↑

Learn more

Refine search

Lowest zero	Conductor	Analytic conductor	Central character	Analytic rank

Degree	Bad \(p\)	Root analytic conductor	Motivic weight	Spectral label

Root number	Primitive	Origin	Exclude origin

				Sort order

Columns to display		Euler factor constraints
	e.g. 3,7,19		e.g. F3=1-T,F5=1+T+5T^2

Results (displaying both matches)

Download displayed columns for results to

		$L(s) = \prod_p F_p(p^{-s})^{-1}$
Label	Origin	\(F_{ 2 }(T)\)	\(F_{ 3 }(T)\)	\(F_{ 5 }(T)\)	\(F_{ 7 }(T)\)	\(F_{ 83 }(T)\)
4-382989-1.1-c1e2-0-0	Genus 2 curve 382989.a	$( 1 - T + 2 T^{2} )( 1 + 2 T + 2 T^{2} )$	$( 1 + T )( 1 - T + 3 T^{2} )$	$1 + T - T^{2} + 5 T^{3} + 25 T^{4}$	$1 + 2 T^{2} + 49 T^{4}$	$1 - 31 T + 403 T^{2} - 2573 T^{3} + 6889 T^{4}$
4-3598e2-1.1-c1e2-0-1	Modular form 3598.2.a.f	$( 1 + T )^{2}$	$1 - T + 3 T^{2} - 3 T^{3} + 9 T^{4}$	$( 1 + 2 T + 5 T^{2} )^{2}$	$( 1 + T )^{2}$	$1 - 31 T + 403 T^{2} - 2573 T^{3} + 6889 T^{4}$