Properties

Label 44880.s
Number of curves $4$
Conductor $44880$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("s1")
 
E.isogeny_class()
 

Elliptic curves in class 44880.s

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
44880.s1 44880bi4 \([0, -1, 0, -2854816, 1616922880]\) \(628200507126935410849/88124751829125000\) \(360958983492096000000\) \([2]\) \(1990656\) \(2.6708\)  
44880.s2 44880bi2 \([0, -1, 0, -729376, -239239424]\) \(10476561483361670689/13992628953600\) \(57313808193945600\) \([2]\) \(663552\) \(2.1215\)  
44880.s3 44880bi1 \([0, -1, 0, -33056, -5832960]\) \(-975276594443809/3037581803520\) \(-12441935067217920\) \([2]\) \(331776\) \(1.7749\) \(\Gamma_0(N)\)-optimal
44880.s4 44880bi3 \([0, -1, 0, 289504, 135319296]\) \(655127711084516831/2313151512408000\) \(-9474668594823168000\) \([2]\) \(995328\) \(2.3242\)  

Rank

sage: E.rank()
 

The elliptic curves in class 44880.s have rank \(1\).

Complex multiplication

The elliptic curves in class 44880.s do not have complex multiplication.

Modular form 44880.2.a.s

sage: E.q_eigenform(10)
 
\(q - q^{3} - q^{5} + 4 q^{7} + q^{9} + q^{11} + 2 q^{13} + q^{15} - q^{17} - 2 q^{19} + O(q^{20})\) 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.