↑

Properties

Label 14079.c
Number of curves $1$
Conductor $14079$
CM no
Rank $1$

Related objects

Downloads

Learn more

Show commands: SageMath
Copy content sage:E = EllipticCurve("c1") E.isogeny_class()
 

Rank

Copy content sage:E.rank()
 

The elliptic curve 14079.c1 has rank \(1\).

L-function data

 
Bad L-factors:
Prime L-Factor
\(3\)\(1 - T\)
\(13\)\(1 + T\)
\(19\)\(1\)
 
Good L-factors:
Prime L-Factor Isogeny Class over \(\mathbb{F}_p\)
\(2\) \( 1 + T + 2 T^{2}\) 1.2.b
\(5\) \( 1 + 3 T + 5 T^{2}\) 1.5.d
\(7\) \( 1 - T + 7 T^{2}\) 1.7.ab
\(11\) \( 1 - 4 T + 11 T^{2}\) 1.11.ae
\(17\) \( 1 - 2 T + 17 T^{2}\) 1.17.ac
\(23\) \( 1 - 5 T + 23 T^{2}\) 1.23.af
\(29\) \( 1 + 10 T + 29 T^{2}\) 1.29.k
$\cdots$$\cdots$$\cdots$
 
See L-function page for more information

Complex multiplication

The elliptic curves in class 14079.c do not have complex multiplication.

Modular form 14079.2.a.c

Copy content sage:E.q_eigenform(10)
 
\(q - q^{2} + q^{3} - q^{4} - 3 q^{5} - q^{6} + q^{7} + 3 q^{8} + q^{9} + 3 q^{10} + 4 q^{11} - q^{12} - q^{13} - q^{14} - 3 q^{15} - q^{16} + 2 q^{17} - q^{18} + O(q^{20})\) Copy content Toggle raw display

Elliptic curves in class 14079.c

Copy content sage:E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
14079.c1 14079e1 \([1, 0, 0, 2010943, 301655646]\) \(19116191615070887/11897257043061\) \(-559716939074259681741\) \([]\) \(604800\) \(2.6703\) \(\Gamma_0(N)\)-optimal