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Properties

Label 210210.br
Number of curves $1$
Conductor $210210$
CM no
Rank $1$

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Show commands: SageMath
Copy content sage:E = EllipticCurve("br1") E.isogeny_class()
 

Rank

Copy content sage:E.rank()
 

The elliptic curve 210210.br1 has rank \(1\).

L-function data

 
Bad L-factors:
Prime L-Factor
\(2\)\(1 + T\)
\(3\)\(1 - T\)
\(5\)\(1 + T\)
\(7\)\(1\)
\(11\)\(1 - T\)
\(13\)\(1 + T\)
 
Good L-factors:
Prime L-Factor Isogeny Class over \(\mathbb{F}_p\)
\(17\) \( 1 + 4 T + 17 T^{2}\) 1.17.e
\(19\) \( 1 - 4 T + 19 T^{2}\) 1.19.ae
\(23\) \( 1 - 8 T + 23 T^{2}\) 1.23.ai
\(29\) \( 1 + 6 T + 29 T^{2}\) 1.29.g
$\cdots$$\cdots$$\cdots$
 
See L-function page for more information

Complex multiplication

The elliptic curves in class 210210.br do not have complex multiplication.

Modular form 210210.2.a.br

Copy content sage:E.q_eigenform(10)
 
\(q - q^{2} + q^{3} + q^{4} - q^{5} - q^{6} - q^{8} + q^{9} + q^{10} + q^{11} + q^{12} - q^{13} - q^{15} + q^{16} - 4 q^{17} - q^{18} + 4 q^{19} + O(q^{20})\) Copy content Toggle raw display

Elliptic curves in class 210210.br

Copy content sage:E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
210210.br1 210210eh1 \([1, 0, 1, 20701, -4077538]\) \(170193717911/1345481280\) \(-7756431828425280\) \([]\) \(1693440\) \(1.7304\) \(\Gamma_0(N)\)-optimal