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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 (36 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
184.1.e.a	$184$	$1$	184.e	184.e	$2$	$1$	$1$	$0.092$	$\Q$	$D_{2}$	$\Q(\sqrt{-23}) $, $\Q(\sqrt{-46}) $	$\Q(\sqrt{2}) $	✓	$4$	$0$	$-1$	$0$	$0$	$0$	$1$		$q-q^{2}+q^{4}-q^{8}+q^{9}+q^{16}-q^{18}+\cdots$
736.1.e.a	$736$	$1$	736.e	184.e	$2$	$1$	$1$	$0.367$	$\Q$	$D_{2}$	$\Q(\sqrt{-23}) $, $\Q(\sqrt{-46}) $	$\Q(\sqrt{2}) $	✓	$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q+q^{9}+q^{23}-q^{25}+2q^{31}-2q^{41}+\cdots$
920.1.p.e	$920$	$1$	920.p	920.p	$2$	$4$	$4$	$0.459$	$\Q(\zeta_{8})$	$D_{4}$	$\Q(\sqrt{-46}) $	None		$8$	$0$	$0$	$0$	$0$	$0$	$1$		$q-\zeta_{8}^{2}q^{2}-q^{4}-\zeta_{8}q^{5}+\zeta_{8}^{2}q^{8}+\cdots$
1656.1.l.a	$1656$	$1$	1656.l	184.e	$2$	$1$	$1$	$0.826$	$\Q$	$D_{2}$	$\Q(\sqrt{-23}) $, $\Q(\sqrt{-46}) $	$\Q(\sqrt{2}) $	✓	$4$	$0$	$1$	$0$	$0$	$0$	$1$		$q+q^{2}+q^{4}+q^{8}+q^{16}+q^{23}-q^{25}+\cdots$
1656.1.l.b	$1656$	$1$	1656.l	184.e	$2$	$2$	$2$	$0.826$	$\Q(\sqrt{2}) $	$D_{4}$	$\Q(\sqrt{-46}) $	None	✓	$4$	$0$	$-2$	$0$	$0$	$0$	$1$		$q-q^{2}+q^{4}-\beta q^{5}-q^{8}+\beta q^{10}+\beta q^{11}+\cdots$
1656.1.l.d	$1656$	$1$	1656.l	184.e	$2$	$2$	$2$	$0.826$	$\Q(\sqrt{2}) $	$D_{4}$	$\Q(\sqrt{-46}) $	None	✓	$4$	$0$	$2$	$0$	$0$	$0$	$1$		$q+q^{2}+q^{4}-\beta q^{5}+q^{8}-\beta q^{10}+\beta q^{11}+\cdots$
2024.1.bb.a	$2024$	$1$	2024.bb	2024.ab	$10$	$4$	$1$	$1.010$	$\Q(\zeta_{10})$	$D_{5}$	$\Q(\sqrt{-46}) $	None		$4$	$0$	$-1$	$0$	$-2$	$0$	$1$		$q-\zeta_{10}q^{2}+\zeta_{10}^{2}q^{4}+(-\zeta_{10}+\zeta_{10}^{2}+\cdots)q^{5}+\cdots$
2024.1.bb.b	$2024$	$1$	2024.bb	2024.ab	$10$	$4$	$1$	$1.010$	$\Q(\zeta_{10})$	$D_{5}$	$\Q(\sqrt{-46}) $	None		$4$	$0$	$-1$	$0$	$2$	$0$	$1$		$q-\zeta_{10}q^{2}+\zeta_{10}^{2}q^{4}+(\zeta_{10}-\zeta_{10}^{2}+\cdots)q^{5}+\cdots$
2024.1.bb.c	$2024$	$1$	2024.bb	2024.ab	$10$	$8$	$2$	$1.010$	$\Q(\zeta_{20})$	$D_{10}$	$\Q(\sqrt{-46}) $	None		$8$	$0$	$2$	$0$	$0$	$0$	$1$		$q+\zeta_{20}^{2}q^{2}+\zeta_{20}^{4}q^{4}+(\zeta_{20}^{7}+\zeta_{20}^{9}+\cdots)q^{5}+\cdots$
2944.1.e.a	$2944$	$1$	2944.e	184.e	$2$	$2$	$2$	$1.469$	$\Q(\sqrt{2}) $	$D_{4}$	$\Q(\sqrt{-46}) $	None	✓	$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q+\beta q^{5}+q^{9}-\beta q^{11}+\beta q^{19}-q^{23}+\cdots$
2944.1.e.b	$2944$	$1$	2944.e	184.e	$2$	$2$	$2$	$1.469$	$\Q(\sqrt{2}) $	$D_{4}$	$\Q(\sqrt{-46}) $	None	✓	$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q-\beta q^{5}+q^{9}-\beta q^{11}+\beta q^{19}+q^{23}+\cdots$
3496.1.z.a	$3496$	$1$	3496.z	3496.z	$6$	$2$	$1$	$1.745$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-46}) $	None		$4$	$0$	$-1$	$0$	$-1$	$0$	$1$		$q+\zeta_{6}^{2}q^{2}-\zeta_{6}q^{4}+\zeta_{6}^{2}q^{5}+q^{8}+\cdots$
3496.1.z.b	$3496$	$1$	3496.z	3496.z	$6$	$2$	$1$	$1.745$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-46}) $	None		$4$	$0$	$-1$	$0$	$1$	$0$	$1$		$q+\zeta_{6}^{2}q^{2}-\zeta_{6}q^{4}-\zeta_{6}^{2}q^{5}+q^{8}+\cdots$
3496.1.z.d	$3496$	$1$	3496.z	3496.z	$6$	$4$	$2$	$1.745$	$\Q(\zeta_{12})$	$D_{6}$	$\Q(\sqrt{-46}) $	None		$8$	$0$	$2$	$0$	$0$	$0$	$1$		$q+\zeta_{12}^{2}q^{2}+\zeta_{12}^{4}q^{4}+(\zeta_{12}+\zeta_{12}^{3}+\cdots)q^{5}+\cdots$
3496.1.bs.a	$3496$	$1$	3496.bs	3496.as	$18$	$6$	$1$	$1.745$	$\Q(\zeta_{18})$	$D_{9}$	$\Q(\sqrt{-46}) $	None		$4$	$0$	$0$	$0$	$-3$	$0$	$1$		$q+\zeta_{18}^{2}q^{2}+\zeta_{18}^{4}q^{4}+(\zeta_{18}^{4}+\zeta_{18}^{6}+\cdots)q^{5}+\cdots$
3496.1.bs.b	$3496$	$1$	3496.bs	3496.as	$18$	$6$	$1$	$1.745$	$\Q(\zeta_{18})$	$D_{9}$	$\Q(\sqrt{-46}) $	None		$4$	$0$	$0$	$0$	$3$	$0$	$1$		$q+\zeta_{18}^{2}q^{2}+\zeta_{18}^{4}q^{4}+(-\zeta_{18}^{4}-\zeta_{18}^{6}+\cdots)q^{5}+\cdots$
3496.1.bs.c	$3496$	$1$	3496.bs	3496.as	$18$	$12$	$2$	$1.745$	$\Q(\zeta_{36})$	$D_{18}$	$\Q(\sqrt{-46}) $	None		$8$	$0$	$0$	$0$	$0$	$0$	$1$		$q-\zeta_{36}^{4}q^{2}+\zeta_{36}^{8}q^{4}+(-\zeta_{36}^{3}-\zeta_{36}^{17}+\cdots)q^{5}+\cdots$
3680.1.p.e	$3680$	$1$	3680.p	920.p	$2$	$4$	$4$	$1.837$	$\Q(\zeta_{8})$	$D_{4}$	$\Q(\sqrt{-46}) $	None		$8$	$0$	$0$	$0$	$0$	$0$	$1$		$q-\zeta_{8}^{3}q^{5}-q^{9}+(-\zeta_{8}+\zeta_{8}^{3})q^{11}+\cdots$
184.3.e.a	$184$	$3$	184.e	184.e	$2$	$2$	$2$	$5.014$	$\Q(\sqrt{23}) $	$_{}$	$\Q(\sqrt{-46}) $	None	✓	$4$	$0$	$-4$	$0$	$0$	$0$	$2$	$\mathrm{U}(1)[D_{2}]$	$q-2q^{2}+4q^{4}+\beta q^{5}-8q^{8}+9q^{9}+\cdots$
184.3.e.b	$184$	$3$	184.e	184.e	$2$	$2$	$2$	$5.014$	$\Q(\sqrt{2}) $	$_{}$	$\Q(\sqrt{-46}) $	None	✓	$4$	$0$	$4$	$0$	$0$	$0$	$2$	$\mathrm{U}(1)[D_{2}]$	$q+2q^{2}+4q^{4}+\beta q^{5}+8q^{8}+9q^{9}+\cdots$
920.2.x.a	$920$	$2$	920.x	920.x	$4$	$8$	$4$	$7.346$	8.0.$\cdots$.4	$_{}$	$\Q(\sqrt{-46}) $	None		$8$	$0$	$-8$	$0$	$0$	$0$	$1$	$\mathrm{U}(1)[D_{4}]$	$q+(-1+\beta _{4})q^{2}-2\beta _{4}q^{4}+\beta _{1}q^{5}+\cdots$
920.2.x.b	$920$	$2$	920.x	920.x	$4$	$8$	$4$	$7.346$	8.0.$\cdots$.4	$_{}$	$\Q(\sqrt{-46}) $	None		$8$	$0$	$8$	$0$	$0$	$0$	$5$	$\mathrm{U}(1)[D_{4}]$	$q+(1-\beta _{3})q^{2}-2\beta _{3}q^{4}-\beta _{4}q^{5}+(-2+\cdots)q^{8}+\cdots$
1472.2.h.a	$1472$	$2$	1472.h	184.h	$2$	$8$	$8$	$11.754$	8.0.$\cdots$.3	$_{}$	$\Q(\sqrt{-46}) $	None		$8$	$0$	$0$	$0$	$0$	$0$	$2^{10}$	$\mathrm{U}(1)[D_{2}]$	$q+\beta _{3}q^{5}-3q^{9}-\beta _{4}q^{11}+\beta _{7}q^{19}+\cdots$
1656.2.b.a	$1656$	$2$	1656.b	552.b	$2$	$8$	$8$	$13.223$	8.0.$\cdots$.17	$_{}$	$\Q(\sqrt{-46}) $	None		$8$	$0$	$0$	$0$	$0$	$0$	$2^{4}$	$\mathrm{U}(1)[D_{2}]$	$q+\beta _{1}q^{2}-2q^{4}+\beta _{5}q^{5}-2\beta _{1}q^{8}+\cdots$
1656.2.b.b	$1656$	$2$	1656.b	552.b	$2$	$8$	$8$	$13.223$	8.0.$\cdots$.17	$_{}$	$\Q(\sqrt{-46}) $	None		$8$	$0$	$0$	$0$	$0$	$0$	$2^{4}\cdot 3^{2}$	$\mathrm{U}(1)[D_{2}]$	$q+\beta _{1}q^{2}-2q^{4}-\beta _{4}q^{5}-2\beta _{1}q^{8}+\cdots$
184.5.e.a	$184$	$5$	184.e	184.e	$2$	$1$	$1$	$19.020$	$\Q$	$_{}$	$\Q(\sqrt{-46}) $	None	✓	$2$	$0$	$4$	$0$	$-42$	$0$	$1$	$\mathrm{U}(1)[D_{2}]$	$q+4q^{2}+2^{4}q^{4}-42q^{5}+2^{6}q^{8}+3^{4}q^{9}+\cdots$
184.5.e.b	$184$	$5$	184.e	184.e	$2$	$1$	$1$	$19.020$	$\Q$	$_{}$	$\Q(\sqrt{-46}) $	None	✓	$2$	$0$	$4$	$0$	$42$	$0$	$1$	$\mathrm{U}(1)[D_{2}]$	$q+4q^{2}+2^{4}q^{4}+42q^{5}+2^{6}q^{8}+3^{4}q^{9}+\cdots$
184.5.e.c	$184$	$5$	184.e	184.e	$2$	$2$	$2$	$19.020$	$\Q(\sqrt{46}) $	$_{}$	$\Q(\sqrt{-46}) $	None	✓	$4$	$0$	$-8$	$0$	$0$	$0$	$2^{2}$	$\mathrm{U}(1)[D_{2}]$	$q-4q^{2}+2^{4}q^{4}+\beta q^{5}-2^{6}q^{8}+3^{4}q^{9}+\cdots$
736.3.e.a	$736$	$3$	736.e	184.e	$2$	$2$	$2$	$20.055$	$\Q(\sqrt{23}) $	$_{}$	$\Q(\sqrt{-46}) $	None	✓	$4$	$0$	$0$	$0$	$0$	$0$	$2$	$\mathrm{U}(1)[D_{2}]$	$q-\beta q^{5}+9q^{9}-\beta q^{11}-\beta q^{19}-23q^{23}+\cdots$
736.3.e.b	$736$	$3$	736.e	184.e	$2$	$2$	$2$	$20.055$	$\Q(\sqrt{2}) $	$_{}$	$\Q(\sqrt{-46}) $	None	✓	$4$	$0$	$0$	$0$	$0$	$0$	$2$	$\mathrm{U}(1)[D_{2}]$	$q+\beta q^{5}+9q^{9}+7\beta q^{11}-13\beta q^{19}+\cdots$
2944.2.h.a	$2944$	$2$	2944.h	184.h	$2$	$8$	$8$	$23.508$	8.0.$\cdots$.1	$_{}$	$\Q(\sqrt{-46}) $	None		$8$	$0$	$0$	$0$	$0$	$0$	$2^{10}$	$\mathrm{U}(1)[D_{2}]$	$q+\beta _{4}q^{5}-3q^{9}-\beta _{5}q^{11}-\beta _{2}q^{19}+\cdots$
6624.2.b.a	$6624$	$2$	6624.b	552.b	$2$	$8$	$8$	$52.893$	8.0.$\cdots$.17	$_{}$	$\Q(\sqrt{-46}) $	None		$8$	$0$	$0$	$0$	$0$	$0$	$2^{4}$	$\mathrm{U}(1)[D_{2}]$	$q+\beta _{5}q^{5}+(-\beta _{5}+2\beta _{6})q^{11}+\beta _{2}q^{19}+\cdots$
6624.2.b.b	$6624$	$2$	6624.b	552.b	$2$	$8$	$8$	$52.893$	8.0.$\cdots$.17	$_{}$	$\Q(\sqrt{-46}) $	None		$8$	$0$	$0$	$0$	$0$	$0$	$2^{4}\cdot 3^{2}$	$\mathrm{U}(1)[D_{2}]$	$q-\beta _{4}q^{5}-\beta _{4}q^{11}+(-\beta _{5}+\beta _{6})q^{19}+\cdots$
736.5.e.a	$736$	$5$	736.e	184.e	$2$	$1$	$1$	$76.080$	$\Q$	$_{}$	$\Q(\sqrt{-46}) $	None	✓	$2$	$0$	$0$	$0$	$-42$	$0$	$1$	$\mathrm{U}(1)[D_{2}]$	$q-42q^{5}+3^{4}q^{9}-150q^{11}-630q^{19}+\cdots$
736.5.e.b	$736$	$5$	736.e	184.e	$2$	$1$	$1$	$76.080$	$\Q$	$_{}$	$\Q(\sqrt{-46}) $	None	✓	$2$	$0$	$0$	$0$	$42$	$0$	$1$	$\mathrm{U}(1)[D_{2}]$	$q+42q^{5}+3^{4}q^{9}+150q^{11}+630q^{19}+\cdots$
736.5.e.c	$736$	$5$	736.e	184.e	$2$	$2$	$2$	$76.080$	$\Q(\sqrt{46}) $	$_{}$	$\Q(\sqrt{-46}) $	None	✓	$4$	$0$	$0$	$0$	$0$	$0$	$2^{2}$	$\mathrm{U}(1)[D_{2}]$	$q+\beta q^{5}+3^{4}q^{9}-7\beta q^{11}+13\beta q^{19}+\cdots$

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Hilbert	Bianchi

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.