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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 (47 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
264.1.p.a	$264$	$1$	264.p	264.p	$2$	$1$	$1$	$0.132$	$\Q$	$D_{2}$	$\Q(\sqrt{-2}) $, $\Q(\sqrt{-66}) $	$\Q(\sqrt{33}) $	✓	$4$	$0$	$-1$	$-1$	$0$	$0$	$1$		$q-q^{2}-q^{3}+q^{4}+q^{6}-q^{8}+q^{9}+\cdots$
264.1.p.b	$264$	$1$	264.p	264.p	$2$	$1$	$1$	$0.132$	$\Q$	$D_{2}$	$\Q(\sqrt{-2}) $, $\Q(\sqrt{-66}) $	$\Q(\sqrt{33}) $	✓	$4$	$0$	$1$	$-1$	$0$	$0$	$1$		$q+q^{2}-q^{3}+q^{4}-q^{6}+q^{8}+q^{9}+\cdots$
1056.1.p.a	$1056$	$1$	1056.p	264.p	$2$	$1$	$1$	$0.527$	$\Q$	$D_{2}$	$\Q(\sqrt{-2}) $, $\Q(\sqrt{-66}) $	$\Q(\sqrt{33}) $	✓	$4$	$0$	$0$	$1$	$0$	$0$	$1$		$q+q^{3}+q^{9}-q^{11}+2q^{17}-q^{25}+\cdots$
1056.1.p.b	$1056$	$1$	1056.p	264.p	$2$	$1$	$1$	$0.527$	$\Q$	$D_{2}$	$\Q(\sqrt{-2}) $, $\Q(\sqrt{-66}) $	$\Q(\sqrt{33}) $	✓	$4$	$0$	$0$	$1$	$0$	$0$	$1$		$q+q^{3}+q^{9}+q^{11}-2q^{17}-q^{25}+\cdots$
1320.1.b.a	$1320$	$1$	1320.b	1320.b	$2$	$4$	$4$	$0.659$	$\Q(\zeta_{8})$	$D_{4}$	$\Q(\sqrt{-66}) $	None		$8$	$0$	$0$	$0$	$0$	$0$	$1$		$q-\zeta_{8}^{2}q^{2}-\zeta_{8}^{2}q^{3}-q^{4}-\zeta_{8}q^{5}+\cdots$
1320.1.b.b	$1320$	$1$	1320.b	1320.b	$2$	$4$	$4$	$0.659$	$\Q(\zeta_{8})$	$D_{4}$	$\Q(\sqrt{-66}) $	None		$8$	$0$	$0$	$0$	$0$	$0$	$1$		$q+\zeta_{8}^{2}q^{2}-\zeta_{8}^{2}q^{3}-q^{4}-\zeta_{8}q^{5}+\cdots$
1848.1.br.a	$1848$	$1$	1848.br	1848.ar	$6$	$2$	$1$	$0.922$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-66}) $	None		$4$	$0$	$-1$	$-1$	$-1$	$1$	$1$		$q+\zeta_{6}^{2}q^{2}-\zeta_{6}q^{3}-\zeta_{6}q^{4}+\zeta_{6}^{2}q^{5}+\cdots$
1848.1.br.b	$1848$	$1$	1848.br	1848.ar	$6$	$2$	$1$	$0.922$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-66}) $	None		$4$	$0$	$-1$	$-1$	$1$	$-1$	$1$		$q+\zeta_{6}^{2}q^{2}-\zeta_{6}q^{3}-\zeta_{6}q^{4}-\zeta_{6}^{2}q^{5}+\cdots$
1848.1.br.c	$1848$	$1$	1848.br	1848.ar	$6$	$2$	$1$	$0.922$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-66}) $	None		$4$	$0$	$1$	$-1$	$-1$	$-1$	$1$		$q-\zeta_{6}^{2}q^{2}-\zeta_{6}q^{3}-\zeta_{6}q^{4}+\zeta_{6}^{2}q^{5}+\cdots$
1848.1.br.d	$1848$	$1$	1848.br	1848.ar	$6$	$2$	$1$	$0.922$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-66}) $	None		$4$	$0$	$1$	$-1$	$1$	$1$	$1$		$q-\zeta_{6}^{2}q^{2}-\zeta_{6}q^{3}-\zeta_{6}q^{4}-\zeta_{6}^{2}q^{5}+\cdots$
1848.1.br.e	$1848$	$1$	1848.br	1848.ar	$6$	$4$	$2$	$0.922$	$\Q(\zeta_{12})$	$D_{6}$	$\Q(\sqrt{-66}) $	None		$8$	$0$	$-2$	$2$	$0$	$0$	$1$		$q-\zeta_{12}^{2}q^{2}-\zeta_{12}^{4}q^{3}+\zeta_{12}^{4}q^{4}+\cdots$
1848.1.br.f	$1848$	$1$	1848.br	1848.ar	$6$	$4$	$2$	$0.922$	$\Q(\zeta_{12})$	$D_{6}$	$\Q(\sqrt{-66}) $	None		$8$	$0$	$2$	$2$	$0$	$0$	$1$		$q+\zeta_{12}^{2}q^{2}-\zeta_{12}^{4}q^{3}+\zeta_{12}^{4}q^{4}+\cdots$
2376.1.p.a	$2376$	$1$	2376.p	264.p	$2$	$1$	$1$	$1.186$	$\Q$	$D_{3}$	$\Q(\sqrt{-66}) $	None	✓	$2$	$0$	$-1$	$0$	$-1$	$-2$	$1$		$q-q^{2}+q^{4}-q^{5}-2q^{7}-q^{8}+q^{10}+\cdots$
2376.1.p.b	$2376$	$1$	2376.p	264.p	$2$	$1$	$1$	$1.186$	$\Q$	$D_{3}$	$\Q(\sqrt{-66}) $	None	✓	$2$	$0$	$-1$	$0$	$1$	$2$	$1$		$q-q^{2}+q^{4}+q^{5}+2q^{7}-q^{8}-q^{10}+\cdots$
2376.1.p.c	$2376$	$1$	2376.p	264.p	$2$	$1$	$1$	$1.186$	$\Q$	$D_{3}$	$\Q(\sqrt{-66}) $	None	✓	$2$	$0$	$1$	$0$	$-1$	$2$	$1$		$q+q^{2}+q^{4}-q^{5}+2q^{7}+q^{8}-q^{10}+\cdots$
2376.1.p.d	$2376$	$1$	2376.p	264.p	$2$	$1$	$1$	$1.186$	$\Q$	$D_{3}$	$\Q(\sqrt{-66}) $	None	✓	$2$	$0$	$1$	$0$	$1$	$-2$	$1$		$q+q^{2}+q^{4}+q^{5}-2q^{7}+q^{8}+q^{10}+\cdots$
2376.1.p.e	$2376$	$1$	2376.p	264.p	$2$	$2$	$2$	$1.186$	$\Q(\sqrt{3}) $	$D_{6}$	$\Q(\sqrt{-66}) $	None	✓	$4$	$0$	$-2$	$0$	$0$	$0$	$1$		$q-q^{2}+q^{4}-\beta q^{5}-q^{8}+\beta q^{10}+q^{11}+\cdots$
2376.1.p.f	$2376$	$1$	2376.p	264.p	$2$	$2$	$2$	$1.186$	$\Q(\sqrt{3}) $	$D_{6}$	$\Q(\sqrt{-66}) $	None	✓	$4$	$0$	$2$	$0$	$0$	$0$	$1$		$q+q^{2}+q^{4}-\beta q^{5}+q^{8}-\beta q^{10}-q^{11}+\cdots$
2904.1.r.b	$2904$	$1$	2904.r	264.r	$10$	$4$	$1$	$1.449$	$\Q(\zeta_{10})$	$D_{2}$	$\Q(\sqrt{-2}) $, $\Q(\sqrt{-66}) $	$\Q(\sqrt{33}) $		$16$	$0$	$-1$	$1$	$0$	$0$	$1$		$q-\zeta_{10}^{3}q^{2}-\zeta_{10}^{4}q^{3}-\zeta_{10}q^{4}-\zeta_{10}^{2}q^{6}+\cdots$
2904.1.r.f	$2904$	$1$	2904.r	264.r	$10$	$4$	$1$	$1.449$	$\Q(\zeta_{10})$	$D_{2}$	$\Q(\sqrt{-2}) $, $\Q(\sqrt{-66}) $	$\Q(\sqrt{33}) $		$16$	$0$	$1$	$1$	$0$	$0$	$1$		$q+\zeta_{10}^{3}q^{2}-\zeta_{10}^{4}q^{3}-\zeta_{10}q^{4}+\zeta_{10}^{2}q^{6}+\cdots$
3432.1.i.e	$3432$	$1$	3432.i	3432.i	$2$	$2$	$2$	$1.713$	$\Q(\sqrt{-1}) $	$D_{2}$	$\Q(\sqrt{-143}) $, $\Q(\sqrt{-66}) $	$\Q(\sqrt{78}) $		$8$	$0$	$0$	$-2$	$0$	$0$	$1$		$q-iq^{2}-q^{3}-q^{4}+iq^{6}-iq^{7}+iq^{8}+\cdots$
3432.1.i.f	$3432$	$1$	3432.i	3432.i	$2$	$2$	$2$	$1.713$	$\Q(\sqrt{-1}) $	$D_{2}$	$\Q(\sqrt{-143}) $, $\Q(\sqrt{-66}) $	$\Q(\sqrt{78}) $		$8$	$0$	$0$	$-2$	$0$	$0$	$1$		$q+iq^{2}-q^{3}-q^{4}-iq^{6}-iq^{7}-iq^{8}+\cdots$
3432.1.i.g	$3432$	$1$	3432.i	3432.i	$2$	$2$	$2$	$1.713$	$\Q(\sqrt{-1}) $	$D_{2}$	$\Q(\sqrt{-39}) $, $\Q(\sqrt{-66}) $	$\Q(\sqrt{286}) $		$8$	$0$	$0$	$2$	$0$	$0$	$1$		$q-iq^{2}+q^{3}-q^{4}-iq^{5}-iq^{6}+iq^{8}+\cdots$
3432.1.i.h	$3432$	$1$	3432.i	3432.i	$2$	$2$	$2$	$1.713$	$\Q(\sqrt{-1}) $	$D_{2}$	$\Q(\sqrt{-39}) $, $\Q(\sqrt{-66}) $	$\Q(\sqrt{286}) $		$8$	$0$	$0$	$2$	$0$	$0$	$1$		$q+iq^{2}+q^{3}-q^{4}-iq^{5}+iq^{6}-iq^{8}+\cdots$
3432.1.cg.a	$3432$	$1$	3432.cg	3432.bg	$6$	$4$	$2$	$1.713$	$\Q(\zeta_{12})$	$D_{6}$	$\Q(\sqrt{-66}) $	None		$8$	$0$	$0$	$-2$	$0$	$-6$	$1$		$q+\zeta_{12}q^{2}+\zeta_{12}^{4}q^{3}+\zeta_{12}^{2}q^{4}+\zeta_{12}^{3}q^{5}+\cdots$
3432.1.cg.b	$3432$	$1$	3432.cg	3432.bg	$6$	$4$	$2$	$1.713$	$\Q(\zeta_{12})$	$D_{6}$	$\Q(\sqrt{-66}) $	None		$8$	$0$	$0$	$-2$	$0$	$6$	$1$		$q-\zeta_{12}q^{2}+\zeta_{12}^{4}q^{3}+\zeta_{12}^{2}q^{4}+\zeta_{12}^{3}q^{5}+\cdots$
3432.1.cg.c	$3432$	$1$	3432.cg	3432.bg	$6$	$4$	$2$	$1.713$	$\Q(\zeta_{12})$	$D_{6}$	$\Q(\sqrt{-66}) $	None		$8$	$0$	$0$	$2$	$0$	$0$	$1$		$q-\zeta_{12}q^{2}-\zeta_{12}^{4}q^{3}+\zeta_{12}^{2}q^{4}+(\zeta_{12}^{2}+\cdots)q^{5}+\cdots$
3432.1.cg.d	$3432$	$1$	3432.cg	3432.bg	$6$	$4$	$2$	$1.713$	$\Q(\zeta_{12})$	$D_{6}$	$\Q(\sqrt{-66}) $	None		$8$	$0$	$0$	$2$	$0$	$0$	$1$		$q+\zeta_{12}q^{2}-\zeta_{12}^{4}q^{3}+\zeta_{12}^{2}q^{4}+(-\zeta_{12}^{2}+\cdots)q^{5}+\cdots$
3432.1.cp.a	$3432$	$1$	3432.cp	3432.bp	$6$	$2$	$1$	$1.713$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-66}) $	None		$4$	$0$	$-1$	$-1$	$-2$	$1$	$1$		$q-\zeta_{6}q^{2}-\zeta_{6}q^{3}+\zeta_{6}^{2}q^{4}-q^{5}+\zeta_{6}^{2}q^{6}+\cdots$
3432.1.cp.b	$3432$	$1$	3432.cp	3432.bp	$6$	$2$	$1$	$1.713$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-66}) $	None		$4$	$0$	$-1$	$-1$	$2$	$-1$	$1$		$q-\zeta_{6}q^{2}-\zeta_{6}q^{3}+\zeta_{6}^{2}q^{4}+q^{5}+\zeta_{6}^{2}q^{6}+\cdots$
3432.1.cp.c	$3432$	$1$	3432.cp	3432.bp	$6$	$2$	$1$	$1.713$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-66}) $	None		$4$	$0$	$1$	$-1$	$-2$	$-1$	$1$		$q+\zeta_{6}q^{2}-\zeta_{6}q^{3}+\zeta_{6}^{2}q^{4}-q^{5}-\zeta_{6}^{2}q^{6}+\cdots$
3432.1.cp.d	$3432$	$1$	3432.cp	3432.bp	$6$	$2$	$1$	$1.713$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-66}) $	None		$4$	$0$	$1$	$-1$	$2$	$1$	$1$		$q+\zeta_{6}q^{2}-\zeta_{6}q^{3}+\zeta_{6}^{2}q^{4}+q^{5}-\zeta_{6}^{2}q^{6}+\cdots$
3432.1.cp.e	$3432$	$1$	3432.cp	3432.bp	$6$	$4$	$2$	$1.713$	$\Q(\zeta_{12})$	$D_{6}$	$\Q(\sqrt{-66}) $	None		$8$	$0$	$-2$	$2$	$0$	$0$	$1$		$q+\zeta_{12}^{4}q^{2}-\zeta_{12}^{4}q^{3}-\zeta_{12}^{2}q^{4}+\cdots$
3432.1.cp.f	$3432$	$1$	3432.cp	3432.bp	$6$	$4$	$2$	$1.713$	$\Q(\zeta_{12})$	$D_{6}$	$\Q(\sqrt{-66}) $	None		$8$	$0$	$2$	$2$	$0$	$0$	$1$		$q-\zeta_{12}^{4}q^{2}-\zeta_{12}^{4}q^{3}-\zeta_{12}^{2}q^{4}+\cdots$
3960.1.bp.a	$3960$	$1$	3960.bp	440.w	$4$	$8$	$4$	$1.976$	$\Q(\zeta_{16})$	$D_{8}$	$\Q(\sqrt{-66}) $	None		$8$	$0$	$0$	$0$	$0$	$0$	$1$		$q-\zeta_{16}^{6}q^{2}-\zeta_{16}^{4}q^{4}-\zeta_{16}^{7}q^{5}+\cdots$
3960.1.bp.b	$3960$	$1$	3960.bp	440.w	$4$	$8$	$4$	$1.976$	$\Q(\zeta_{16})$	$D_{8}$	$\Q(\sqrt{-66}) $	None		$8$	$0$	$0$	$0$	$0$	$0$	$1$		$q-\zeta_{16}^{6}q^{2}-\zeta_{16}^{4}q^{4}-\zeta_{16}^{3}q^{5}+\cdots$
792.2.h.f	$792$	$2$	792.h	88.g	$2$	$8$	$8$	$6.324$	8.0.$\cdots$.5	$_{}$	$\Q(\sqrt{-66}) $	None		$8$	$0$	$0$	$0$	$0$	$0$	$2^{6}$	$\mathrm{U}(1)[D_{2}]$	$q-\beta _{3}q^{2}-2q^{4}-\beta _{1}q^{5}+\beta _{2}q^{7}+2\beta _{3}q^{8}+\cdots$
264.3.p.a	$264$	$3$	264.p	264.p	$2$	$2$	$2$	$7.193$	$\Q(\sqrt{22}) $	$_{}$	$\Q(\sqrt{-66}) $	None	✓	$4$	$0$	$-4$	$-6$	$0$	$0$	$2$	$\mathrm{U}(1)[D_{2}]$	$q-2q^{2}-3q^{3}+4q^{4}+\beta q^{5}+6q^{6}+\cdots$
264.3.p.c	$264$	$3$	264.p	264.p	$2$	$2$	$2$	$7.193$	$\Q(\sqrt{3}) $	$_{}$	$\Q(\sqrt{-66}) $	None	✓	$4$	$0$	$-4$	$6$	$0$	$0$	$2$	$\mathrm{U}(1)[D_{2}]$	$q-2q^{2}+3q^{3}+4q^{4}+\beta q^{5}-6q^{6}+\cdots$
264.3.p.d	$264$	$3$	264.p	264.p	$2$	$2$	$2$	$7.193$	$\Q(\sqrt{22}) $	$_{}$	$\Q(\sqrt{-66}) $	None	✓	$4$	$0$	$4$	$-6$	$0$	$0$	$2$	$\mathrm{U}(1)[D_{2}]$	$q+2q^{2}-3q^{3}+4q^{4}+\beta q^{5}-6q^{6}+\cdots$
264.3.p.f	$264$	$3$	264.p	264.p	$2$	$2$	$2$	$7.193$	$\Q(\sqrt{3}) $	$_{}$	$\Q(\sqrt{-66}) $	None	✓	$4$	$0$	$4$	$6$	$0$	$0$	$2$	$\mathrm{U}(1)[D_{2}]$	$q+2q^{2}+3q^{3}+4q^{4}+\beta q^{5}+6q^{6}+\cdots$
2112.2.m.m	$2112$	$2$	2112.m	264.m	$2$	$16$	$16$	$16.864$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	$_{}$	$\Q(\sqrt{-66}) $	None		$16$	$0$	$0$	$0$	$0$	$0$	$2^{28}$	$\mathrm{U}(1)[D_{2}]$	$q-\beta _{5}q^{3}+\beta _{10}q^{5}+\beta _{8}q^{7}-3q^{9}+\cdots$
3168.2.h.f	$3168$	$2$	3168.h	88.g	$2$	$8$	$8$	$25.297$	8.0.$\cdots$.5	$_{}$	$\Q(\sqrt{-66}) $	None		$8$	$0$	$0$	$0$	$0$	$0$	$2^{8}$	$\mathrm{U}(1)[D_{2}]$	$q-\beta _{1}q^{5}-\beta _{2}q^{7}+\beta _{6}q^{11}+(-\beta _{2}+\cdots)q^{13}+\cdots$
1056.3.p.a	$1056$	$3$	1056.p	264.p	$2$	$2$	$2$	$28.774$	$\Q(\sqrt{3}) $	$_{}$	$\Q(\sqrt{-66}) $	None	✓	$4$	$0$	$0$	$-6$	$0$	$0$	$2$	$\mathrm{U}(1)[D_{2}]$	$q-3q^{3}+\beta q^{5}-3\beta q^{7}+9q^{9}-11q^{11}+\cdots$
1056.3.p.b	$1056$	$3$	1056.p	264.p	$2$	$2$	$2$	$28.774$	$\Q(\sqrt{3}) $	$_{}$	$\Q(\sqrt{-66}) $	None	✓	$4$	$0$	$0$	$-6$	$0$	$0$	$2$	$\mathrm{U}(1)[D_{2}]$	$q-3q^{3}+\beta q^{5}+3\beta q^{7}+9q^{9}+11q^{11}+\cdots$
1056.3.p.e	$1056$	$3$	1056.p	264.p	$2$	$2$	$2$	$28.774$	$\Q(\sqrt{22}) $	$_{}$	$\Q(\sqrt{-66}) $	None	✓	$4$	$0$	$0$	$6$	$0$	$0$	$2$	$\mathrm{U}(1)[D_{2}]$	$q+3q^{3}+\beta q^{5}+\beta q^{7}+9q^{9}-11q^{11}+\cdots$
1056.3.p.f	$1056$	$3$	1056.p	264.p	$2$	$2$	$2$	$28.774$	$\Q(\sqrt{22}) $	$_{}$	$\Q(\sqrt{-66}) $	None	✓	$4$	$0$	$0$	$6$	$0$	$0$	$2$	$\mathrm{U}(1)[D_{2}]$	$q+3q^{3}+\beta q^{5}-\beta q^{7}+9q^{9}+11q^{11}+\cdots$

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Elliptic 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.