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Level	Weight	Analytic conductor	$Nk^2$	Dim.

Bad $p$	Char.	Primitive character	Character order	Coefficient field

Self-twists	CM/RM discriminant	Inner twist count	Is self-dual	Analytic rank

Coefficient ring index	Coefficient ring gens.		Projective image	Projective image type
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Results (20 matches)

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Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	Image	CM	RM	Self-dual	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	Image	CM	RM	Self-dual	Inner twists	Rank*	$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$	Coefficient ring index	Sato-Tate	$q$-expansion
319.1.d.a	$319$	$1$	319.d	319.d	$2$	$2$	$2$	$0.159$	$\Q(\sqrt{5}) $	$D_{5}$	$\Q(\sqrt{-319}) $	None	✓	$2$	$0$	$-1$	$0$	$-1$	$0$	$1$		$q+(-1+\beta )q^{2}+(1-\beta )q^{4}+(-1+\beta )q^{5}+\cdots$
319.1.d.b	$319$	$1$	319.d	319.d	$2$	$2$	$2$	$0.159$	$\Q(\sqrt{5}) $	$D_{5}$	$\Q(\sqrt{-319}) $	None	✓	$2$	$0$	$1$	$0$	$-1$	$0$	$1$		$q+(1-\beta )q^{2}+(1-\beta )q^{4}+(-1+\beta )q^{5}+\cdots$
1595.1.e.a	$1595$	$1$	1595.e	1595.e	$2$	$1$	$1$	$0.796$	$\Q$	$D_{2}$	$\Q(\sqrt{-319}) $, $\Q(\sqrt{-1595}) $	$\Q(\sqrt{5}) $	✓	$4$	$0$	$0$	$0$	$1$	$0$	$1$		$q+q^{4}+q^{5}-q^{9}-q^{11}+q^{16}+2q^{19}+\cdots$
1595.1.e.b	$1595$	$1$	1595.e	1595.e	$2$	$1$	$1$	$0.796$	$\Q$	$D_{2}$	$\Q(\sqrt{-319}) $, $\Q(\sqrt{-1595}) $	$\Q(\sqrt{5}) $	✓	$4$	$0$	$0$	$0$	$1$	$0$	$1$		$q+q^{4}+q^{5}-q^{9}+q^{11}+q^{16}-2q^{19}+\cdots$
1595.1.e.e	$1595$	$1$	1595.e	1595.e	$2$	$4$	$4$	$0.796$	$\Q(\zeta_{10})$	$D_{10}$	$\Q(\sqrt{-319}) $	None		$4$	$0$	$0$	$0$	$-1$	$0$	$1$		$q+(-\zeta_{10}^{2}-\zeta_{10}^{3})q^{2}+(-1-\zeta_{10}+\cdots)q^{4}+\cdots$
1595.1.e.f	$1595$	$1$	1595.e	1595.e	$2$	$4$	$4$	$0.796$	$\Q(\zeta_{10})$	$D_{10}$	$\Q(\sqrt{-319}) $	None		$4$	$0$	$0$	$0$	$-1$	$0$	$1$		$q+(-\zeta_{10}^{2}-\zeta_{10}^{3})q^{2}+(-1-\zeta_{10}+\cdots)q^{4}+\cdots$
2552.1.k.c	$2552$	$1$	2552.k	2552.k	$2$	$2$	$2$	$1.274$	$\Q(\sqrt{-1}) $	$D_{2}$	$\Q(\sqrt{-22}) $, $\Q(\sqrt{-319}) $	$\Q(\sqrt{58}) $		$8$	$0$	$0$	$0$	$0$	$0$	$1$		$q-iq^{2}-q^{4}+iq^{8}-q^{9}+iq^{11}+\cdots$
2552.1.k.f	$2552$	$1$	2552.k	2552.k	$2$	$8$	$8$	$1.274$	$\Q(\zeta_{20})$	$D_{10}$	$\Q(\sqrt{-319}) $	None		$8$	$0$	$0$	$0$	$0$	$0$	$1$		$q-\zeta_{20}q^{2}+\zeta_{20}^{2}q^{4}+(-\zeta_{20}^{4}-\zeta_{20}^{6}+\cdots)q^{5}+\cdots$
2871.1.h.a	$2871$	$1$	2871.h	319.d	$2$	$1$	$1$	$1.433$	$\Q$	$D_{2}$	$\Q(\sqrt{-87}) $, $\Q(\sqrt{-319}) $	$\Q(\sqrt{33}) $	✓	$4$	$0$	$-2$	$0$	$0$	$0$	$1$		$q-2q^{2}+3q^{4}-4q^{8}+q^{11}+5q^{16}+\cdots$
2871.1.h.b	$2871$	$1$	2871.h	319.d	$2$	$1$	$1$	$1.433$	$\Q$	$D_{2}$	$\Q(\sqrt{-87}) $, $\Q(\sqrt{-319}) $	$\Q(\sqrt{33}) $	✓	$4$	$0$	$2$	$0$	$0$	$0$	$1$		$q+2q^{2}+3q^{4}+4q^{8}-q^{11}+5q^{16}+\cdots$
2871.1.h.d	$2871$	$1$	2871.h	319.d	$2$	$2$	$2$	$1.433$	$\Q(\sqrt{5}) $	$D_{5}$	$\Q(\sqrt{-319}) $	None	✓	$2$	$0$	$-1$	$0$	$1$	$0$	$1$		$q+(-1+\beta )q^{2}+(1-\beta )q^{4}+(1-\beta )q^{5}+\cdots$
2871.1.h.e	$2871$	$1$	2871.h	319.d	$2$	$2$	$2$	$1.433$	$\Q(\sqrt{5}) $	$D_{5}$	$\Q(\sqrt{-319}) $	None	✓	$2$	$0$	$1$	$0$	$1$	$0$	$1$		$q+(1-\beta )q^{2}+(1-\beta )q^{4}+(1-\beta )q^{5}+\cdots$
2871.1.h.g	$2871$	$1$	2871.h	319.d	$2$	$4$	$4$	$1.433$	$\Q(\zeta_{20})^+$	$D_{10}$	$\Q(\sqrt{-319}) $	None	✓	$4$	$0$	$-2$	$0$	$0$	$0$	$1$		$q+\beta _{2}q^{2}-\beta _{2}q^{4}-\beta _{1}q^{5}-q^{8}-\beta _{3}q^{10}+\cdots$
2871.1.h.h	$2871$	$1$	2871.h	319.d	$2$	$4$	$4$	$1.433$	$\Q(\zeta_{20})^+$	$D_{10}$	$\Q(\sqrt{-319}) $	None	✓	$4$	$0$	$2$	$0$	$0$	$0$	$1$		$q-\beta _{2}q^{2}-\beta _{2}q^{4}-\beta _{1}q^{5}+q^{8}+\beta _{3}q^{10}+\cdots$
3509.1.i.a	$3509$	$1$	3509.i	319.i	$10$	$4$	$1$	$1.751$	$\Q(\zeta_{10})$	$D_{5}$	$\Q(\sqrt{-319}) $	None		$4$	$0$	$-3$	$0$	$3$	$0$	$1$		$q+(-1-\zeta_{10}^{2})q^{2}+(1+\zeta_{10}^{2}+\zeta_{10}^{4}+\cdots)q^{4}+\cdots$
3509.1.i.b	$3509$	$1$	3509.i	319.i	$10$	$4$	$1$	$1.751$	$\Q(\zeta_{10})$	$D_{5}$	$\Q(\sqrt{-319}) $	None		$4$	$0$	$-2$	$0$	$-2$	$0$	$1$		$q+(-\zeta_{10}^{3}+\zeta_{10}^{4})q^{2}+(-\zeta_{10}+\zeta_{10}^{2}+\cdots)q^{4}+\cdots$
3509.1.i.c	$3509$	$1$	3509.i	319.i	$10$	$4$	$1$	$1.751$	$\Q(\zeta_{10})$	$D_{5}$	$\Q(\sqrt{-319}) $	None		$4$	$0$	$2$	$0$	$-2$	$0$	$1$		$q+(\zeta_{10}^{3}-\zeta_{10}^{4})q^{2}+(-\zeta_{10}+\zeta_{10}^{2}+\cdots)q^{4}+\cdots$
3509.1.i.d	$3509$	$1$	3509.i	319.i	$10$	$4$	$1$	$1.751$	$\Q(\zeta_{10})$	$D_{5}$	$\Q(\sqrt{-319}) $	None		$4$	$0$	$3$	$0$	$3$	$0$	$1$		$q+(1+\zeta_{10}^{2})q^{2}+(1+\zeta_{10}^{2}+\zeta_{10}^{4}+\cdots)q^{4}+\cdots$
319.3.d.a	$319$	$3$	319.d	319.d	$2$	$5$	$5$	$8.692$	5.5.318003125.1	$_{}$	$\Q(\sqrt{-319}) $	None	✓	$2$	$0$	$0$	$0$	$0$	$0$	$1$	$\mathrm{U}(1)[D_{2}]$	$q+\beta _{1}q^{2}+(4+\beta _{3})q^{4}+(-\beta _{1}-\beta _{4})q^{5}+\cdots$
319.3.d.b	$319$	$3$	319.d	319.d	$2$	$5$	$5$	$8.692$	5.5.318003125.1	$_{}$	$\Q(\sqrt{-319}) $	None	✓	$2$	$0$	$0$	$0$	$0$	$0$	$1$	$\mathrm{U}(1)[D_{2}]$	$q-\beta _{1}q^{2}+(4+\beta _{3})q^{4}+(-\beta _{1}-\beta _{4})q^{5}+\cdots$

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Elliptic curves over $\Q$
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Genus 2 curves over $\Q$
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This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.