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Properties

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

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Show commands: SageMath
Copy content sage:E = EllipticCurve("do1") E.isogeny_class()
 

Rank

Copy content sage:E.rank()
 

The elliptic curve 210210.do1 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 \(\mathbb{F}_p\)
\(17\) \( 1 - 7 T + 17 T^{2}\) 1.17.ah
\(19\) \( 1 + 5 T + 19 T^{2}\) 1.19.f
\(23\) \( 1 - 8 T + 23 T^{2}\) 1.23.ai
\(29\) \( 1 + 10 T + 29 T^{2}\) 1.29.k
$\cdots$$\cdots$$\cdots$
 
See L-function page for more information

Complex multiplication

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

Modular form 210210.2.a.do

Copy content sage:E.q_eigenform(10)
 
\(q + q^{2} - q^{3} + q^{4} + q^{5} - q^{6} + q^{8} + q^{9} + q^{10} - q^{11} - q^{12} - q^{13} - q^{15} + q^{16} + 7 q^{17} + q^{18} - 5 q^{19} + O(q^{20})\) Copy content Toggle raw display

Elliptic curves in class 210210.do

Copy content sage:E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
210210.do1 210210ci1 \([1, 1, 1, 5445075, 2211044835]\) \(3097069742116095599/2157882876864000\) \(-12439765366428464064000\) \([]\) \(23950080\) \(2.9281\) \(\Gamma_0(N)\)-optimal