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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
248.1.g.a	$248$	$1$	248.g	248.g	$2$	$1$	$1$	$0.124$	$\Q$	$D_{2}$	$\Q(\sqrt{-31}) $, $\Q(\sqrt{-62}) $	$\Q(\sqrt{2}) $	✓	$4$	$0$	$1$	$0$	$0$	$-2$	$1$		$q+q^{2}+q^{4}-2q^{7}+q^{8}-q^{9}-2q^{14}+\cdots$
248.1.g.b	$248$	$1$	248.g	248.g	$2$	$2$	$2$	$0.124$	$\Q(\sqrt{2}) $	$D_{4}$	$\Q(\sqrt{-62}) $	None	✓	$4$	$0$	$-2$	$0$	$0$	$0$	$1$		$q-q^{2}-\beta q^{3}+q^{4}+\beta q^{6}-q^{8}+q^{9}+\cdots$
992.1.g.a	$992$	$1$	992.g	248.g	$2$	$1$	$1$	$0.495$	$\Q$	$D_{2}$	$\Q(\sqrt{-31}) $, $\Q(\sqrt{-62}) $	$\Q(\sqrt{2}) $	✓	$4$	$0$	$0$	$0$	$0$	$2$	$1$		$q+2q^{7}-q^{9}+q^{25}-q^{31}-2q^{41}+\cdots$
992.1.g.c	$992$	$1$	992.g	248.g	$2$	$2$	$2$	$0.495$	$\Q(\sqrt{2}) $	$D_{4}$	$\Q(\sqrt{-62}) $	None	✓	$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q-\beta q^{3}+q^{9}+\beta q^{11}-\beta q^{13}+q^{25}+\cdots$
1736.1.br.a	$1736$	$1$	1736.br	1736.ar	$6$	$2$	$1$	$0.866$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-62}) $	None		$4$	$0$	$-1$	$-1$	$0$	$-1$	$1$		$q+\zeta_{6}^{2}q^{2}-\zeta_{6}q^{3}-\zeta_{6}q^{4}+q^{6}-\zeta_{6}q^{7}+\cdots$
1736.1.br.b	$1736$	$1$	1736.br	1736.ar	$6$	$2$	$1$	$0.866$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-62}) $	None		$4$	$0$	$-1$	$1$	$0$	$-1$	$1$		$q+\zeta_{6}^{2}q^{2}+\zeta_{6}q^{3}-\zeta_{6}q^{4}-q^{6}-\zeta_{6}q^{7}+\cdots$
1736.1.br.c	$1736$	$1$	1736.br	1736.ar	$6$	$4$	$2$	$0.866$	$\Q(\zeta_{12})$	$D_{6}$	$\Q(\sqrt{-62}) $	None		$8$	$0$	$-2$	$0$	$0$	$2$	$3$		$q-\zeta_{12}^{2}q^{2}+(-\zeta_{12}^{3}-\zeta_{12}^{5})q^{3}+\cdots$
1736.1.br.f	$1736$	$1$	1736.br	1736.ar	$6$	$8$	$4$	$0.866$	$\Q(\zeta_{24})$	$D_{12}$	$\Q(\sqrt{-62}) $	None		$8$	$0$	$4$	$0$	$0$	$0$	$1$		$q+\zeta_{24}^{4}q^{2}+(\zeta_{24}^{7}+\zeta_{24}^{9})q^{3}+\zeta_{24}^{8}q^{4}+\cdots$
2232.1.i.a	$2232$	$1$	2232.i	248.g	$2$	$1$	$1$	$1.114$	$\Q$	$D_{2}$	$\Q(\sqrt{-31}) $, $\Q(\sqrt{-62}) $	$\Q(\sqrt{2}) $	✓	$4$	$0$	$-1$	$0$	$0$	$-2$	$1$		$q-q^{2}+q^{4}-2q^{7}-q^{8}+2q^{14}+q^{16}+\cdots$
2232.1.i.d	$2232$	$1$	2232.i	248.g	$2$	$2$	$2$	$1.114$	$\Q(\sqrt{2}) $	$D_{4}$	$\Q(\sqrt{-62}) $	None	✓	$4$	$0$	$2$	$0$	$0$	$0$	$1$		$q+q^{2}+q^{4}+q^{8}-\beta q^{11}+\beta q^{13}+\cdots$
2232.1.ca.a	$2232$	$1$	2232.ca	2232.ba	$6$	$2$	$1$	$1.114$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-62}) $	None		$4$	$0$	$-1$	$-1$	$0$	$1$	$1$		$q-\zeta_{6}q^{2}-\zeta_{6}q^{3}+\zeta_{6}^{2}q^{4}+\zeta_{6}^{2}q^{6}+\cdots$
2232.1.ca.b	$2232$	$1$	2232.ca	2232.ba	$6$	$2$	$1$	$1.114$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-62}) $	None		$4$	$0$	$-1$	$1$	$0$	$1$	$1$		$q-\zeta_{6}q^{2}+\zeta_{6}q^{3}+\zeta_{6}^{2}q^{4}-\zeta_{6}^{2}q^{6}+\cdots$
2232.1.ca.c	$2232$	$1$	2232.ca	2232.ba	$6$	$4$	$2$	$1.114$	$\Q(\zeta_{12})$	$D_{6}$	$\Q(\sqrt{-62}) $	None		$8$	$0$	$-2$	$0$	$0$	$-2$	$1$		$q+\zeta_{12}^{4}q^{2}-\zeta_{12}q^{3}-\zeta_{12}^{2}q^{4}-\zeta_{12}^{5}q^{6}+\cdots$
2232.1.ca.d	$2232$	$1$	2232.ca	2232.ba	$6$	$8$	$4$	$1.114$	$\Q(\zeta_{24})$	$D_{12}$	$\Q(\sqrt{-62}) $	None		$8$	$0$	$4$	$0$	$0$	$0$	$1$		$q-\zeta_{24}^{8}q^{2}-\zeta_{24}^{5}q^{3}-\zeta_{24}^{4}q^{4}+\cdots$
2728.1.co.a	$2728$	$1$	2728.co	2728.bo	$10$	$4$	$1$	$1.361$	$\Q(\zeta_{10})$	$D_{5}$	$\Q(\sqrt{-62}) $	None		$4$	$0$	$-1$	$-3$	$0$	$3$	$1$		$q-\zeta_{10}q^{2}+(-1+\zeta_{10})q^{3}+\zeta_{10}^{2}q^{4}+\cdots$
2728.1.co.b	$2728$	$1$	2728.co	2728.bo	$10$	$4$	$1$	$1.361$	$\Q(\zeta_{10})$	$D_{5}$	$\Q(\sqrt{-62}) $	None		$4$	$0$	$-1$	$3$	$0$	$3$	$1$		$q-\zeta_{10}q^{2}+(1-\zeta_{10})q^{3}+\zeta_{10}^{2}q^{4}+\cdots$
2728.1.co.c	$2728$	$1$	2728.co	2728.bo	$10$	$8$	$2$	$1.361$	$\Q(\zeta_{20})$	$D_{10}$	$\Q(\sqrt{-62}) $	None		$8$	$0$	$-2$	$0$	$0$	$-6$	$1$		$q-\zeta_{20}^{2}q^{2}+(\zeta_{20}^{5}+\zeta_{20}^{7})q^{3}+\zeta_{20}^{4}q^{4}+\cdots$
2728.1.co.d	$2728$	$1$	2728.co	2728.bo	$10$	$16$	$4$	$1.361$	$\Q(\zeta_{40})$	$D_{20}$	$\Q(\sqrt{-62}) $	None		$8$	$0$	$4$	$0$	$0$	$0$	$1$		$q+\zeta_{40}^{4}q^{2}+(\zeta_{40}^{9}+\zeta_{40}^{15})q^{3}+\zeta_{40}^{8}q^{4}+\cdots$
3224.1.n.e	$3224$	$1$	3224.n	3224.n	$2$	$8$	$8$	$1.609$	$\Q(\zeta_{16})$	$D_{8}$	$\Q(\sqrt{-62}) $	None		$8$	$0$	$0$	$0$	$0$	$0$	$1$		$q-\zeta_{16}^{4}q^{2}+(\zeta_{16}^{3}-\zeta_{16}^{5})q^{3}-q^{4}+\cdots$
3224.1.bl.a	$3224$	$1$	3224.bl	3224.al	$6$	$2$	$1$	$1.609$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-62}) $	None		$4$	$0$	$-1$	$-1$	$0$	$-2$	$1$		$q-\zeta_{6}q^{2}-\zeta_{6}q^{3}+\zeta_{6}^{2}q^{4}+\zeta_{6}^{2}q^{6}+\cdots$
3224.1.bl.b	$3224$	$1$	3224.bl	3224.al	$6$	$2$	$1$	$1.609$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-62}) $	None		$4$	$0$	$-1$	$1$	$0$	$-2$	$1$		$q-\zeta_{6}q^{2}+\zeta_{6}q^{3}+\zeta_{6}^{2}q^{4}-\zeta_{6}^{2}q^{6}+\cdots$
3224.1.bl.c	$3224$	$1$	3224.bl	3224.al	$6$	$4$	$2$	$1.609$	$\Q(\zeta_{12})$	$D_{6}$	$\Q(\sqrt{-62}) $	None		$8$	$0$	$-2$	$0$	$0$	$4$	$1$		$q+\zeta_{12}^{4}q^{2}+(-\zeta_{12}^{3}-\zeta_{12}^{5})q^{3}+\cdots$
3224.1.bl.d	$3224$	$1$	3224.bl	3224.al	$6$	$8$	$4$	$1.609$	$\Q(\zeta_{24})$	$D_{12}$	$\Q(\sqrt{-62}) $	None		$8$	$0$	$4$	$0$	$0$	$0$	$1$		$q-\zeta_{24}^{8}q^{2}+(\zeta_{24}^{7}+\zeta_{24}^{9})q^{3}-\zeta_{24}^{4}q^{4}+\cdots$
3224.1.cf.a	$3224$	$1$	3224.cf	3224.bf	$6$	$16$	$8$	$1.609$	$\Q(\zeta_{48})$	$D_{24}$	$\Q(\sqrt{-62}) $	None		$8$	$0$	$0$	$0$	$0$	$0$	$1$		$q-\zeta_{48}^{4}q^{2}+(-\zeta_{48}^{15}-\zeta_{48}^{17})q^{3}+\cdots$
3968.1.g.a	$3968$	$1$	3968.g	248.g	$2$	$4$	$4$	$1.980$	$\Q(\zeta_{16})^+$	$D_{8}$	$\Q(\sqrt{-62}) $	None	✓	$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q-\beta _{3}q^{3}+\beta _{2}q^{7}+(1-\beta _{2})q^{9}-\beta _{1}q^{11}+\cdots$
3968.1.g.b	$3968$	$1$	3968.g	248.g	$2$	$4$	$4$	$1.980$	$\Q(\zeta_{16})^+$	$D_{8}$	$\Q(\sqrt{-62}) $	None	✓	$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q-\beta _{3}q^{3}-\beta _{2}q^{7}+(1-\beta _{2})q^{9}-\beta _{1}q^{11}+\cdots$
744.2.o.d	$744$	$2$	744.o	744.o	$2$	$16$	$16$	$5.941$	$\mathbb{Q}[x]/(x^{16} + \cdots)$	$_{}$	$\Q(\sqrt{-62}) $	None		$8$	$0$	$0$	$0$	$0$	$0$	$2^{7}\cdot 3^{3}$	$\mathrm{U}(1)[D_{2}]$	$q+\beta _{4}q^{2}+\beta _{1}q^{3}-2q^{4}+\beta _{9}q^{6}+\beta _{6}q^{7}+\cdots$
248.3.g.a	$248$	$3$	248.g	248.g	$2$	$4$	$4$	$6.758$	4.4.492032.1	$_{}$	$\Q(\sqrt{-62}) $	None	✓	$4$	$0$	$-8$	$0$	$0$	$0$	$2^{3}$	$\mathrm{U}(1)[D_{2}]$	$q-2q^{2}+\beta _{1}q^{3}+4q^{4}-2\beta _{1}q^{6}-\beta _{3}q^{7}+\cdots$
248.3.g.b	$248$	$3$	248.g	248.g	$2$	$4$	$4$	$6.758$	4.4.31744.1	$_{}$	$\Q(\sqrt{-62}) $	None	✓	$4$	$0$	$8$	$0$	$0$	$0$	$2^{3}$	$\mathrm{U}(1)[D_{2}]$	$q+2q^{2}+\beta _{1}q^{3}+4q^{4}+2\beta _{1}q^{6}+3\beta _{3}q^{7}+\cdots$
1984.2.b.b	$1984$	$2$	1984.b	248.b	$2$	$16$	$16$	$15.842$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	$_{}$	$\Q(\sqrt{-62}) $	None		$8$	$0$	$0$	$0$	$0$	$0$	$2^{22}$	$\mathrm{U}(1)[D_{2}]$	$q-\beta _{5}q^{3}-\beta _{3}q^{7}+(-3+\beta _{8})q^{9}-\beta _{2}q^{11}+\cdots$
992.3.g.a	$992$	$3$	992.g	248.g	$2$	$4$	$4$	$27.030$	4.4.492032.1	$_{}$	$\Q(\sqrt{-62}) $	None	✓	$4$	$0$	$0$	$0$	$0$	$0$	$2^{3}$	$\mathrm{U}(1)[D_{2}]$	$q+\beta _{1}q^{3}+\beta _{3}q^{7}+(9+\beta _{3})q^{9}+(3\beta _{1}+\cdots)q^{11}+\cdots$
992.3.g.b	$992$	$3$	992.g	248.g	$2$	$4$	$4$	$27.030$	4.4.31744.1	$_{}$	$\Q(\sqrt{-62}) $	None	✓	$4$	$0$	$0$	$0$	$0$	$0$	$2^{3}$	$\mathrm{U}(1)[D_{2}]$	$q+\beta _{1}q^{3}-3\beta _{3}q^{7}+(9-5\beta _{3})q^{9}+(-3\beta _{1}+\cdots)q^{11}+\cdots$

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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.