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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 (32 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
299.1.c.a	$299$	$1$	299.c	299.c	$2$	$1$	$1$	$0.149$	$\Q$	$D_{2}$	$\Q(\sqrt{-23}) $, $\Q(\sqrt{-299}) $	$\Q(\sqrt{13}) $	✓	$4$	$0$	$0$	$-2$	$0$	$0$	$1$		$q-2q^{3}+q^{4}+3q^{9}-2q^{12}+q^{13}+\cdots$
299.1.c.b	$299$	$1$	299.c	299.c	$2$	$2$	$2$	$0.149$	$\Q(\sqrt{2}) $	$D_{4}$	$\Q(\sqrt{-299}) $	None	✓	$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q+q^{4}-\beta q^{5}+\beta q^{7}-q^{9}+\beta q^{11}+\cdots$
1196.1.h.a	$1196$	$1$	1196.h	299.c	$2$	$1$	$1$	$0.597$	$\Q$	$D_{3}$	$\Q(\sqrt{-299}) $	None	✓	$2$	$0$	$0$	$-1$	$-1$	$2$	$1$		$q-q^{3}-q^{5}+2q^{7}-q^{11}+q^{13}+q^{15}+\cdots$
1196.1.h.b	$1196$	$1$	1196.h	299.c	$2$	$1$	$1$	$0.597$	$\Q$	$D_{3}$	$\Q(\sqrt{-299}) $	None	✓	$2$	$0$	$0$	$-1$	$1$	$-2$	$1$		$q-q^{3}+q^{5}-2q^{7}+q^{11}+q^{13}-q^{15}+\cdots$
1196.1.h.c	$1196$	$1$	1196.h	299.c	$2$	$2$	$2$	$0.597$	$\Q(\sqrt{3}) $	$D_{6}$	$\Q(\sqrt{-299}) $	None	✓	$4$	$0$	$0$	$2$	$0$	$0$	$1$		$q+q^{3}-\beta q^{5}+\beta q^{11}+q^{13}-\beta q^{15}+\cdots$
1196.1.h.d	$1196$	$1$	1196.h	299.c	$2$	$4$	$4$	$0.597$	$\Q(\zeta_{24})^+$	$D_{12}$	$\Q(\sqrt{-299}) $	None	✓	$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q-\beta _{2}q^{3}-\beta _{1}q^{5}+(-\beta _{1}-\beta _{3})q^{7}+\cdots$
1495.1.f.e	$1495$	$1$	1495.f	1495.f	$2$	$8$	$8$	$0.746$	$\Q(\zeta_{16})$	$D_{8}$	$\Q(\sqrt{-299}) $	None		$8$	$0$	$0$	$0$	$0$	$0$	$1$		$q+(-\zeta_{16}^{2}-\zeta_{16}^{6})q^{3}-q^{4}-\zeta_{16}q^{5}+\cdots$
2093.1.bg.a	$2093$	$1$	2093.bg	2093.ag	$6$	$2$	$1$	$1.045$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-299}) $	None		$4$	$0$	$0$	$1$	$-2$	$2$	$1$		$q+\zeta_{6}q^{3}-\zeta_{6}q^{4}+\zeta_{6}^{2}q^{5}+q^{7}+\zeta_{6}q^{11}+\cdots$
2093.1.bg.b	$2093$	$1$	2093.bg	2093.ag	$6$	$2$	$1$	$1.045$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-299}) $	None		$4$	$0$	$0$	$1$	$2$	$-2$	$1$		$q+\zeta_{6}q^{3}-\zeta_{6}q^{4}-\zeta_{6}^{2}q^{5}-q^{7}-\zeta_{6}q^{11}+\cdots$
2093.1.bg.c	$2093$	$1$	2093.bg	2093.ag	$6$	$4$	$2$	$1.045$	$\Q(\zeta_{12})$	$D_{6}$	$\Q(\sqrt{-299}) $	None		$8$	$0$	$0$	$-2$	$0$	$0$	$1$		$q+\zeta_{12}^{4}q^{3}+\zeta_{12}^{4}q^{4}-\zeta_{12}^{3}q^{7}+\cdots$
2093.1.bg.d	$2093$	$1$	2093.bg	2093.ag	$6$	$8$	$4$	$1.045$	$\Q(\zeta_{24})$	$D_{12}$	$\Q(\sqrt{-299}) $	None		$8$	$0$	$0$	$0$	$0$	$0$	$1$		$q+(-\zeta_{24}^{6}-\zeta_{24}^{10})q^{3}+\zeta_{24}^{8}q^{4}+\cdots$
2691.1.e.a	$2691$	$1$	2691.e	299.c	$2$	$1$	$1$	$1.343$	$\Q$	$D_{2}$	$\Q(\sqrt{-23}) $, $\Q(\sqrt{-299}) $	$\Q(\sqrt{13}) $	✓	$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q+q^{4}+q^{13}+q^{16}-q^{23}-q^{25}+\cdots$
2691.1.e.c	$2691$	$1$	2691.e	299.c	$2$	$2$	$2$	$1.343$	$\Q(\sqrt{2}) $	$D_{4}$	$\Q(\sqrt{-299}) $	None	✓	$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q+q^{4}-\beta q^{5}-\beta q^{7}+\beta q^{11}-q^{13}+\cdots$
2691.1.bg.a	$2691$	$1$	2691.bg	2691.ag	$6$	$2$	$1$	$1.343$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-299}) $	None		$4$	$0$	$0$	$-1$	$-2$	$1$	$1$		$q-\zeta_{6}q^{3}+\zeta_{6}^{2}q^{4}+\zeta_{6}^{2}q^{5}+\zeta_{6}q^{7}+\cdots$
2691.1.bg.b	$2691$	$1$	2691.bg	2691.ag	$6$	$2$	$1$	$1.343$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-299}) $	None		$4$	$0$	$0$	$-1$	$2$	$-1$	$1$		$q-\zeta_{6}q^{3}+\zeta_{6}^{2}q^{4}-\zeta_{6}^{2}q^{5}-\zeta_{6}q^{7}+\cdots$
2691.1.bg.c	$2691$	$1$	2691.bg	2691.ag	$6$	$4$	$2$	$1.343$	$\Q(\zeta_{12})$	$D_{6}$	$\Q(\sqrt{-299}) $	None		$8$	$0$	$0$	$2$	$0$	$0$	$3$		$q-\zeta_{12}^{4}q^{3}-\zeta_{12}^{2}q^{4}+(-\zeta_{12}^{3}-\zeta_{12}^{5}+\cdots)q^{7}+\cdots$
2691.1.bg.f	$2691$	$1$	2691.bg	2691.ag	$6$	$8$	$4$	$1.343$	$\Q(\zeta_{24})$	$D_{12}$	$\Q(\sqrt{-299}) $	None		$8$	$0$	$0$	$0$	$0$	$0$	$1$		$q+\zeta_{24}^{10}q^{3}+\zeta_{24}^{8}q^{4}+(-\zeta_{24}^{5}+\cdots)q^{5}+\cdots$
3289.1.y.a	$3289$	$1$	3289.y	3289.y	$10$	$4$	$1$	$1.641$	$\Q(\zeta_{10})$	$D_{5}$	$\Q(\sqrt{-299}) $	None		$4$	$0$	$0$	$3$	$-2$	$-2$	$1$		$q+(1+\zeta_{10}^{2})q^{3}+\zeta_{10}^{4}q^{4}+(\zeta_{10}^{2}+\cdots)q^{5}+\cdots$
3289.1.y.b	$3289$	$1$	3289.y	3289.y	$10$	$4$	$1$	$1.641$	$\Q(\zeta_{10})$	$D_{5}$	$\Q(\sqrt{-299}) $	None		$4$	$0$	$0$	$3$	$2$	$2$	$1$		$q+(1+\zeta_{10}^{2})q^{3}+\zeta_{10}^{4}q^{4}+(-\zeta_{10}^{2}+\cdots)q^{5}+\cdots$
3289.1.y.c	$3289$	$1$	3289.y	3289.y	$10$	$8$	$2$	$1.641$	$\Q(\zeta_{20})$	$D_{10}$	$\Q(\sqrt{-299}) $	None		$8$	$0$	$0$	$-6$	$0$	$0$	$1$		$q+(-1-\zeta_{20}^{4})q^{3}+\zeta_{20}^{8}q^{4}+(-\zeta_{20}^{3}+\cdots)q^{5}+\cdots$
3289.1.y.d	$3289$	$1$	3289.y	3289.y	$10$	$16$	$4$	$1.641$	$\Q(\zeta_{40})$	$D_{20}$	$\Q(\sqrt{-299}) $	None		$8$	$0$	$0$	$0$	$0$	$0$	$1$		$q+(-\zeta_{40}^{6}-\zeta_{40}^{10})q^{3}-\zeta_{40}^{12}q^{4}+\cdots$
3887.1.d.a	$3887$	$1$	3887.d	23.b	$2$	$1$	$1$	$1.940$	$\Q$	$D_{2}$	$\Q(\sqrt{-23}) $, $\Q(\sqrt{-299}) $	$\Q(\sqrt{13}) $	✓	$4$	$0$	$0$	$-2$	$0$	$0$	$1$		$q-2q^{3}-q^{4}+3q^{9}+2q^{12}+q^{16}+\cdots$
3887.1.d.c	$3887$	$1$	3887.d	23.b	$2$	$2$	$2$	$1.940$	$\Q(\sqrt{-2}) $	$D_{4}$	$\Q(\sqrt{-299}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q-q^{4}-\beta q^{5}-\beta q^{7}-q^{9}-\beta q^{11}+\cdots$
3887.1.h.b	$3887$	$1$	3887.h	299.h	$6$	$2$	$1$	$1.940$	$\Q(\sqrt{-3}) $	$D_{2}$	$\Q(\sqrt{-23}) $, $\Q(\sqrt{-299}) $	$\Q(\sqrt{13}) $		$8$	$0$	$0$	$2$	$0$	$0$	$1$		$q+\zeta_{6}q^{3}-\zeta_{6}^{2}q^{4}+3\zeta_{6}^{2}q^{9}+2q^{12}+\cdots$
3887.1.h.e	$3887$	$1$	3887.h	299.h	$6$	$4$	$2$	$1.940$	$\Q(\sqrt{-2}, \sqrt{-3})$	$D_{4}$	$\Q(\sqrt{-299}) $	None		$8$	$0$	$0$	$0$	$0$	$0$	$1$		$q+(1-\beta _{2})q^{4}-\beta _{3}q^{5}+\beta _{1}q^{7}+(1-\beta _{2}+\cdots)q^{9}+\cdots$
3887.1.j.b	$3887$	$1$	3887.j	299.j	$6$	$2$	$1$	$1.940$	$\Q(\sqrt{-3}) $	$D_{2}$	$\Q(\sqrt{-23}) $, $\Q(\sqrt{-299}) $	$\Q(\sqrt{13}) $		$8$	$0$	$0$	$2$	$0$	$0$	$1$		$q+\zeta_{6}q^{3}+\zeta_{6}^{2}q^{4}+3\zeta_{6}^{2}q^{9}-2q^{12}+\cdots$
3887.1.j.d	$3887$	$1$	3887.j	299.j	$6$	$4$	$2$	$1.940$	$\Q(\sqrt{2}, \sqrt{-3})$	$D_{4}$	$\Q(\sqrt{-299}) $	None		$8$	$0$	$0$	$0$	$0$	$0$	$1$		$q+(-1-\beta _{2})q^{4}-\beta _{3}q^{5}+\beta _{1}q^{7}+(1+\cdots)q^{9}+\cdots$
897.2.g.c	$897$	$2$	897.g	897.g	$2$	$16$	$16$	$7.163$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	$_{}$	$\Q(\sqrt{-299}) $	None		$8$	$0$	$0$	$0$	$0$	$0$	$2^{8}\cdot 3^{4}$	$\mathrm{U}(1)[D_{2}]$	$q+\beta _{4}q^{3}-2q^{4}+\beta _{12}q^{5}+\beta _{10}q^{7}+\cdots$
299.3.c.a	$299$	$3$	299.c	299.c	$2$	$4$	$4$	$8.147$	4.4.62192.1	$_{}$	$\Q(\sqrt{-299}) $	None	✓	$4$	$0$	$0$	$0$	$0$	$0$	$2^{2}\cdot 3$	$\mathrm{U}(1)[D_{2}]$	$q+\beta _{3}q^{3}+4q^{4}-\beta _{2}q^{5}+(\beta _{1}-\beta _{2}+\cdots)q^{7}+\cdots$
299.3.c.b	$299$	$3$	299.c	299.c	$2$	$4$	$4$	$8.147$	4.4.1760512.1	$_{}$	$\Q(\sqrt{-299}) $	None	✓	$4$	$0$	$0$	$0$	$0$	$0$	$1$	$\mathrm{U}(1)[D_{2}]$	$q+\beta _{2}q^{3}+4q^{4}+\beta _{3}q^{5}+(-3\beta _{1}-\beta _{3})q^{7}+\cdots$
1196.3.h.a	$1196$	$3$	1196.h	299.c	$2$	$8$	$8$	$32.589$	8.8.$\cdots$.18	$_{}$	$\Q(\sqrt{-299}) $	None	✓	$4$	$0$	$0$	$0$	$0$	$0$	$2^{5}$	$\mathrm{U}(1)[D_{2}]$	$q+\beta _{4}q^{3}+\beta _{2}q^{5}+(\beta _{1}+\beta _{2}-2\beta _{3}+\cdots)q^{7}+\cdots$
1196.3.h.b	$1196$	$3$	1196.h	299.c	$2$	$8$	$8$	$32.589$	8.8.$\cdots$.8	$_{}$	$\Q(\sqrt{-299}) $	None	✓	$4$	$0$	$0$	$0$	$0$	$0$	$2^{8}\cdot 3$	$\mathrm{U}(1)[D_{2}]$	$q+\beta _{1}q^{3}+\beta _{3}q^{5}+(-\beta _{3}+\beta _{4}-\beta _{6}+\cdots)q^{7}+\cdots$

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Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
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.