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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 (1-50 of 90 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				Fricke sign	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*	$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
2200.1.d.a	$2200$	$1$	2200.d	88.b	$2$	$1$	$1$	$1.098$	$\Q$	$D_{3}$	$\Q(\sqrt{-22}) $	None	✓	$2$	$0$	$-1$	$0$	$0$	$0$		$1$		$q-q^{2}+q^{4}-q^{8}+q^{9}-q^{11}+q^{13}+\cdots$
2200.1.d.b	$2200$	$1$	2200.d	88.b	$2$	$1$	$1$	$1.098$	$\Q$	$D_{3}$	$\Q(\sqrt{-22}) $	None	✓	$2$	$0$	$-1$	$0$	$0$	$0$		$1$		$q-q^{2}+q^{4}-q^{8}+q^{9}+q^{11}+q^{13}+\cdots$
2200.1.d.c	$2200$	$1$	2200.d	88.b	$2$	$1$	$1$	$1.098$	$\Q$	$D_{3}$	$\Q(\sqrt{-22}) $	None	✓	$2$	$0$	$1$	$0$	$0$	$0$		$1$		$q+q^{2}+q^{4}+q^{8}+q^{9}-q^{11}-q^{13}+\cdots$
2200.1.d.d	$2200$	$1$	2200.d	88.b	$2$	$1$	$1$	$1.098$	$\Q$	$D_{3}$	$\Q(\sqrt{-22}) $	None	✓	$2$	$0$	$1$	$0$	$0$	$0$		$1$		$q+q^{2}+q^{4}+q^{8}+q^{9}+q^{11}-q^{13}+\cdots$
2200.1.d.e	$2200$	$1$	2200.d	88.b	$2$	$2$	$2$	$1.098$	$\Q(\sqrt{-1}) $	$D_{3}$	$\Q(\sqrt{-110}) $	None		$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q-iq^{2}-iq^{3}-q^{4}-q^{6}+iq^{7}+iq^{8}+\cdots$
2200.1.d.f	$2200$	$1$	2200.d	88.b	$2$	$2$	$2$	$1.098$	$\Q(\sqrt{-1}) $	$D_{3}$	$\Q(\sqrt{-110}) $	None		$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q+iq^{2}-iq^{3}-q^{4}+q^{6}-iq^{7}-iq^{8}+\cdots$
2200.1.d.g	$2200$	$1$	2200.d	88.b	$2$	$4$	$4$	$1.098$	$\Q(\zeta_{8})$	$D_{4}$	$\Q(\sqrt{-55}) $	None		$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{8}q^{2}+\zeta_{8}^{2}q^{4}+(-\zeta_{8}-\zeta_{8}^{3})q^{7}+\cdots$
2200.1.o.a	$2200$	$1$	2200.o	440.o	$2$	$2$	$2$	$1.098$	$\Q(\sqrt{-1}) $	$D_{3}$	$\Q(\sqrt{-22}) $	None		$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q-iq^{2}-q^{4}+iq^{8}-q^{9}-q^{11}-iq^{13}+\cdots$
2200.1.o.b	$2200$	$1$	2200.o	440.o	$2$	$2$	$2$	$1.098$	$\Q(\sqrt{-1}) $	$D_{3}$	$\Q(\sqrt{-22}) $	None		$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q-iq^{2}-q^{4}+iq^{8}-q^{9}+q^{11}-iq^{13}+\cdots$
2200.1.w.a	$2200$	$1$	2200.w	440.w	$4$	$4$	$2$	$1.098$	$\Q(\zeta_{8})$	$D_{2}$	$\Q(\sqrt{-10}) $, $\Q(\sqrt{-55}) $	$\Q(\sqrt{22}) $		$16$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{8}q^{2}+\zeta_{8}^{2}q^{4}+\zeta_{8}q^{7}-\zeta_{8}^{3}q^{8}+\cdots$
2200.1.w.b	$2200$	$1$	2200.w	440.w	$4$	$4$	$2$	$1.098$	$\Q(\zeta_{8})$	$D_{2}$	$\Q(\sqrt{-2}) $, $\Q(\sqrt{-55}) $	$\Q(\sqrt{110}) $		$16$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{8}^{3}q^{2}-\zeta_{8}^{2}q^{4}-\zeta_{8}q^{8}+\zeta_{8}^{2}q^{9}+\cdots$
2200.1.w.c	$2200$	$1$	2200.w	440.w	$4$	$8$	$4$	$1.098$	$\Q(\zeta_{24})$	$D_{6}$	$\Q(\sqrt{-2}) $	None		$16$	$0$	$0$	$0$	$0$	$0$		$1$		$q+\zeta_{24}^{9}q^{2}+(\zeta_{24}^{7}+\zeta_{24}^{11})q^{3}-\zeta_{24}^{6}q^{4}+\cdots$
2200.1.cl.a	$2200$	$1$	2200.cl	88.l	$10$	$4$	$1$	$1.098$	$\Q(\zeta_{10})$	$D_{5}$	$\Q(\sqrt{-2}) $	None		$4$	$0$	$1$	$2$	$0$	$0$		$1$		$q+\zeta_{10}q^{2}+(-\zeta_{10}^{2}-\zeta_{10}^{4})q^{3}+\zeta_{10}^{2}q^{4}+\cdots$
2200.1.cl.b	$2200$	$1$	2200.cl	88.l	$10$	$8$	$2$	$1.098$	$\Q(\zeta_{15})$	$D_{15}$	$\Q(\sqrt{-2}) $	None		$4$	$0$	$-2$	$2$	$0$	$0$		$1$		$q-\zeta_{30}^{3}q^{2}+(-\zeta_{30}^{7}-\zeta_{30}^{11})q^{3}+\cdots$
2200.1.cl.c	$2200$	$1$	2200.cl	88.l	$10$	$8$	$2$	$1.098$	$\Q(\zeta_{20})$	$D_{5}$	$\Q(\sqrt{-10}) $	None		$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{20}^{7}q^{2}-\zeta_{20}^{4}q^{4}+(-\zeta_{20}^{3}+\zeta_{20}^{5}+\cdots)q^{7}+\cdots$
2200.1.cl.d	$2200$	$1$	2200.cl	88.l	$10$	$8$	$2$	$1.098$	$\Q(\zeta_{15})$	$D_{15}$	$\Q(\sqrt{-2}) $	None		$4$	$0$	$2$	$-2$	$0$	$0$		$1$		$q+\zeta_{30}^{3}q^{2}+(\zeta_{30}^{7}+\zeta_{30}^{11})q^{3}+\zeta_{30}^{6}q^{4}+\cdots$
2200.1.dd.a	$2200$	$1$	2200.dd	440.ah	$10$	$8$	$2$	$1.098$	$\Q(\zeta_{20})$	$D_{5}$	$\Q(\sqrt{-2}) $	None		$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q+\zeta_{20}^{3}q^{2}+(\zeta_{20}-\zeta_{20}^{7})q^{3}+\zeta_{20}^{6}q^{4}+\cdots$
2200.1.dd.b	$2200$	$1$	2200.dd	440.ah	$10$	$16$	$4$	$1.098$	$\Q(\zeta_{60})$	$D_{15}$	$\Q(\sqrt{-2}) $	None		$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q+\zeta_{60}^{9}q^{2}+(-\zeta_{60}+\zeta_{60}^{23})q^{3}+\cdots$
2200.1.fr.a	$2200$	$1$	2200.fr	440.ar	$20$	$16$	$2$	$1.098$	$\Q(\zeta_{40})$	$D_{10}$	$\Q(\sqrt{-2}) $	None		$16$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{40}^{9}q^{2}+(\zeta_{40}^{3}-\zeta_{40}^{11})q^{3}+\zeta_{40}^{18}q^{4}+\cdots$
2200.1.fr.b	$2200$	$1$	2200.fr	440.ar	$20$	$16$	$2$	$1.098$	$\Q(\zeta_{40})$	$D_{10}$	$\Q(\sqrt{-10}) $	None		$16$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{40}^{19}q^{2}-\zeta_{40}^{18}q^{4}+(\zeta_{40}^{11}+\cdots)q^{7}+\cdots$
2200.1.fr.c	$2200$	$1$	2200.fr	440.ar	$20$	$32$	$4$	$1.098$	$\Q(\zeta_{120})$	$D_{30}$	$\Q(\sqrt{-2}) $	None		$16$	$0$	$0$	$0$	$0$	$0$		$1$		$q+\zeta_{120}^{39}q^{2}+(-\zeta_{120}-\zeta_{120}^{53})q^{3}+\cdots$
2200.2.a.a	$2200$	$2$	2200.a	1.a	$1$	$1$	$1$	$17.567$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$0$	$-3$	$0$	$-1$	$-$	$1$	$\mathrm{SU}(2)$	$q-3q^{3}-q^{7}+6q^{9}-q^{11}+6q^{13}+\cdots$
2200.2.a.b	$2200$	$2$	2200.a	1.a	$1$	$1$	$1$	$17.567$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$0$	$-2$	$0$	$-4$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{3}-4q^{7}+q^{9}+q^{11}+6q^{13}+\cdots$
2200.2.a.c	$2200$	$2$	2200.a	1.a	$1$	$1$	$1$	$17.567$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$0$	$-2$	$0$	$2$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{3}+2q^{7}+q^{9}-q^{11}-4q^{17}+\cdots$
2200.2.a.d	$2200$	$2$	2200.a	1.a	$1$	$1$	$1$	$17.567$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$0$	$-1$	$0$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+q^{7}-2q^{9}-q^{11}+q^{17}+q^{19}+\cdots$
2200.2.a.e	$2200$	$2$	2200.a	1.a	$1$	$1$	$1$	$17.567$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$0$	$0$	$0$	$-4$	$-$	$1$	$\mathrm{SU}(2)$	$q-4q^{7}-3q^{9}-q^{11}-6q^{13}+6q^{17}+\cdots$
2200.2.a.f	$2200$	$2$	2200.a	1.a	$1$	$1$	$1$	$17.567$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$0$	$0$	$0$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{7}-3q^{9}-q^{11}-8q^{19}+8q^{23}+\cdots$
2200.2.a.g	$2200$	$2$	2200.a	1.a	$1$	$1$	$1$	$17.567$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$0$	$0$	$0$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{7}-3q^{9}+q^{11}+4q^{13}+4q^{17}+\cdots$
2200.2.a.h	$2200$	$2$	2200.a	1.a	$1$	$1$	$1$	$17.567$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$0$	$1$	$0$	$-1$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-q^{7}-2q^{9}-q^{11}-q^{17}+q^{19}+\cdots$
2200.2.a.i	$2200$	$2$	2200.a	1.a	$1$	$1$	$1$	$17.567$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$0$	$2$	$0$	$-2$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{3}-2q^{7}+q^{9}-q^{11}+4q^{17}+\cdots$
2200.2.a.j	$2200$	$2$	2200.a	1.a	$1$	$1$	$1$	$17.567$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$0$	$2$	$0$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{3}+4q^{7}+q^{9}+q^{11}-6q^{13}+\cdots$
2200.2.a.k	$2200$	$2$	2200.a	1.a	$1$	$1$	$1$	$17.567$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$0$	$3$	$0$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q+3q^{3}+2q^{7}+6q^{9}-q^{11}+6q^{17}+\cdots$
2200.2.a.l	$2200$	$2$	2200.a	1.a	$1$	$2$	$2$	$17.567$	$\Q(\sqrt{17}) $	$_{}$	None	None	✓	$1$	$1$	$0$	$-1$	$0$	$-5$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta q^{3}+(-2-\beta )q^{7}+(1+\beta )q^{9}-q^{11}+\cdots$
2200.2.a.m	$2200$	$2$	2200.a	1.a	$1$	$2$	$2$	$17.567$	$\Q(\sqrt{17}) $	$_{}$	None	None	✓	$1$	$1$	$0$	$-1$	$0$	$-3$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta q^{3}+(-2+\beta )q^{7}+(1+\beta )q^{9}+q^{11}+\cdots$
2200.2.a.n	$2200$	$2$	2200.a	1.a	$1$	$2$	$2$	$17.567$	$\Q(\sqrt{5}) $	$_{}$	None	None	✓	$1$	$1$	$0$	$-1$	$0$	$1$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta q^{3}+(1-\beta )q^{7}+(-2+\beta )q^{9}-q^{11}+\cdots$
2200.2.a.o	$2200$	$2$	2200.a	1.a	$1$	$2$	$2$	$17.567$	$\Q(\sqrt{17}) $	$_{}$	None	None	✓	$1$	$1$	$0$	$-1$	$0$	$2$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta q^{3}+2\beta q^{7}+(1+\beta )q^{9}-q^{11}+\cdots$
2200.2.a.p	$2200$	$2$	2200.a	1.a	$1$	$2$	$2$	$17.567$	$\Q(\sqrt{5}) $	$_{}$	None	None	✓	$1$	$1$	$0$	$-1$	$0$	$3$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta q^{3}+(1+\beta )q^{7}+(-2+\beta )q^{9}+q^{11}+\cdots$
2200.2.a.q	$2200$	$2$	2200.a	1.a	$1$	$2$	$2$	$17.567$	$\Q(\sqrt{5}) $	$_{}$	None	None	✓	$1$	$1$	$0$	$1$	$0$	$-3$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{3}+(-1-\beta )q^{7}+(-2+\beta )q^{9}+\cdots$
2200.2.a.r	$2200$	$2$	2200.a	1.a	$1$	$2$	$2$	$17.567$	$\Q(\sqrt{5}) $	$_{}$	None	None	✓	$1$	$1$	$0$	$1$	$0$	$-1$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{3}+(-1+\beta )q^{7}+(-2+\beta )q^{9}+\cdots$
2200.2.a.s	$2200$	$2$	2200.a	1.a	$1$	$2$	$2$	$17.567$	$\Q(\sqrt{17}) $	$_{}$	None	None	✓	$1$	$0$	$0$	$1$	$0$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{3}+\beta q^{7}+(1+\beta )q^{9}+q^{11}-2q^{13}+\cdots$
2200.2.a.t	$2200$	$2$	2200.a	1.a	$1$	$3$	$3$	$17.567$	3.3.837.1	$_{}$	None	None	✓	$1$	$0$	$0$	$-3$	$0$	$-3$	$-$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta _{1})q^{3}+(-1+\beta _{2})q^{7}+(2+\cdots)q^{9}+\cdots$
2200.2.a.u	$2200$	$2$	2200.a	1.a	$1$	$3$	$3$	$17.567$	3.3.1229.1	$_{}$	None	None	✓	$1$	$0$	$0$	$-1$	$0$	$-3$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{3}+(-1-\beta _{2})q^{7}+(2+\beta _{2})q^{9}+\cdots$
2200.2.a.v	$2200$	$2$	2200.a	1.a	$1$	$3$	$3$	$17.567$	3.3.1229.1	$_{}$	None	None	✓	$1$	$0$	$0$	$1$	$0$	$3$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{3}+(1+\beta _{2})q^{7}+(2+\beta _{2})q^{9}+\cdots$
2200.2.a.w	$2200$	$2$	2200.a	1.a	$1$	$3$	$3$	$17.567$	3.3.837.1	$_{}$	None	None	✓	$1$	$0$	$0$	$3$	$0$	$3$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1-\beta _{1})q^{3}+(1-\beta _{2})q^{7}+(2-2\beta _{1}+\cdots)q^{9}+\cdots$
2200.2.a.x	$2200$	$2$	2200.a	1.a	$1$	$4$	$4$	$17.567$	4.4.54764.1	$_{}$	None	None	✓	$1$	$1$	$0$	$-1$	$0$	$-1$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{3}-\beta _{3}q^{7}+(1+\beta _{1}+\beta _{2}+\beta _{3})q^{9}+\cdots$
2200.2.a.y	$2200$	$2$	2200.a	1.a	$1$	$4$	$4$	$17.567$	4.4.54764.1	$_{}$	None	None	✓	$1$	$0$	$0$	$1$	$0$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{3}+\beta _{3}q^{7}+(1+\beta _{1}+\beta _{2}+\beta _{3})q^{9}+\cdots$
2200.2.b.a	$2200$	$2$	2200.b	5.b	$2$	$2$	$2$	$17.567$	$\Q(\sqrt{-1}) $	$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+3iq^{3}-2iq^{7}-6q^{9}-q^{11}-6iq^{17}+\cdots$
2200.2.b.b	$2200$	$2$	2200.b	5.b	$2$	$2$	$2$	$17.567$	$\Q(\sqrt{-1}) $	$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+3iq^{3}-iq^{7}-6q^{9}-q^{11}-6iq^{13}+\cdots$
2200.2.b.c	$2200$	$2$	2200.b	5.b	$2$	$2$	$2$	$17.567$	$\Q(\sqrt{-1}) $	$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q+2iq^{7}+3q^{9}-q^{11}-3iq^{13}-3iq^{17}+\cdots$
2200.2.b.d	$2200$	$2$	2200.b	5.b	$2$	$2$	$2$	$17.567$	$\Q(\sqrt{-1}) $	$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q+iq^{7}+3q^{9}-q^{11}+8q^{19}-4iq^{23}+\cdots$

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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.