Properties

Label 2646.v
Number of curves $1$
Conductor $2646$
CM no
Rank $0$

Related objects

Downloads

Learn more

Show commands: SageMath
Copy content sage:E = EllipticCurve("v1") E.isogeny_class()
 

Rank

Copy content sage:E.rank()
 

The elliptic curve 2646.v1 has rank \(0\).

L-function data

 
Bad L-factors:
Prime L-Factor
\(2\)\(1 - T\)
\(3\)\(1\)
\(7\)\(1\)
 
Good L-factors:
Prime L-Factor Isogeny Class over \(\mathbb{F}_p\)
\(5\) \( 1 + T + 5 T^{2}\) 1.5.b
\(11\) \( 1 - 5 T + 11 T^{2}\) 1.11.af
\(13\) \( 1 + 13 T^{2}\) 1.13.a
\(17\) \( 1 + 2 T + 17 T^{2}\) 1.17.c
\(19\) \( 1 - T + 19 T^{2}\) 1.19.ab
\(23\) \( 1 + T + 23 T^{2}\) 1.23.b
\(29\) \( 1 - 4 T + 29 T^{2}\) 1.29.ae
$\cdots$$\cdots$$\cdots$
 
See L-function page for more information

Complex multiplication

The elliptic curves in class 2646.v do not have complex multiplication.

Modular form 2646.2.a.v

Copy content sage:E.q_eigenform(10)
 
\(q + q^{2} + q^{4} - q^{5} + q^{8} - q^{10} + 5 q^{11} + q^{16} - 2 q^{17} + q^{19} + O(q^{20})\) Copy content Toggle raw display

Elliptic curves in class 2646.v

Copy content sage:E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
2646.v1 2646y1 \([1, -1, 1, -83, 36775]\) \(-3/28\) \(-583552687284\) \([]\) \(3456\) \(0.93661\) \(\Gamma_0(N)\)-optimal