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Properties

Label 166464gb
Number of curves $6$
Conductor $166464$
CM no
Rank $0$
Graph

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Show commands: SageMath
Copy content sage:E = EllipticCurve("gb1") E.isogeny_class()
 

Rank

Copy content sage:E.rank()
 

The elliptic curves in class 166464gb have rank \(0\).

L-function data

 
Bad L-factors:
Prime L-Factor
\(2\)\(1\)
\(3\)\(1\)
\(17\)\(1\)
 
Good L-factors:
Prime L-Factor Isogeny Class over \(\mathbb{F}_p\)
\(5\) \( 1 - 2 T + 5 T^{2}\) 1.5.ac
\(7\) \( 1 - T + 7 T^{2}\) 1.7.ab
\(11\) \( 1 + 6 T + 11 T^{2}\) 1.11.g
\(13\) \( 1 + T + 13 T^{2}\) 1.13.b
\(19\) \( 1 + 5 T + 19 T^{2}\) 1.19.f
\(23\) \( 1 + 2 T + 23 T^{2}\) 1.23.c
\(29\) \( 1 - 6 T + 29 T^{2}\) 1.29.ag
$\cdots$$\cdots$$\cdots$
 
See L-function page for more information

Complex multiplication

The elliptic curves in class 166464gb do not have complex multiplication.

Modular form 166464.2.a.gb

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

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

Isogeny graph

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

The vertices are labelled with Cremona labels.

Elliptic curves in class 166464gb

Copy content sage:E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
166464.fz5 166464gb1 \([0, 0, 0, -5663244, -4810888208]\) \(4354703137/352512\) \(1626053700565365424128\) \([2]\) \(7077888\) \(2.8130\) \(\Gamma_0(N)\)-optimal
166464.fz4 166464gb2 \([0, 0, 0, -18980364, 26249962480]\) \(163936758817/30338064\) \(139942246604906761814016\) \([2, 2]\) \(14155776\) \(3.1596\)  
166464.fz2 166464gb3 \([0, 0, 0, -288652044, 1887523897840]\) \(576615941610337/27060804\) \(124825028607463130136576\) \([2, 2]\) \(28311552\) \(3.5061\)  
166464.fz6 166464gb4 \([0, 0, 0, 37617396, 152870471152]\) \(1276229915423/2927177028\) \(-13502368823158724474437632\) \([2]\) \(28311552\) \(3.5061\)  
166464.fz1 166464gb5 \([0, 0, 0, -4618380684, 120804386941168]\) \(2361739090258884097/5202\) \(23995584122926399488\) \([2]\) \(56623104\) \(3.8527\)  
166464.fz3 166464gb6 \([0, 0, 0, -273670284, 2092192717552]\) \(-491411892194497/125563633938\) \(-579195067462440449563164672\) \([2]\) \(56623104\) \(3.8527\)