Properties

Label 209814.l
Number of curves $1$
Conductor $209814$
CM no
Rank $0$

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Show commands: SageMath
Copy content sage:E = EllipticCurve("l1") E.isogeny_class()
 

Rank

Copy content sage:E.rank()
 

The elliptic curve 209814.l1 has rank \(0\).

L-function data

 
Bad L-factors:
Prime L-Factor
\(2\)\(1 + T\)
\(3\)\(1 + T\)
\(11\)\(1\)
\(17\)\(1\)
 
Good L-factors:
Prime L-Factor Isogeny Class over \(\mathbb{F}_p\)
\(5\) \( 1 + 5 T^{2}\) 1.5.a
\(7\) \( 1 + T + 7 T^{2}\) 1.7.b
\(13\) \( 1 - 5 T + 13 T^{2}\) 1.13.af
\(19\) \( 1 + T + 19 T^{2}\) 1.19.b
\(23\) \( 1 - 6 T + 23 T^{2}\) 1.23.ag
\(29\) \( 1 - 4 T + 29 T^{2}\) 1.29.ae
$\cdots$$\cdots$$\cdots$
 
See L-function page for more information

Complex multiplication

The elliptic curves in class 209814.l do not have complex multiplication.

Modular form 209814.2.a.l

Copy content sage:E.q_eigenform(10)
 
\(q - q^{2} - q^{3} + q^{4} + q^{6} - q^{7} - q^{8} + q^{9} - q^{12} + 5 q^{13} + q^{14} + q^{16} - q^{18} - q^{19} + O(q^{20})\) Copy content Toggle raw display

Elliptic curves in class 209814.l

Copy content sage:E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
209814.l1 209814ct1 \([1, 1, 0, 69210, 10161936]\) \(71608817375/128079468\) \(-65574270628359372\) \([]\) \(1935360\) \(1.9116\) \(\Gamma_0(N)\)-optimal