LMFDB - Rational L-function search results

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	Select

Results (1-50 of 73 matches)

Next Download displayed columns for results to

Label	$\alpha$	$A$	$d$	$N$	$\chi$	$\nu$	$w$	$\epsilon$	$r$	First zero	Origin
4-42e4-1.1-c0e2-0-0	$0.938$	$0.775$	$4$	$2^{4} \cdot 3^{4} \cdot 7^{4}$	1.1	$0.0, 0.0$	0	$1$	$0$	$0.745982$	Artin representation 2.1764.8t11.a Modular form 1764.1.g.c
4-42e4-1.1-c0e2-0-1	$0.938$	$0.775$	$4$	$2^{4} \cdot 3^{4} \cdot 7^{4}$	1.1	$0.0, 0.0$	0	$1$	$0$	$0.840214$	Artin representation 2.1764.8t6.b Modular form 1764.1.g.b
4-42e4-1.1-c0e2-0-2	$0.938$	$0.775$	$4$	$2^{4} \cdot 3^{4} \cdot 7^{4}$	1.1	$0.0, 0.0$	0	$1$	$0$	$0.942561$	Modular form 1764.1.d.a
4-42e4-1.1-c0e2-0-3	$0.938$	$0.775$	$4$	$2^{4} \cdot 3^{4} \cdot 7^{4}$	1.1	$0.0, 0.0$	0	$1$	$0$	$1.04076$	Modular form 1764.1.z.a
4-42e4-1.1-c0e2-0-4	$0.938$	$0.775$	$4$	$2^{4} \cdot 3^{4} \cdot 7^{4}$	1.1	$0.0, 0.0$	0	$1$	$0$	$1.04314$	Modular form 1764.1.y.a
4-42e4-1.1-c0e2-0-5	$0.938$	$0.775$	$4$	$2^{4} \cdot 3^{4} \cdot 7^{4}$	1.1	$0.0, 0.0$	0	$1$	$0$	$1.39157$	Artin representation 2.1764.8t6.a Modular form 1764.1.g.d
4-42e4-1.1-c1e2-0-0	$3.75$	$198.$	$4$	$2^{4} \cdot 3^{4} \cdot 7^{4}$	1.1	$1.0, 1.0$	$1$	$1$	$0$	$0.170572$	Modular form 1764.2.k.d
4-42e4-1.1-c1e2-0-1	$3.75$	$198.$	$4$	$2^{4} \cdot 3^{4} \cdot 7^{4}$	1.1	$1.0, 1.0$	$1$	$1$	$0$	$0.325189$	Modular form 1764.2.k.e
4-42e4-1.1-c1e2-0-10	$3.75$	$198.$	$4$	$2^{4} \cdot 3^{4} \cdot 7^{4}$	1.1	$1.0, 1.0$	$1$	$1$	$0$	$0.671580$	Modular form 1764.2.k.h
4-42e4-1.1-c1e2-0-11	$3.75$	$198.$	$4$	$2^{4} \cdot 3^{4} \cdot 7^{4}$	1.1	$1.0, 1.0$	$1$	$1$	$0$	$0.693354$	Modular form 1764.2.k.g
4-42e4-1.1-c1e2-0-12	$3.75$	$198.$	$4$	$2^{4} \cdot 3^{4} \cdot 7^{4}$	1.1	$1.0, 1.0$	$1$	$1$	$0$	$0.747841$	Modular form 1764.2.k.j
4-42e4-1.1-c1e2-0-13	$3.75$	$198.$	$4$	$2^{4} \cdot 3^{4} \cdot 7^{4}$	1.1	$1.0, 1.0$	$1$	$1$	$0$	$0.755221$	Modular form 1764.2.k.c
4-42e4-1.1-c1e2-0-14	$3.75$	$198.$	$4$	$2^{4} \cdot 3^{4} \cdot 7^{4}$	1.1	$1.0, 1.0$	$1$	$1$	$0$	$0.780908$	Modular form 1764.2.e.b
4-42e4-1.1-c1e2-0-15	$3.75$	$198.$	$4$	$2^{4} \cdot 3^{4} \cdot 7^{4}$	1.1	$1.0, 1.0$	$1$	$1$	$0$	$0.851548$	Modular form 1764.2.i.c
4-42e4-1.1-c1e2-0-16	$3.75$	$198.$	$4$	$2^{4} \cdot 3^{4} \cdot 7^{4}$	1.1	$1.0, 1.0$	$1$	$1$	$0$	$0.882924$	Modular form 1764.2.i.b
4-42e4-1.1-c1e2-0-17	$3.75$	$198.$	$4$	$2^{4} \cdot 3^{4} \cdot 7^{4}$	1.1	$1.0, 1.0$	$1$	$1$	$0$	$0.983440$	Modular form 1764.2.j.c
4-42e4-1.1-c1e2-0-18	$3.75$	$198.$	$4$	$2^{4} \cdot 3^{4} \cdot 7^{4}$	1.1	$1.0, 1.0$	$1$	$1$	$2$	$1.15256$	Modular form 1764.2.i.a
4-42e4-1.1-c1e2-0-19	$3.75$	$198.$	$4$	$2^{4} \cdot 3^{4} \cdot 7^{4}$	1.1	$1.0, 1.0$	$1$	$1$	$0$	$1.17537$	Modular form 1764.2.l.c
4-42e4-1.1-c1e2-0-2	$3.75$	$198.$	$4$	$2^{4} \cdot 3^{4} \cdot 7^{4}$	1.1	$1.0, 1.0$	$1$	$1$	$0$	$0.334337$	Modular form 1764.2.k.f
4-42e4-1.1-c1e2-0-20	$3.75$	$198.$	$4$	$2^{4} \cdot 3^{4} \cdot 7^{4}$	1.1	$1.0, 1.0$	$1$	$1$	$2$	$1.19679$	Modular form 1764.2.l.a
4-42e4-1.1-c1e2-0-21	$3.75$	$198.$	$4$	$2^{4} \cdot 3^{4} \cdot 7^{4}$	1.1	$1.0, 1.0$	$1$	$1$	$2$	$1.29658$	Modular form 1764.2.e.a
4-42e4-1.1-c1e2-0-22	$3.75$	$198.$	$4$	$2^{4} \cdot 3^{4} \cdot 7^{4}$	1.1	$1.0, 1.0$	$1$	$1$	$2$	$1.31596$	Modular form 1764.2.j.a
4-42e4-1.1-c1e2-0-23	$3.75$	$198.$	$4$	$2^{4} \cdot 3^{4} \cdot 7^{4}$	1.1	$1.0, 1.0$	$1$	$1$	$2$	$1.62213$	Modular form 1764.2.a.l
4-42e4-1.1-c1e2-0-3	$3.75$	$198.$	$4$	$2^{4} \cdot 3^{4} \cdot 7^{4}$	1.1	$1.0, 1.0$	$1$	$1$	$0$	$0.378398$	Modular form 1764.2.k.b
4-42e4-1.1-c1e2-0-4	$3.75$	$198.$	$4$	$2^{4} \cdot 3^{4} \cdot 7^{4}$	1.1	$1.0, 1.0$	$1$	$1$	$0$	$0.451634$	Modular form 1764.2.j.b
4-42e4-1.1-c1e2-0-5	$3.75$	$198.$	$4$	$2^{4} \cdot 3^{4} \cdot 7^{4}$	1.1	$1.0, 1.0$	$1$	$1$	$0$	$0.520776$	Modular form 1764.2.k.k
4-42e4-1.1-c1e2-0-6	$3.75$	$198.$	$4$	$2^{4} \cdot 3^{4} \cdot 7^{4}$	1.1	$1.0, 1.0$	$1$	$1$	$0$	$0.526516$	Modular form 1764.2.k.a
4-42e4-1.1-c1e2-0-7	$3.75$	$198.$	$4$	$2^{4} \cdot 3^{4} \cdot 7^{4}$	1.1	$1.0, 1.0$	$1$	$1$	$0$	$0.533406$	Modular form 1764.2.l.b
4-42e4-1.1-c1e2-0-8	$3.75$	$198.$	$4$	$2^{4} \cdot 3^{4} \cdot 7^{4}$	1.1	$1.0, 1.0$	$1$	$1$	$0$	$0.565433$	Modular form 1764.2.e.c
4-42e4-1.1-c1e2-0-9	$3.75$	$198.$	$4$	$2^{4} \cdot 3^{4} \cdot 7^{4}$	1.1	$1.0, 1.0$	$1$	$1$	$0$	$0.623410$	Modular form 1764.2.k.i
4-42e4-1.1-c2e2-0-0	$6.93$	$2.31\times 10^{3}$	$4$	$2^{4} \cdot 3^{4} \cdot 7^{4}$	1.1	$2.0, 2.0$	$2$	$1$	$0$	$0.188013$	Modular form 1764.3.z.c
4-42e4-1.1-c2e2-0-1	$6.93$	$2.31\times 10^{3}$	$4$	$2^{4} \cdot 3^{4} \cdot 7^{4}$	1.1	$2.0, 2.0$	$2$	$1$	$0$	$0.193162$	Modular form 1764.3.z.a
4-42e4-1.1-c2e2-0-10	$6.93$	$2.31\times 10^{3}$	$4$	$2^{4} \cdot 3^{4} \cdot 7^{4}$	1.1	$2.0, 2.0$	$2$	$1$	$0$	$0.645692$	Modular form 1764.3.z.e
4-42e4-1.1-c2e2-0-11	$6.93$	$2.31\times 10^{3}$	$4$	$2^{4} \cdot 3^{4} \cdot 7^{4}$	1.1	$2.0, 2.0$	$2$	$1$	$0$	$0.714801$	Modular form 1764.3.z.f
4-42e4-1.1-c2e2-0-12	$6.93$	$2.31\times 10^{3}$	$4$	$2^{4} \cdot 3^{4} \cdot 7^{4}$	1.1	$2.0, 2.0$	$2$	$1$	$0$	$0.726408$	Modular form 1764.3.z.g
4-42e4-1.1-c2e2-0-13	$6.93$	$2.31\times 10^{3}$	$4$	$2^{4} \cdot 3^{4} \cdot 7^{4}$	1.1	$2.0, 2.0$	$2$	$1$	$0$	$0.728720$	Modular form 1764.3.c.c
4-42e4-1.1-c2e2-0-2	$6.93$	$2.31\times 10^{3}$	$4$	$2^{4} \cdot 3^{4} \cdot 7^{4}$	1.1	$2.0, 2.0$	$2$	$1$	$0$	$0.243626$	Modular form 1764.3.d.b
4-42e4-1.1-c2e2-0-3	$6.93$	$2.31\times 10^{3}$	$4$	$2^{4} \cdot 3^{4} \cdot 7^{4}$	1.1	$2.0, 2.0$	$2$	$1$	$0$	$0.366986$	Modular form 1764.3.z.b
4-42e4-1.1-c2e2-0-4	$6.93$	$2.31\times 10^{3}$	$4$	$2^{4} \cdot 3^{4} \cdot 7^{4}$	1.1	$2.0, 2.0$	$2$	$1$	$0$	$0.375096$	Modular form 1764.3.c.b
4-42e4-1.1-c2e2-0-5	$6.93$	$2.31\times 10^{3}$	$4$	$2^{4} \cdot 3^{4} \cdot 7^{4}$	1.1	$2.0, 2.0$	$2$	$1$	$0$	$0.436877$	Modular form 1764.3.z.d
4-42e4-1.1-c2e2-0-6	$6.93$	$2.31\times 10^{3}$	$4$	$2^{4} \cdot 3^{4} \cdot 7^{4}$	1.1	$2.0, 2.0$	$2$	$1$	$0$	$0.531802$	Modular form 1764.3.c.a
4-42e4-1.1-c2e2-0-7	$6.93$	$2.31\times 10^{3}$	$4$	$2^{4} \cdot 3^{4} \cdot 7^{4}$	1.1	$2.0, 2.0$	$2$	$1$	$0$	$0.542571$	Modular form 1764.3.c.d
4-42e4-1.1-c2e2-0-8	$6.93$	$2.31\times 10^{3}$	$4$	$2^{4} \cdot 3^{4} \cdot 7^{4}$	1.1	$2.0, 2.0$	$2$	$1$	$0$	$0.577347$	Modular form 1764.3.d.a
4-42e4-1.1-c2e2-0-9	$6.93$	$2.31\times 10^{3}$	$4$	$2^{4} \cdot 3^{4} \cdot 7^{4}$	1.1	$2.0, 2.0$	$2$	$1$	$0$	$0.642099$	Modular form 1764.3.d.c
4-42e4-1.1-c3e2-0-0	$10.2$	$1.08\times 10^{4}$	$4$	$2^{4} \cdot 3^{4} \cdot 7^{4}$	1.1	$3.0, 3.0$	$3$	$1$	$0$	$0.183022$	Modular form 1764.4.k.g
4-42e4-1.1-c3e2-0-1	$10.2$	$1.08\times 10^{4}$	$4$	$2^{4} \cdot 3^{4} \cdot 7^{4}$	1.1	$3.0, 3.0$	$3$	$1$	$0$	$0.255756$	Modular form 1764.4.k.c
4-42e4-1.1-c3e2-0-10	$10.2$	$1.08\times 10^{4}$	$4$	$2^{4} \cdot 3^{4} \cdot 7^{4}$	1.1	$3.0, 3.0$	$3$	$1$	$0$	$0.449468$	Modular form 1764.4.k.n
4-42e4-1.1-c3e2-0-11	$10.2$	$1.08\times 10^{4}$	$4$	$2^{4} \cdot 3^{4} \cdot 7^{4}$	1.1	$3.0, 3.0$	$3$	$1$	$0$	$0.457530$	Modular form 1764.4.k.i
4-42e4-1.1-c3e2-0-12	$10.2$	$1.08\times 10^{4}$	$4$	$2^{4} \cdot 3^{4} \cdot 7^{4}$	1.1	$3.0, 3.0$	$3$	$1$	$0$	$0.468112$	Modular form 1764.4.a.s
4-42e4-1.1-c3e2-0-13	$10.2$	$1.08\times 10^{4}$	$4$	$2^{4} \cdot 3^{4} \cdot 7^{4}$	1.1	$3.0, 3.0$	$3$	$1$	$0$	$0.468308$	Modular form 1764.4.k.p

Next Download displayed columns for results to

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Learn more

Refine search

Results (1-50 of 73 matches)

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.