↑

Properties

Label 176400.qb
Number of curves $2$
Conductor $176400$
CM no
Rank $0$
Graph

Related objects

Downloads

Learn more

Show commands: SageMath
Copy content sage:E = EllipticCurve("qb1") E.isogeny_class()
 

Rank

Copy content sage:E.rank()
 

The elliptic curves in class 176400.qb have rank \(0\).

L-function data

 
Bad L-factors:
Prime L-Factor
\(2\)\(1\)
\(3\)\(1\)
\(5\)\(1\)
\(7\)\(1\)
 
Good L-factors:
Prime L-Factor Isogeny Class over \(\mathbb{F}_p\)
\(11\) \( 1 - 3 T + 11 T^{2}\) 1.11.ad
\(13\) \( 1 + 5 T + 13 T^{2}\) 1.13.f
\(17\) \( 1 - 2 T + 17 T^{2}\) 1.17.ac
\(19\) \( 1 - 5 T + 19 T^{2}\) 1.19.af
\(23\) \( 1 + 7 T + 23 T^{2}\) 1.23.h
\(29\) \( 1 - 4 T + 29 T^{2}\) 1.29.ae
$\cdots$$\cdots$$\cdots$
 
See L-function page for more information

Complex multiplication

The elliptic curves in class 176400.qb do not have complex multiplication.

Modular form 176400.2.a.qb

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

\(\left(\begin{array}{rr} 1 & 13 \\ 13 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.

Elliptic curves in class 176400.qb

Copy content sage:E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
176400.qb1 176400di2 \([0, 0, 0, -1204315875, 16086414881250]\) \(-5745702166029/8192\) \(-275417656786944000000000\) \([]\) \(50319360\) \(3.7692\)  
176400.qb2 176400di1 \([0, 0, 0, -385875, -405168750]\) \(-189/2\) \(-67240638864000000000\) \([]\) \(3870720\) \(2.4867\) \(\Gamma_0(N)\)-optimal