↑

Properties

Label 126400.cd
Number of curves $2$
Conductor $126400$
CM no
Rank $1$
Graph

Related objects

Downloads

Learn more

Show commands: SageMath
Copy content sage:E = EllipticCurve("cd1") E.isogeny_class()
 

Rank

Copy content sage:E.rank()
 

The elliptic curves in class 126400.cd have rank \(1\).

L-function data

 
Bad L-factors:
Prime L-Factor
\(2\)\(1\)
\(5\)\(1\)
\(79\)\(1 - T\)
 
Good L-factors:
Prime L-Factor Isogeny Class over \(\mathbb{F}_p\)
\(3\) \( 1 - T + 3 T^{2}\) 1.3.ab
\(7\) \( 1 - 3 T + 7 T^{2}\) 1.7.ad
\(11\) \( 1 - 2 T + 11 T^{2}\) 1.11.ac
\(13\) \( 1 + T + 13 T^{2}\) 1.13.b
\(17\) \( 1 - 2 T + 17 T^{2}\) 1.17.ac
\(19\) \( 1 + 19 T^{2}\) 1.19.a
\(23\) \( 1 + 6 T + 23 T^{2}\) 1.23.g
\(29\) \( 1 - 10 T + 29 T^{2}\) 1.29.ak
$\cdots$$\cdots$$\cdots$
 
See L-function page for more information

Complex multiplication

The elliptic curves in class 126400.cd do not have complex multiplication.

Modular form 126400.2.a.cd

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

\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.

Elliptic curves in class 126400.cd

Copy content sage:E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
126400.cd1 126400by2 \([0, 1, 0, -37408033, 88048276063]\) \(1413378216646643521/49232902384\) \(201657968164864000000\) \([]\) \(6451200\) \(2.9865\)  
126400.cd2 126400by1 \([0, 1, 0, -672033, -210411937]\) \(8194759433281/82837504\) \(339302416384000000\) \([]\) \(1290240\) \(2.1818\) \(\Gamma_0(N)\)-optimal