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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 (24 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
247.1.d.a	$247$	$1$	247.d	247.d	$2$	$1$	$1$	$0.123$	$\Q$	$D_{3}$	$\Q(\sqrt{-247}) $	None	✓	$2$	$0$	$-1$	$0$	$0$	$0$	$1$		$q-q^{2}+q^{8}+q^{9}+q^{13}-q^{16}-q^{17}+\cdots$
247.1.d.b	$247$	$1$	247.d	247.d	$2$	$1$	$1$	$0.123$	$\Q$	$D_{3}$	$\Q(\sqrt{-247}) $	None	✓	$2$	$0$	$1$	$0$	$0$	$0$	$1$		$q+q^{2}-q^{8}+q^{9}-q^{13}-q^{16}-q^{17}+\cdots$
1976.1.o.a	$1976$	$1$	1976.o	1976.o	$2$	$2$	$2$	$0.986$	$\Q(\sqrt{-1}) $	$D_{2}$	$\Q(\sqrt{-38}) $, $\Q(\sqrt{-247}) $	$\Q(\sqrt{26}) $		$8$	$0$	$0$	$0$	$0$	$0$	$1$		$q-iq^{2}-q^{4}+iq^{8}-q^{9}+iq^{13}+\cdots$
1976.1.o.g	$1976$	$1$	1976.o	1976.o	$2$	$4$	$4$	$0.986$	$\Q(\zeta_{12})$	$D_{6}$	$\Q(\sqrt{-247}) $	None		$8$	$0$	$0$	$0$	$0$	$0$	$1$		$q-\zeta_{12}q^{2}+\zeta_{12}^{2}q^{4}-\zeta_{12}^{3}q^{8}-q^{9}+\cdots$
2223.1.f.a	$2223$	$1$	2223.f	247.d	$2$	$1$	$1$	$1.109$	$\Q$	$D_{3}$	$\Q(\sqrt{-247}) $	None	✓	$2$	$0$	$-1$	$0$	$0$	$0$	$1$		$q-q^{2}+q^{8}-q^{13}-q^{16}+q^{17}-q^{19}+\cdots$
2223.1.f.b	$2223$	$1$	2223.f	247.d	$2$	$1$	$1$	$1.109$	$\Q$	$D_{2}$	$\Q(\sqrt{-3}) $, $\Q(\sqrt{-247}) $	$\Q(\sqrt{741}) $	✓	$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q-q^{4}-q^{13}+q^{16}+q^{19}+q^{25}+\cdots$
2223.1.f.c	$2223$	$1$	2223.f	247.d	$2$	$1$	$1$	$1.109$	$\Q$	$D_{2}$	$\Q(\sqrt{-3}) $, $\Q(\sqrt{-247}) $	$\Q(\sqrt{741}) $	✓	$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q-q^{4}+q^{13}+q^{16}-q^{19}+q^{25}+\cdots$
2223.1.f.d	$2223$	$1$	2223.f	247.d	$2$	$1$	$1$	$1.109$	$\Q$	$D_{3}$	$\Q(\sqrt{-247}) $	None	✓	$2$	$0$	$1$	$0$	$0$	$0$	$1$		$q+q^{2}-q^{8}+q^{13}-q^{16}+q^{17}+q^{19}+\cdots$
2223.1.f.e	$2223$	$1$	2223.f	247.d	$2$	$2$	$2$	$1.109$	$\Q(\sqrt{3}) $	$D_{6}$	$\Q(\sqrt{-247}) $	None	✓	$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q-\beta q^{2}+2q^{4}-\beta q^{8}-q^{13}+q^{16}+\cdots$
2223.1.f.f	$2223$	$1$	2223.f	247.d	$2$	$2$	$2$	$1.109$	$\Q(\sqrt{3}) $	$D_{6}$	$\Q(\sqrt{-247}) $	None	✓	$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q-\beta q^{2}+2q^{4}-\beta q^{8}+q^{13}+q^{16}+\cdots$
3211.1.b.a	$3211$	$1$	3211.b	19.b	$2$	$2$	$2$	$1.602$	$\Q(\sqrt{-1}) $	$D_{3}$	$\Q(\sqrt{-247}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q-iq^{2}-iq^{8}+q^{9}-q^{16}+q^{17}+\cdots$
3211.1.m.a	$3211$	$1$	3211.m	247.m	$6$	$2$	$1$	$1.602$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-247}) $	None		$4$	$0$	$-1$	$0$	$0$	$0$	$1$		$q+\zeta_{6}^{2}q^{2}-q^{8}-\zeta_{6}q^{9}-\zeta_{6}^{2}q^{16}+\cdots$
3211.1.m.b	$3211$	$1$	3211.m	247.m	$6$	$2$	$1$	$1.602$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-247}) $	None		$4$	$0$	$1$	$0$	$0$	$0$	$1$		$q-\zeta_{6}^{2}q^{2}+q^{8}-\zeta_{6}q^{9}-\zeta_{6}^{2}q^{16}+\cdots$
3211.1.u.a	$3211$	$1$	3211.u	247.u	$6$	$4$	$2$	$1.602$	$\Q(\zeta_{12})$	$D_{3}$	$\Q(\sqrt{-247}) $	None		$8$	$0$	$0$	$0$	$0$	$0$	$1$		$q-\zeta_{12}q^{2}+\zeta_{12}^{3}q^{8}-\zeta_{12}^{2}q^{9}-\zeta_{12}^{4}q^{16}+\cdots$
3952.1.b.a	$3952$	$1$	3952.b	247.d	$2$	$1$	$1$	$1.972$	$\Q$	$D_{3}$	$\Q(\sqrt{-247}) $	None	✓	$2$	$0$	$0$	$0$	$0$	$0$	$1$		$q+q^{9}-q^{13}-q^{17}+q^{19}+q^{23}+\cdots$
3952.1.b.b	$3952$	$1$	3952.b	247.d	$2$	$1$	$1$	$1.972$	$\Q$	$D_{3}$	$\Q(\sqrt{-247}) $	None	✓	$2$	$0$	$0$	$0$	$0$	$0$	$1$		$q+q^{9}+q^{13}-q^{17}-q^{19}+q^{23}+\cdots$
3952.1.bi.a	$3952$	$1$	3952.bi	3952.ai	$4$	$4$	$2$	$1.972$	$\Q(\zeta_{8})$	$D_{4}$	$\Q(\sqrt{-247}) $	None		$8$	$0$	$0$	$0$	$0$	$0$	$1$		$q-\zeta_{8}^{3}q^{2}-\zeta_{8}^{2}q^{4}-\zeta_{8}q^{8}+\zeta_{8}^{2}q^{9}+\cdots$
3952.1.bi.b	$3952$	$1$	3952.bi	3952.ai	$4$	$8$	$4$	$1.972$	$\Q(\zeta_{24})$	$D_{12}$	$\Q(\sqrt{-247}) $	None		$8$	$0$	$0$	$0$	$0$	$0$	$1$		$q-\zeta_{24}^{7}q^{2}-\zeta_{24}^{2}q^{4}+\zeta_{24}^{9}q^{8}+\cdots$
247.3.d.a	$247$	$3$	247.d	247.d	$2$	$3$	$3$	$6.730$	3.3.6669.1	$_{}$	$\Q(\sqrt{-247}) $	None	✓	$2$	$0$	$0$	$0$	$0$	$0$	$1$	$\mathrm{U}(1)[D_{2}]$	$q-\beta _{1}q^{2}+(4+\beta _{2})q^{4}+(-3-4\beta _{1}+\cdots)q^{8}+\cdots$
247.3.d.b	$247$	$3$	247.d	247.d	$2$	$3$	$3$	$6.730$	3.3.6669.1	$_{}$	$\Q(\sqrt{-247}) $	None	✓	$2$	$0$	$0$	$0$	$0$	$0$	$1$	$\mathrm{U}(1)[D_{2}]$	$q+\beta _{1}q^{2}+(4+\beta _{2})q^{4}+(3+4\beta _{1})q^{8}+\cdots$
988.2.g.b	$988$	$2$	988.g	988.g	$2$	$12$	$12$	$7.889$	12.0.$\cdots$.1	$_{}$	$\Q(\sqrt{-247}) $	None		$8$	$0$	$0$	$0$	$0$	$0$	$2^{8}$	$\mathrm{U}(1)[D_{2}]$	$q-\beta _{1}q^{2}+\beta _{2}q^{4}-\beta _{3}q^{8}-3q^{9}+(-\beta _{3}+\cdots)q^{13}+\cdots$
2223.2.d.b	$2223$	$2$	2223.d	741.d	$2$	$24$	$24$	$17.751$		$_{}$	$\Q(\sqrt{-247}) $	None		$8$	$0$	$0$	$0$	$0$	$0$		$\mathrm{U}(1)[D_{2}]$
247.5.d.a	$247$	$5$	247.d	247.d	$2$	$3$	$3$	$25.532$	3.3.6669.1	$_{}$	$\Q(\sqrt{-247}) $	None	✓	$2$	$0$	$0$	$0$	$0$	$0$	$3$	$\mathrm{U}(1)[D_{2}]$	$q+\beta _{2}q^{2}+(2^{4}+\beta _{1}-4\beta _{2})q^{4}+(-119+\cdots)q^{8}+\cdots$
247.5.d.b	$247$	$5$	247.d	247.d	$2$	$3$	$3$	$25.532$	3.3.6669.1	$_{}$	$\Q(\sqrt{-247}) $	None	✓	$2$	$0$	$0$	$0$	$0$	$0$	$3$	$\mathrm{U}(1)[D_{2}]$	$q-\beta _{2}q^{2}+(2^{4}+\beta _{1}-4\beta _{2})q^{4}+(119+\cdots)q^{8}+\cdots$

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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.