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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 (39 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
1512.1.e.a	$1512$	$1$	1512.e	168.e	$2$	$1$	$1$	$0.755$	$\Q$	$D_{3}$	$\Q(\sqrt{-42}) $	None	✓	$2$	$0$	$-1$	$0$	$0$	$-1$	$1$		$q-q^{2}+q^{4}-q^{7}-q^{8}+q^{13}+q^{14}+\cdots$
1512.1.e.b	$1512$	$1$	1512.e	168.e	$2$	$1$	$1$	$0.755$	$\Q$	$D_{3}$	$\Q(\sqrt{-42}) $	None	✓	$2$	$0$	$-1$	$0$	$0$	$1$	$1$		$q-q^{2}+q^{4}+q^{7}-q^{8}-q^{13}-q^{14}+\cdots$
1512.1.e.c	$1512$	$1$	1512.e	168.e	$2$	$1$	$1$	$0.755$	$\Q$	$D_{3}$	$\Q(\sqrt{-42}) $	None	✓	$2$	$0$	$1$	$0$	$0$	$-1$	$1$		$q+q^{2}+q^{4}-q^{7}+q^{8}+q^{13}-q^{14}+\cdots$
1512.1.e.d	$1512$	$1$	1512.e	168.e	$2$	$1$	$1$	$0.755$	$\Q$	$D_{3}$	$\Q(\sqrt{-42}) $	None	✓	$2$	$0$	$1$	$0$	$0$	$1$	$1$		$q+q^{2}+q^{4}+q^{7}+q^{8}-q^{13}+q^{14}+\cdots$
2184.1.bf.i	$2184$	$1$	2184.bf	2184.af	$2$	$2$	$2$	$1.090$	$\Q(\sqrt{-1}) $	$D_{2}$	$\Q(\sqrt{-26}) $, $\Q(\sqrt{-42}) $	$\Q(\sqrt{273}) $		$8$	$0$	$0$	$-2$	$0$	$0$	$1$		$q-iq^{2}-q^{3}-q^{4}+iq^{6}+iq^{7}+iq^{8}+\cdots$
2184.1.bf.j	$2184$	$1$	2184.bf	2184.af	$2$	$2$	$2$	$1.090$	$\Q(\sqrt{-1}) $	$D_{2}$	$\Q(\sqrt{-26}) $, $\Q(\sqrt{-42}) $	$\Q(\sqrt{273}) $		$8$	$0$	$0$	$2$	$0$	$0$	$1$		$q-iq^{2}+q^{3}-q^{4}-iq^{6}-iq^{7}+iq^{8}+\cdots$
2184.1.cj.a	$2184$	$1$	2184.cj	2184.bj	$6$	$2$	$1$	$1.090$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-42}) $	None		$4$	$0$	$-1$	$-1$	$0$	$-1$	$1$		$q-\zeta_{6}q^{2}-\zeta_{6}q^{3}+\zeta_{6}^{2}q^{4}+\zeta_{6}^{2}q^{6}+\cdots$
2184.1.cj.b	$2184$	$1$	2184.cj	2184.bj	$6$	$2$	$1$	$1.090$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-42}) $	None		$4$	$0$	$-1$	$1$	$0$	$1$	$1$		$q-\zeta_{6}q^{2}+\zeta_{6}q^{3}+\zeta_{6}^{2}q^{4}-\zeta_{6}^{2}q^{6}+\cdots$
2184.1.cj.c	$2184$	$1$	2184.cj	2184.bj	$6$	$2$	$1$	$1.090$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-42}) $	None		$4$	$0$	$1$	$-1$	$0$	$1$	$1$		$q+\zeta_{6}q^{2}-\zeta_{6}q^{3}+\zeta_{6}^{2}q^{4}-\zeta_{6}^{2}q^{6}+\cdots$
2184.1.cj.d	$2184$	$1$	2184.cj	2184.bj	$6$	$2$	$1$	$1.090$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-42}) $	None		$4$	$0$	$1$	$1$	$0$	$-1$	$1$		$q+\zeta_{6}q^{2}+\zeta_{6}q^{3}+\zeta_{6}^{2}q^{4}+\zeta_{6}^{2}q^{6}+\cdots$
2184.1.gf.a	$2184$	$1$	2184.gf	2184.ff	$6$	$4$	$2$	$1.090$	$\Q(\zeta_{12})$	$D_{6}$	$\Q(\sqrt{-42}) $	None		$8$	$0$	$0$	$-2$	$0$	$0$	$1$		$q+\zeta_{12}q^{2}+\zeta_{12}^{4}q^{3}+\zeta_{12}^{2}q^{4}+\zeta_{12}^{5}q^{6}+\cdots$
2184.1.gf.b	$2184$	$1$	2184.gf	2184.ff	$6$	$4$	$2$	$1.090$	$\Q(\zeta_{12})$	$D_{6}$	$\Q(\sqrt{-42}) $	None		$8$	$0$	$0$	$2$	$0$	$0$	$1$		$q-\zeta_{12}q^{2}-\zeta_{12}^{4}q^{3}+\zeta_{12}^{2}q^{4}+\zeta_{12}^{5}q^{6}+\cdots$
2688.1.e.a	$2688$	$1$	2688.e	168.e	$2$	$1$	$1$	$1.341$	$\Q$	$D_{2}$	$\Q(\sqrt{-6}) $, $\Q(\sqrt{-42}) $	$\Q(\sqrt{7}) $	✓	$4$	$0$	$0$	$-1$	$0$	$-1$	$1$		$q-q^{3}-q^{7}+q^{9}+q^{21}+q^{25}-q^{27}+\cdots$
2688.1.e.b	$2688$	$1$	2688.e	168.e	$2$	$1$	$1$	$1.341$	$\Q$	$D_{2}$	$\Q(\sqrt{-6}) $, $\Q(\sqrt{-42}) $	$\Q(\sqrt{7}) $	✓	$4$	$0$	$0$	$-1$	$0$	$1$	$1$		$q-q^{3}+q^{7}+q^{9}-q^{21}+q^{25}-q^{27}+\cdots$
2688.1.e.c	$2688$	$1$	2688.e	168.e	$2$	$1$	$1$	$1.341$	$\Q$	$D_{2}$	$\Q(\sqrt{-6}) $, $\Q(\sqrt{-42}) $	$\Q(\sqrt{7}) $	✓	$4$	$0$	$0$	$1$	$0$	$-1$	$1$		$q+q^{3}-q^{7}+q^{9}-q^{21}+q^{25}+q^{27}+\cdots$
2688.1.e.d	$2688$	$1$	2688.e	168.e	$2$	$1$	$1$	$1.341$	$\Q$	$D_{2}$	$\Q(\sqrt{-6}) $, $\Q(\sqrt{-42}) $	$\Q(\sqrt{7}) $	✓	$4$	$0$	$0$	$1$	$0$	$1$	$1$		$q+q^{3}+q^{7}+q^{9}+q^{21}+q^{25}+q^{27}+\cdots$
2856.1.bd.i	$2856$	$1$	2856.bd	2856.ad	$2$	$2$	$2$	$1.425$	$\Q(\sqrt{-1}) $	$D_{2}$	$\Q(\sqrt{-119}) $, $\Q(\sqrt{-42}) $	$\Q(\sqrt{102}) $		$8$	$0$	$-2$	$0$	$0$	$0$	$1$		$q-q^{2}-iq^{3}+q^{4}+iq^{6}+iq^{7}-q^{8}+\cdots$
2856.1.bd.j	$2856$	$1$	2856.bd	2856.ad	$2$	$2$	$2$	$1.425$	$\Q(\sqrt{-1}) $	$D_{2}$	$\Q(\sqrt{-119}) $, $\Q(\sqrt{-42}) $	$\Q(\sqrt{102}) $		$8$	$0$	$2$	$0$	$0$	$0$	$1$		$q+q^{2}-iq^{3}+q^{4}-iq^{6}-iq^{7}+q^{8}+\cdots$
2856.1.bt.a	$2856$	$1$	2856.bt	2856.at	$4$	$4$	$2$	$1.425$	$\Q(\zeta_{8})$	$D_{4}$	$\Q(\sqrt{-42}) $	None		$8$	$0$	$0$	$0$	$0$	$0$	$1$		$q+\zeta_{8}^{2}q^{2}-\zeta_{8}q^{3}-q^{4}-\zeta_{8}^{3}q^{6}+\cdots$
2856.1.bt.b	$2856$	$1$	2856.bt	2856.at	$4$	$4$	$2$	$1.425$	$\Q(\zeta_{8})$	$D_{4}$	$\Q(\sqrt{-42}) $	None		$8$	$0$	$0$	$0$	$0$	$0$	$1$		$q-\zeta_{8}^{2}q^{2}-\zeta_{8}q^{3}-q^{4}+\zeta_{8}^{3}q^{6}+\cdots$
2856.1.dg.a	$2856$	$1$	2856.dg	2856.cg	$8$	$8$	$2$	$1.425$	$\Q(\zeta_{16})$	$D_{8}$	$\Q(\sqrt{-42}) $	None		$8$	$0$	$0$	$0$	$0$	$0$	$1$		$q-\zeta_{16}^{6}q^{2}+\zeta_{16}^{5}q^{3}-\zeta_{16}^{4}q^{4}+\cdots$
2856.1.dg.b	$2856$	$1$	2856.dg	2856.cg	$8$	$8$	$2$	$1.425$	$\Q(\zeta_{16})$	$D_{8}$	$\Q(\sqrt{-42}) $	None		$8$	$0$	$0$	$0$	$0$	$0$	$1$		$q+\zeta_{16}^{6}q^{2}+\zeta_{16}^{5}q^{3}-\zeta_{16}^{4}q^{4}+\cdots$
3528.1.g.b	$3528$	$1$	3528.g	8.d	$2$	$2$	$2$	$1.761$	$\Q(\sqrt{-1}) $	$D_{2}$	$\Q(\sqrt{-7}) $, $\Q(\sqrt{-42}) $	$\Q(\sqrt{6}) $		$8$	$0$	$0$	$0$	$0$	$0$	$1$		$q-iq^{2}-q^{4}+iq^{8}+q^{16}-iq^{23}+\cdots$
3528.1.bx.c	$3528$	$1$	3528.bx	56.k	$6$	$4$	$2$	$1.761$	$\Q(\zeta_{12})$	$D_{2}$	$\Q(\sqrt{-7}) $, $\Q(\sqrt{-42}) $	$\Q(\sqrt{6}) $		$16$	$0$	$0$	$0$	$0$	$0$	$1$		$q-\zeta_{12}q^{2}+\zeta_{12}^{2}q^{4}-\zeta_{12}^{3}q^{8}+\zeta_{12}^{4}q^{16}+\cdots$
3864.1.dl.a	$3864$	$1$	3864.dl	3864.cl	$22$	$10$	$1$	$1.928$	$\Q(\zeta_{22})$	$D_{11}$	$\Q(\sqrt{-42}) $	None		$4$	$0$	$-1$	$-1$	$0$	$-1$	$1$		$q-\zeta_{22}^{5}q^{2}-\zeta_{22}^{7}q^{3}+\zeta_{22}^{10}q^{4}+\cdots$
3864.1.dl.b	$3864$	$1$	3864.dl	3864.cl	$22$	$10$	$1$	$1.928$	$\Q(\zeta_{22})$	$D_{11}$	$\Q(\sqrt{-42}) $	None		$4$	$0$	$-1$	$1$	$0$	$1$	$1$		$q-\zeta_{22}^{5}q^{2}+\zeta_{22}^{7}q^{3}+\zeta_{22}^{10}q^{4}+\cdots$
3864.1.dl.c	$3864$	$1$	3864.dl	3864.cl	$22$	$10$	$1$	$1.928$	$\Q(\zeta_{22})$	$D_{11}$	$\Q(\sqrt{-42}) $	None		$4$	$0$	$1$	$-1$	$0$	$1$	$1$		$q+\zeta_{22}^{5}q^{2}-\zeta_{22}^{7}q^{3}+\zeta_{22}^{10}q^{4}+\cdots$
3864.1.dl.d	$3864$	$1$	3864.dl	3864.cl	$22$	$10$	$1$	$1.928$	$\Q(\zeta_{22})$	$D_{11}$	$\Q(\sqrt{-42}) $	None		$4$	$0$	$1$	$1$	$0$	$-1$	$1$		$q+\zeta_{22}^{5}q^{2}+\zeta_{22}^{7}q^{3}+\zeta_{22}^{10}q^{4}+\cdots$
504.2.p.c	$504$	$2$	504.p	56.e	$2$	$4$	$4$	$4.024$	$\Q(\sqrt{-2}, \sqrt{7})$	$_{}$	$\Q(\sqrt{-42}) $	None		$8$	$0$	$0$	$0$	$0$	$0$	$2$	$\mathrm{U}(1)[D_{2}]$	$q+\beta _{1}q^{2}-2q^{4}-\beta _{3}q^{7}-2\beta _{1}q^{8}+\cdots$
168.3.e.a	$168$	$3$	168.e	168.e	$2$	$1$	$1$	$4.578$	$\Q$	$_{}$	$\Q(\sqrt{-42}) $	None	✓	$2$	$0$	$-2$	$-3$	$0$	$-7$	$1$	$\mathrm{U}(1)[D_{2}]$	$q-2q^{2}-3q^{3}+4q^{4}+6q^{6}-7q^{7}+\cdots$
168.3.e.b	$168$	$3$	168.e	168.e	$2$	$1$	$1$	$4.578$	$\Q$	$_{}$	$\Q(\sqrt{-42}) $	None	✓	$2$	$0$	$-2$	$3$	$0$	$7$	$1$	$\mathrm{U}(1)[D_{2}]$	$q-2q^{2}+3q^{3}+4q^{4}-6q^{6}+7q^{7}+\cdots$
168.3.e.c	$168$	$3$	168.e	168.e	$2$	$1$	$1$	$4.578$	$\Q$	$_{}$	$\Q(\sqrt{-42}) $	None	✓	$2$	$0$	$2$	$-3$	$0$	$7$	$1$	$\mathrm{U}(1)[D_{2}]$	$q+2q^{2}-3q^{3}+4q^{4}-6q^{6}+7q^{7}+\cdots$
168.3.e.d	$168$	$3$	168.e	168.e	$2$	$1$	$1$	$4.578$	$\Q$	$_{}$	$\Q(\sqrt{-42}) $	None	✓	$2$	$0$	$2$	$3$	$0$	$-7$	$1$	$\mathrm{U}(1)[D_{2}]$	$q+2q^{2}+3q^{3}+4q^{4}+6q^{6}-7q^{7}+\cdots$
1344.2.i.c	$1344$	$2$	1344.i	168.i	$2$	$8$	$8$	$10.732$	8.0.49787136.1	$_{}$	$\Q(\sqrt{-42}) $	None		$16$	$0$	$0$	$0$	$0$	$0$	$2^{12}$	$\mathrm{U}(1)[D_{2}]$	$q-\beta _{1}q^{3}+\beta _{3}q^{7}-3q^{9}+\beta _{7}q^{13}+\cdots$
2016.2.p.c	$2016$	$2$	2016.p	56.e	$2$	$4$	$4$	$16.098$	$\Q(\sqrt{-2}, \sqrt{7})$	$_{}$	$\Q(\sqrt{-42}) $	None		$8$	$0$	$0$	$0$	$0$	$0$	$2^{3}$	$\mathrm{U}(1)[D_{2}]$	$q+\beta _{3}q^{7}-2\beta _{3}q^{13}+\beta _{2}q^{17}+\beta _{1}q^{23}+\cdots$
672.3.e.a	$672$	$3$	672.e	168.e	$2$	$1$	$1$	$18.311$	$\Q$	$_{}$	$\Q(\sqrt{-42}) $	None	✓	$2$	$0$	$0$	$-3$	$0$	$-7$	$1$	$\mathrm{U}(1)[D_{2}]$	$q-3q^{3}-7q^{7}+9q^{9}+2q^{13}-22q^{17}+\cdots$
672.3.e.b	$672$	$3$	672.e	168.e	$2$	$1$	$1$	$18.311$	$\Q$	$_{}$	$\Q(\sqrt{-42}) $	None	✓	$2$	$0$	$0$	$-3$	$0$	$7$	$1$	$\mathrm{U}(1)[D_{2}]$	$q-3q^{3}+7q^{7}+9q^{9}-2q^{13}-22q^{17}+\cdots$
672.3.e.c	$672$	$3$	672.e	168.e	$2$	$1$	$1$	$18.311$	$\Q$	$_{}$	$\Q(\sqrt{-42}) $	None	✓	$2$	$0$	$0$	$3$	$0$	$-7$	$1$	$\mathrm{U}(1)[D_{2}]$	$q+3q^{3}-7q^{7}+9q^{9}+2q^{13}+22q^{17}+\cdots$
672.3.e.d	$672$	$3$	672.e	168.e	$2$	$1$	$1$	$18.311$	$\Q$	$_{}$	$\Q(\sqrt{-42}) $	None	✓	$2$	$0$	$0$	$3$	$0$	$7$	$1$	$\mathrm{U}(1)[D_{2}]$	$q+3q^{3}+7q^{7}+9q^{9}-2q^{13}+22q^{17}+\cdots$

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

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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.