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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 (46 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
3344.1.p.a	$3344$	$1$	3344.p	836.h	$2$	$1$	$1$	$1.669$	$\Q$	$D_{2}$	$\Q(\sqrt{-19}) $, $\Q(\sqrt{-209}) $	$\Q(\sqrt{11}) $	✓	$4$	$0$	$0$	$0$	$-2$	$-2$		$1$		$q-2q^{5}-2q^{7}-q^{9}-q^{11}+q^{19}+\cdots$
3344.1.p.b	$3344$	$1$	3344.p	836.h	$2$	$1$	$1$	$1.669$	$\Q$	$D_{2}$	$\Q(\sqrt{-19}) $, $\Q(\sqrt{-209}) $	$\Q(\sqrt{11}) $	✓	$4$	$0$	$0$	$0$	$-2$	$2$		$1$		$q-2q^{5}+2q^{7}-q^{9}+q^{11}-q^{19}+\cdots$
3344.1.p.c	$3344$	$1$	3344.p	836.h	$2$	$2$	$2$	$1.669$	$\Q(\sqrt{-3}) $	$D_{6}$	$\Q(\sqrt{-19}) $	None		$4$	$0$	$0$	$0$	$2$	$-2$		$1$		$q+q^{5}-q^{7}-q^{9}+\zeta_{6}^{2}q^{11}+(\zeta_{6}+\zeta_{6}^{2}+\cdots)q^{17}+\cdots$
3344.1.p.d	$3344$	$1$	3344.p	836.h	$2$	$2$	$2$	$1.669$	$\Q(\sqrt{-3}) $	$D_{6}$	$\Q(\sqrt{-19}) $	None		$4$	$0$	$0$	$0$	$2$	$2$		$1$		$q+q^{5}+q^{7}-q^{9}-\zeta_{6}^{2}q^{11}+(\zeta_{6}+\zeta_{6}^{2}+\cdots)q^{17}+\cdots$
3344.1.p.e	$3344$	$1$	3344.p	836.h	$2$	$4$	$4$	$1.669$	$\Q(\zeta_{20})^+$	$D_{10}$	$\Q(\sqrt{-209}) $	None	✓	$4$	$0$	$0$	$0$	$2$	$-2$		$1$		$q+\beta _{3}q^{3}+(1+\beta _{2})q^{5}+\beta _{2}q^{7}+(1-\beta _{2}+\cdots)q^{9}+\cdots$
3344.1.p.f	$3344$	$1$	3344.p	836.h	$2$	$4$	$4$	$1.669$	$\Q(\zeta_{20})^+$	$D_{10}$	$\Q(\sqrt{-209}) $	None	✓	$4$	$0$	$0$	$0$	$2$	$2$		$1$		$q-\beta _{1}q^{3}-\beta _{2}q^{5}+(1+\beta _{2})q^{7}+(2+\beta _{2}+\cdots)q^{9}+\cdots$
3344.1.bb.a	$3344$	$1$	3344.bb	209.h	$6$	$4$	$2$	$1.669$	$\Q(\zeta_{12})$	$A_{4}$	None	None		$4$	$0$	$0$	$2$	$-2$	$0$		$1$		$q-\zeta_{12}^{4}q^{3}+\zeta_{12}^{4}q^{5}-\zeta_{12}^{3}q^{11}+\cdots$
3344.1.bc.a	$3344$	$1$	3344.bc	836.m	$6$	$2$	$1$	$1.669$	$\Q(\sqrt{-3}) $	$D_{6}$	None	$\Q(\sqrt{11}) $		$4$	$0$	$0$	$0$	$-1$	$-2$		$1$		$q+\zeta_{6}^{2}q^{5}-q^{7}+\zeta_{6}q^{9}+q^{11}-\zeta_{6}^{2}q^{19}+\cdots$
3344.1.bc.b	$3344$	$1$	3344.bc	836.m	$6$	$2$	$1$	$1.669$	$\Q(\sqrt{-3}) $	$D_{6}$	None	$\Q(\sqrt{11}) $		$4$	$0$	$0$	$0$	$-1$	$2$		$1$		$q+\zeta_{6}^{2}q^{5}+q^{7}+\zeta_{6}q^{9}-q^{11}+\zeta_{6}^{2}q^{19}+\cdots$
3344.1.bq.a	$3344$	$1$	3344.bq	836.s	$10$	$4$	$1$	$1.669$	$\Q(\zeta_{10})$	$D_{10}$	$\Q(\sqrt{-19}) $	None		$4$	$0$	$0$	$0$	$2$	$-3$		$1$		$q+(\zeta_{10}-\zeta_{10}^{2})q^{5}+(-1-\zeta_{10}^{4})q^{7}+\cdots$
3344.1.bq.b	$3344$	$1$	3344.bq	836.s	$10$	$4$	$1$	$1.669$	$\Q(\zeta_{10})$	$D_{10}$	$\Q(\sqrt{-19}) $	None		$4$	$0$	$0$	$0$	$2$	$3$		$1$		$q+(\zeta_{10}-\zeta_{10}^{2})q^{5}+(1+\zeta_{10}^{4})q^{7}+\cdots$
3344.1.bq.c	$3344$	$1$	3344.bq	836.s	$10$	$8$	$2$	$1.669$	$\Q(\zeta_{15})$	$D_{30}$	$\Q(\sqrt{-19}) $	None		$4$	$0$	$0$	$0$	$-2$	$-3$		$1$		$q+(\zeta_{30}^{11}+\zeta_{30}^{13})q^{5}+(\zeta_{30}^{2}+\zeta_{30}^{10}+\cdots)q^{7}+\cdots$
3344.1.bq.d	$3344$	$1$	3344.bq	836.s	$10$	$8$	$2$	$1.669$	$\Q(\zeta_{15})$	$D_{30}$	$\Q(\sqrt{-19}) $	None		$4$	$0$	$0$	$0$	$-2$	$3$		$1$		$q+(\zeta_{30}-\zeta_{30}^{8})q^{5}+(\zeta_{30}^{5}+\zeta_{30}^{7}+\cdots)q^{7}+\cdots$
3344.1.bx.a	$3344$	$1$	3344.bx	209.m	$10$	$4$	$1$	$1.669$	$\Q(\zeta_{10})$	$D_{5}$	$\Q(\sqrt{-19}) $	None		$4$	$0$	$0$	$0$	$-2$	$-3$		$1$		$q+(\zeta_{10}^{2}+\zeta_{10}^{4})q^{5}+(-1+\zeta_{10}^{3}+\cdots)q^{7}+\cdots$
3344.1.bx.b	$3344$	$1$	3344.bx	209.m	$10$	$8$	$2$	$1.669$	$\Q(\zeta_{15})$	$D_{15}$	$\Q(\sqrt{-19}) $	None		$4$	$0$	$0$	$0$	$2$	$3$		$1$		$q+(-\zeta_{30}+\zeta_{30}^{2})q^{5}+(-\zeta_{30}^{10}-\zeta_{30}^{14}+\cdots)q^{7}+\cdots$
3344.1.ck.a	$3344$	$1$	3344.ck	3344.bk	$12$	$8$	$2$	$1.669$	$\Q(\zeta_{24})$	$S_{4}$	None	None		$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{24}^{7}q^{2}-\zeta_{24}^{2}q^{4}+(-\zeta_{24}^{3}+\zeta_{24}^{9}+\cdots)q^{7}+\cdots$
3344.2.a.a	$3344$	$2$	3344.a	1.a	$1$	$1$	$1$	$26.702$	$\Q$	$_{}$	None	None	✓	$1$	$2$	$0$	$-3$	$-2$	$-1$	$-$	$1$	$\mathrm{SU}(2)$	$q-3q^{3}-2q^{5}-q^{7}+6q^{9}-q^{11}+\cdots$
3344.2.a.b	$3344$	$2$	3344.a	1.a	$1$	$1$	$1$	$26.702$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$0$	$-2$	$2$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{3}+2q^{5}+q^{9}-q^{11}+4q^{13}+\cdots$
3344.2.a.c	$3344$	$2$	3344.a	1.a	$1$	$1$	$1$	$26.702$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$0$	$-1$	$-3$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-3q^{5}-2q^{7}-2q^{9}+q^{11}+\cdots$
3344.2.a.d	$3344$	$2$	3344.a	1.a	$1$	$1$	$1$	$26.702$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$0$	$-1$	$-3$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-3q^{5}+4q^{7}-2q^{9}-q^{11}+\cdots$
3344.2.a.e	$3344$	$2$	3344.a	1.a	$1$	$1$	$1$	$26.702$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$0$	$-1$	$2$	$3$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+2q^{5}+3q^{7}-2q^{9}+q^{11}+\cdots$
3344.2.a.f	$3344$	$2$	3344.a	1.a	$1$	$1$	$1$	$26.702$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$0$	$0$	$-2$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{5}+4q^{7}-3q^{9}+q^{11}+2q^{13}+\cdots$
3344.2.a.g	$3344$	$2$	3344.a	1.a	$1$	$1$	$1$	$26.702$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$0$	$0$	$2$	$-2$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{5}-2q^{7}-3q^{9}-q^{11}-2q^{13}+\cdots$
3344.2.a.h	$3344$	$2$	3344.a	1.a	$1$	$1$	$1$	$26.702$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$0$	$1$	$-2$	$3$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-2q^{5}+3q^{7}-2q^{9}+q^{11}+\cdots$
3344.2.a.i	$3344$	$2$	3344.a	1.a	$1$	$1$	$1$	$26.702$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$0$	$1$	$1$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+q^{5}-2q^{9}+q^{11}-2q^{13}+\cdots$
3344.2.a.j	$3344$	$2$	3344.a	1.a	$1$	$2$	$2$	$26.702$	$\Q(\sqrt{13}) $	$_{}$	None	None	✓	$1$	$1$	$0$	$-1$	$-1$	$-1$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta q^{3}-\beta q^{5}+(-1+\beta )q^{7}+\beta q^{9}+\cdots$
3344.2.a.k	$3344$	$2$	3344.a	1.a	$1$	$2$	$2$	$26.702$	$\Q(\sqrt{17}) $	$_{}$	None	None	✓	$1$	$1$	$0$	$-1$	$4$	$-3$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta q^{3}+2q^{5}+(-2+\beta )q^{7}+(1+\beta )q^{9}+\cdots$
3344.2.a.l	$3344$	$2$	3344.a	1.a	$1$	$2$	$2$	$26.702$	$\Q(\sqrt{21}) $	$_{}$	None	None	✓	$1$	$0$	$0$	$1$	$3$	$5$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{3}+(2-\beta )q^{5}+(3-\beta )q^{7}+(2+\beta )q^{9}+\cdots$
3344.2.a.m	$3344$	$2$	3344.a	1.a	$1$	$2$	$2$	$26.702$	$\Q(\sqrt{2}) $	$_{}$	None	None	✓	$1$	$1$	$0$	$2$	$-2$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+(1+\beta )q^{3}-q^{5}-\beta q^{7}+2\beta q^{9}-q^{11}+\cdots$
3344.2.a.n	$3344$	$2$	3344.a	1.a	$1$	$2$	$2$	$26.702$	$\Q(\sqrt{2}) $	$_{}$	None	None	✓	$1$	$0$	$0$	$2$	$-2$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1+\beta )q^{3}-q^{5}+(2+\beta )q^{7}+2\beta q^{9}+\cdots$
3344.2.a.o	$3344$	$2$	3344.a	1.a	$1$	$2$	$2$	$26.702$	$\Q(\sqrt{13}) $	$_{}$	None	None	✓	$1$	$0$	$0$	$3$	$-1$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1+\beta )q^{3}+(-1+\beta )q^{5}+\beta q^{7}+(1+\cdots)q^{9}+\cdots$
3344.2.a.p	$3344$	$2$	3344.a	1.a	$1$	$3$	$3$	$26.702$	3.3.469.1	$_{}$	None	None	✓	$1$	$0$	$0$	$-1$	$5$	$-1$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{3}+(2-\beta _{1})q^{5}+\beta _{2}q^{7}+(1+\beta _{2})q^{9}+\cdots$
3344.2.a.q	$3344$	$2$	3344.a	1.a	$1$	$3$	$3$	$26.702$	3.3.621.1	$_{}$	None	None	✓	$1$	$0$	$0$	$0$	$-3$	$6$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{3}+(-1-\beta _{1}-\beta _{2})q^{5}+(2+\beta _{1}+\cdots)q^{7}+\cdots$
3344.2.a.r	$3344$	$2$	3344.a	1.a	$1$	$3$	$3$	$26.702$	3.3.229.1	$_{}$	None	None	✓	$1$	$1$	$0$	$0$	$0$	$-3$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{3}+\beta _{1}q^{5}+(-1-\beta _{1})q^{7}+\beta _{2}q^{9}+\cdots$
3344.2.a.s	$3344$	$2$	3344.a	1.a	$1$	$4$	$4$	$26.702$	4.4.13676.1	$_{}$	None	None	✓	$1$	$1$	$0$	$1$	$-3$	$3$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{3}+(-1+\beta _{3})q^{5}+(1-\beta _{1})q^{7}+\cdots$
3344.2.a.t	$3344$	$2$	3344.a	1.a	$1$	$5$	$5$	$26.702$	5.5.246832.1	$_{}$	None	None	✓	$1$	$1$	$0$	$-1$	$-5$	$-6$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{3}q^{3}+(-1-\beta _{1}+\beta _{2})q^{5}+(-2+\cdots)q^{7}+\cdots$
3344.2.a.u	$3344$	$2$	3344.a	1.a	$1$	$5$	$5$	$26.702$	5.5.3979184.1	$_{}$	None	None	✓	$1$	$0$	$0$	$-1$	$7$	$-8$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{4}q^{3}+(1+\beta _{1})q^{5}+(-2+\beta _{1})q^{7}+\cdots$
3344.2.a.v	$3344$	$2$	3344.a	1.a	$1$	$6$	$6$	$26.702$	6.6.576096652.1	$_{}$	None	None	✓	$1$	$1$	$0$	$-4$	$1$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta _{1})q^{3}+\beta _{4}q^{5}-\beta _{3}q^{7}+(1+\cdots)q^{9}+\cdots$
3344.2.a.w	$3344$	$2$	3344.a	1.a	$1$	$6$	$6$	$26.702$	6.6.744786576.1	$_{}$	None	None	✓	$1$	$0$	$0$	$-1$	$5$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{3}+(1+\beta _{5})q^{5}+(1-\beta _{1}+\beta _{2}+\cdots)q^{7}+\cdots$
3344.2.a.x	$3344$	$2$	3344.a	1.a	$1$	$6$	$6$	$26.702$	$\mathbb{Q}[x]/(x^{6} - \cdots)$	$_{}$	None	None	✓	$1$	$0$	$0$	$2$	$0$	$-2$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{3}-\beta _{5}q^{5}-\beta _{4}q^{7}+(2+\beta _{2}+\cdots)q^{9}+\cdots$
3344.2.a.y	$3344$	$2$	3344.a	1.a	$1$	$6$	$6$	$26.702$	6.6.57500224.1	$_{}$	None	None	✓	$1$	$0$	$0$	$4$	$-4$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1-\beta _{1})q^{3}+(-1-\beta _{4})q^{5}+(1-\beta _{1}+\cdots)q^{7}+\cdots$
3344.2.a.z	$3344$	$2$	3344.a	1.a	$1$	$6$	$6$	$26.702$	6.6.106392688.1	$_{}$	None	None	✓	$1$	$0$	$0$	$4$	$-3$	$3$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1-\beta _{1})q^{3}+(-1+\beta _{5})q^{5}+\beta _{5}q^{7}+\cdots$
3344.2.a.ba	$3344$	$2$	3344.a	1.a	$1$	$7$	$7$	$26.702$	$\mathbb{Q}[x]/(x^{7} - \cdots)$	$_{}$	None	None	✓	$1$	$1$	$0$	$-2$	$2$	$-10$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta _{2}q^{3}-\beta _{4}q^{5}+(-2-\beta _{2}+\beta _{5}+\cdots)q^{7}+\cdots$
3344.2.a.bb	$3344$	$2$	3344.a	1.a	$1$	$9$	$9$	$26.702$	$\mathbb{Q}[x]/(x^{9} - \cdots)$	$_{}$	None	None	✓	$1$	$0$	$0$	$-1$	$6$	$-3$	$-$	$2$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{3}+(1+\beta _{7})q^{5}-\beta _{8}q^{7}+(2+\beta _{2}+\cdots)q^{9}+\cdots$
3344.2.o.a	$3344$	$2$	3344.o	76.d	$2$	$36$	$36$	$26.702$		$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
3344.2.o.b	$3344$	$2$	3344.o	76.d	$2$	$64$	$64$	$26.702$		$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$

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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.