↑

Properties

Label 158400.go
Number of curves $6$
Conductor $158400$
CM no
Rank $0$
Graph

Related objects

Downloads

Learn more

Show commands: SageMath
Copy content sage:E = EllipticCurve("go1") E.isogeny_class()
 

Rank

Copy content sage:E.rank()
 

The elliptic curves in class 158400.go have rank \(0\).

L-function data

 
Bad L-factors:
Prime L-Factor
\(2\)\(1\)
\(3\)\(1\)
\(5\)\(1\)
\(11\)\(1 + T\)
 
Good L-factors:
Prime L-Factor Isogeny Class over \(\mathbb{F}_p\)
\(7\) \( 1 + 7 T^{2}\) 1.7.a
\(13\) \( 1 + 2 T + 13 T^{2}\) 1.13.c
\(17\) \( 1 + 6 T + 17 T^{2}\) 1.17.g
\(19\) \( 1 - 4 T + 19 T^{2}\) 1.19.ae
\(23\) \( 1 + 23 T^{2}\) 1.23.a
\(29\) \( 1 - 6 T + 29 T^{2}\) 1.29.ag
$\cdots$$\cdots$$\cdots$
 
See L-function page for more information

Complex multiplication

The elliptic curves in class 158400.go do not have complex multiplication.

Modular form 158400.2.a.go

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

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.

Elliptic curves in class 158400.go

Copy content sage:E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
158400.go1 158400lu4 \([0, 0, 0, -47520300, -126086002000]\) \(15897679904620804/2475\) \(1847577600000000\) \([2]\) \(6291456\) \(2.7760\)  
158400.go2 158400lu5 \([0, 0, 0, -25200300, 47758718000]\) \(1185450336504002/26043266205\) \(38882388097935360000000\) \([2]\) \(12582912\) \(3.1226\)  
158400.go3 158400lu3 \([0, 0, 0, -3420300, -1333402000]\) \(5927735656804/2401490025\) \(1792702697702400000000\) \([2, 2]\) \(6291456\) \(2.7760\)  
158400.go4 158400lu2 \([0, 0, 0, -2970300, -1969702000]\) \(15529488955216/6125625\) \(1143188640000000000\) \([2, 2]\) \(3145728\) \(2.4294\)  
158400.go5 158400lu1 \([0, 0, 0, -157800, -40327000]\) \(-37256083456/38671875\) \(-451068750000000000\) \([2]\) \(1572864\) \(2.0828\) \(\Gamma_0(N)\)-optimal
158400.go6 158400lu6 \([0, 0, 0, 11159700, -9702322000]\) \(102949393183198/86815346805\) \(-129614618257090560000000\) \([2]\) \(12582912\) \(3.1226\)