.4692\)  
9555.b5 9555e2 \([1, 1, 1, -5636, -140092]\) \(168288035761/27720225\) \(3261256751025\) \([2, 2]\) \(18432\) \(1.1227\)  
9555.b6 9555e1 \([1, 1, 1, -5391, -154596]\) \(147281603041/5265\) \(619421985\) \([2]\) \(9216\) \(0.77608\) \(\Gamma_0(N)\)-optimal
9555.b7 9555e4 \([1, 1, 1, 10289, -770722]\) \(1023887723039/2798036865\) \(-329186239130385\) \([2]\) \(36864\) \(1.4692\)  
9555.b8 9555e6 \([1, 1, 1, 29644, 6803894]\) \(24487529386319/183539412225\) \(-21593228308859025\) \([2]\) \(73728\) \(1.8158\)  

Rank

sage: E.rank()
 

The elliptic curves in class 9555.b have rank \(0\).

Complex multiplication

The elliptic curves in class 9555.b do not have complex multiplication.

Modular form 9555.2.a.b

sage: E.q_eigenform(10)
 
\(q - q^{2} - q^{3} - q^{4} - q^{5} + q^{6} + 3 q^{8} + q^{9} + q^{10} + 4 q^{11} + q^{12} - q^{13} + q^{15} - q^{16} - 2 q^{17} - q^{18} + 4 q^{19} + O(q^{20})\) 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.

\(\left(\begin{array}{rrrrrrrr} 1 & 2 & 4 & 4 & 8 & 16 & 16 & 8 \\ 2 & 1 & 2 & 2 & 4 & 8 & 8 & 4 \\ 4 & 2 & 1 & 4 & 8 & 16 & 16 & 8 \\ 4 & 2 & 4 & 1 & 2 & 4 & 4 & 2 \\ 8 & 4 & 8 & 2 & 1 & 2 & 2 & 4 \\ 16 & 8 & 16 & 4 & 2 & 1 & 4 & 8 \\ 16 & 8 & 16 & 4 & 2 & 4 & 1 & 8 \\ 8 & 4 & 8 & 2 & 4 & 8 & 8 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.