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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 (28 matches)

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Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	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	CM	Self-dual	Inner twists	Rank*	$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
334.2.a.a	$334$	$2$	334.a	1.a	$1$	$1$	$1$	$2.667$	$\Q$	None	✓	$1$	$0$	$1$	$0$	$3$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+3q^{5}+q^{7}+q^{8}-3q^{9}+\cdots$
334.2.a.b	$334$	$2$	334.a	1.a	$1$	$2$	$2$	$2.667$	$\Q(\sqrt{5}) $	None	✓	$1$	$1$	$-2$	$-1$	$-2$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-\beta q^{3}+q^{4}-q^{5}+\beta q^{6}+(-1+\cdots)q^{7}+\cdots$
334.2.a.c	$334$	$2$	334.a	1.a	$1$	$2$	$2$	$2.667$	$\Q(\sqrt{2}) $	None	✓	$1$	$0$	$-2$	$0$	$2$	$-6$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+2\beta q^{3}+q^{4}+(1-\beta )q^{5}-2\beta q^{6}+\cdots$
334.2.a.d	$334$	$2$	334.a	1.a	$1$	$2$	$2$	$2.667$	$\Q(\sqrt{5}) $	None	✓	$1$	$1$	$2$	$-3$	$-4$	$-6$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+(-1-\beta )q^{3}+q^{4}+(-3+2\beta )q^{5}+\cdots$
334.2.a.e	$334$	$2$	334.a	1.a	$1$	$3$	$3$	$2.667$	3.3.469.1	None	✓	$1$	$0$	$-3$	$-1$	$0$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-\beta _{1}q^{3}+q^{4}+(-\beta _{1}-\beta _{2})q^{5}+\cdots$
334.2.a.f	$334$	$2$	334.a	1.a	$1$	$3$	$3$	$2.667$	3.3.733.1	None	✓	$1$	$0$	$3$	$1$	$-3$	$3$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+\beta _{1}q^{3}+q^{4}-q^{5}+\beta _{1}q^{6}+\cdots$
334.2.c.a	$334$	$2$	334.c	167.c	$83$	$574$	$7$	$2.667$		None		$2$	$0$	$-7$	$-2$	$-2$	$-6$			$\mathrm{SU}(2)[C_{83}]$
334.2.c.b	$334$	$2$	334.c	167.c	$83$	$574$	$7$	$2.667$		None		$2$	$0$	$7$	$2$	$0$	$6$			$\mathrm{SU}(2)[C_{83}]$
334.3.b.a	$334$	$3$	334.b	167.b	$2$	$28$	$28$	$9.101$		None		$2$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
334.3.d.a	$334$	$3$	334.d	167.d	$166$	$2296$	$28$	$9.101$		None		$2$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{166}]$
334.4.a.a	$334$	$4$	334.a	1.a	$1$	$9$	$9$	$19.707$	$\mathbb{Q}[x]/(x^{9} - \cdots)$	None	✓	$1$	$1$	$-18$	$1$	$-10$	$14$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{2}+\beta _{1}q^{3}+4q^{4}+(-1+\beta _{5}+\cdots)q^{5}+\cdots$
334.4.a.b	$334$	$4$	334.a	1.a	$1$	$9$	$9$	$19.707$	$\mathbb{Q}[x]/(x^{9} - \cdots)$	None	✓	$1$	$1$	$18$	$-13$	$-30$	$-56$	$-$	$3$	$\mathrm{SU}(2)$	$q+2q^{2}+(-1+\beta _{2})q^{3}+4q^{4}+(-4+\cdots)q^{5}+\cdots$
334.4.a.c	$334$	$4$	334.a	1.a	$1$	$12$	$12$	$19.707$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	None	✓	$1$	$0$	$-24$	$1$	$10$	$-28$	$+$	$2^{2}$	$\mathrm{SU}(2)$	$q-2q^{2}+\beta _{1}q^{3}+4q^{4}+(1+\beta _{8})q^{5}+\cdots$
334.4.a.d	$334$	$4$	334.a	1.a	$1$	$12$	$12$	$19.707$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	None	✓	$1$	$0$	$24$	$11$	$20$	$70$	$+$	$1$	$\mathrm{SU}(2)$	$q+2q^{2}+(1-\beta _{1})q^{3}+4q^{4}+(2-\beta _{3}+\cdots)q^{5}+\cdots$
334.5.b.a	$334$	$5$	334.b	167.b	$2$	$56$	$56$	$34.526$		None		$2$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
334.6.a.a	$334$	$6$	334.a	1.a	$1$	$16$	$16$	$53.568$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	None	✓	$1$	$1$	$-64$	$5$	$-50$	$196$	$+$	$2^{7}\cdot 3$	$\mathrm{SU}(2)$	$q-4q^{2}+\beta _{1}q^{3}+2^{4}q^{4}+(-3-\beta _{2}+\cdots)q^{5}+\cdots$
334.6.a.b	$334$	$6$	334.a	1.a	$1$	$16$	$16$	$53.568$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	None	✓	$1$	$1$	$64$	$-41$	$-100$	$-490$	$+$	$2^{7}$	$\mathrm{SU}(2)$	$q+4q^{2}+(-3+\beta _{1})q^{3}+2^{4}q^{4}+(-6+\cdots)q^{5}+\cdots$
334.6.a.c	$334$	$6$	334.a	1.a	$1$	$19$	$19$	$53.568$	$\mathbb{Q}[x]/(x^{19} - \cdots)$	None	✓	$1$	$0$	$-76$	$5$	$50$	$-98$	$-$	$2^{7}\cdot 3$	$\mathrm{SU}(2)$	$q-4q^{2}+\beta _{1}q^{3}+2^{4}q^{4}+(3-\beta _{4})q^{5}+\cdots$
334.6.a.d	$334$	$6$	334.a	1.a	$1$	$19$	$19$	$53.568$	$\mathbb{Q}[x]/(x^{19} - \cdots)$	None	✓	$1$	$0$	$76$	$31$	$150$	$392$	$-$	$2^{9}$	$\mathrm{SU}(2)$	$q+4q^{2}+(2-\beta _{1})q^{3}+2^{4}q^{4}+(8-\beta _{6}+\cdots)q^{5}+\cdots$
334.7.b.a	$334$	$7$	334.b	167.b	$2$	$84$	$84$	$76.838$		None		$2$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
334.8.a.a	$334$	$8$	334.a	1.a	$1$	$22$	$22$	$104.337$		None	✓	$1$	$1$	$-176$	$-41$	$-40$	$178$	$-$		$\mathrm{SU}(2)$
334.8.a.b	$334$	$8$	334.a	1.a	$1$	$23$	$23$	$104.337$		None	✓	$1$	$1$	$184$	$-79$	$-750$	$-3252$	$-$		$\mathrm{SU}(2)$
334.8.a.c	$334$	$8$	334.a	1.a	$1$	$25$	$25$	$104.337$		None	✓	$1$	$0$	$-200$	$-41$	$460$	$-1880$	$+$		$\mathrm{SU}(2)$
334.8.a.d	$334$	$8$	334.a	1.a	$1$	$26$	$26$	$104.337$		None	✓	$1$	$0$	$208$	$137$	$500$	$2922$	$+$		$\mathrm{SU}(2)$
334.10.a.a	$334$	$10$	334.a	1.a	$1$	$29$	$29$	$172.022$		None	✓	$1$	$1$	$464$	$-239$	$-3370$	$-23534$	$+$		$\mathrm{SU}(2)$
334.10.a.b	$334$	$10$	334.a	1.a	$1$	$30$	$30$	$172.022$		None	✓	$1$	$1$	$-480$	$71$	$-1250$	$10080$	$+$		$\mathrm{SU}(2)$
334.10.a.c	$334$	$10$	334.a	1.a	$1$	$32$	$32$	$172.022$		None	✓	$1$	$0$	$512$	$409$	$2880$	$19684$	$-$		$\mathrm{SU}(2)$
334.10.a.d	$334$	$10$	334.a	1.a	$1$	$33$	$33$	$172.022$		None	✓	$1$	$0$	$-528$	$71$	$1250$	$-4326$	$-$		$\mathrm{SU}(2)$

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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.