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Properties

Label 283920.gf
Number of curves $6$
Conductor $283920$
CM no
Rank $0$
Graph

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Show commands: SageMath
Copy content sage:E = EllipticCurve("gf1") E.isogeny_class()
 

Rank

Copy content sage:E.rank()
 

The elliptic curves in class 283920.gf have rank \(0\).

L-function data

 
Bad L-factors:
Prime L-Factor
\(2\)\(1\)
\(3\)\(1 - T\)
\(5\)\(1 + T\)
\(7\)\(1 - T\)
\(13\)\(1\)
 
Good L-factors:
Prime L-Factor Isogeny Class over \(\mathbb{F}_p\)
\(11\) \( 1 - 4 T + 11 T^{2}\) 1.11.ae
\(17\) \( 1 - 2 T + 17 T^{2}\) 1.17.ac
\(19\) \( 1 + 4 T + 19 T^{2}\) 1.19.e
\(23\) \( 1 - 8 T + 23 T^{2}\) 1.23.ai
\(29\) \( 1 - 6 T + 29 T^{2}\) 1.29.ag
$\cdots$$\cdots$$\cdots$
 
See L-function page for more information

Complex multiplication

The elliptic curves in class 283920.gf do not have complex multiplication.

Modular form 283920.2.a.gf

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

Isogeny matrix

Copy content 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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.

Elliptic curves in class 283920.gf

Copy content sage:E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
283920.gf1 283920gf5 \([0, 1, 0, -45427256, 117833036244]\) \(524388516989299201/3150\) \(62277420441600\) \([2]\) \(14155776\) \(2.7124\)  
283920.gf2 283920gf3 \([0, 1, 0, -2839256, 1840359444]\) \(128031684631201/9922500\) \(196173874391040000\) \([2, 2]\) \(7077888\) \(2.3658\)  
283920.gf3 283920gf6 \([0, 1, 0, -2649976, 2096493140]\) \(-104094944089921/35880468750\) \(-709378742217600000000\) \([2]\) \(14155776\) \(2.7124\)  
283920.gf4 283920gf4 \([0, 1, 0, -1000536, -364417260]\) \(5602762882081/345888060\) \(6838417821698211840\) \([2]\) \(7077888\) \(2.3658\)  
283920.gf5 283920gf2 \([0, 1, 0, -189336, 24634260]\) \(37966934881/8643600\) \(170889241691750400\) \([2, 2]\) \(3538944\) \(2.0192\)  
283920.gf6 283920gf1 \([0, 1, 0, 26984, 2396564]\) \(109902239/188160\) \(-3720037914378240\) \([2]\) \(1769472\) \(1.6727\) \(\Gamma_0(N)\)-optimal