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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 123 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
68.1.d.a	$68$	$1$	68.d	68.d	$2$	$1$	$1$	$0.034$	$\Q$	$D_{2}$	$\Q(\sqrt{-1}) $, $\Q(\sqrt{-17}) $	$\Q(\sqrt{17}) $	✓	$4$	$0$	$-1$	$0$	$0$	$0$		$1$		$q-q^{2}+q^{4}-q^{8}-q^{9}-2q^{13}+q^{16}+\cdots$
68.1.f.a	$68$	$1$	68.f	68.f	$4$	$2$	$1$	$0.034$	$\Q(\sqrt{-1}) $	$D_{4}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$0$	$0$	$-2$	$0$		$1$		$q+iq^{2}-q^{4}+(-1-i)q^{5}-iq^{8}+\cdots$
68.2.a.a	$68$	$2$	68.a	1.a	$1$	$2$	$2$	$0.543$	$\Q(\sqrt{3}) $	$_{}$	None	None	✓	$1$	$0$	$0$	$2$	$0$	$-2$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1+\beta )q^{3}-2\beta q^{5}+(-1-\beta )q^{7}+\cdots$
68.2.b.a	$68$	$2$	68.b	17.b	$2$	$2$	$2$	$0.543$	$\Q(\sqrt{-2}) $	$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta q^{3}+2\beta q^{5}-3\beta q^{7}+q^{9}-\beta q^{11}+\cdots$
68.2.e.a	$68$	$2$	68.e	17.c	$4$	$4$	$2$	$0.543$	$\Q(i, \sqrt{13})$	$_{}$	None	None		$2$	$0$	$0$	$-2$	$-4$	$2$		$2$	$\mathrm{SU}(2)[C_{4}]$	$q+(-1+\beta _{2})q^{3}+(-1-\beta _{1})q^{5}+(1+\cdots)q^{7}+\cdots$
68.2.h.a	$68$	$2$	68.h	17.d	$8$	$4$	$1$	$0.543$	$\Q(\zeta_{8})$	$_{}$	None	None		$2$	$0$	$0$	$0$	$4$	$0$		$1$	$\mathrm{SU}(2)[C_{8}]$	$q+(\zeta_{8}^{2}-\zeta_{8}^{3})q^{3}+(1-\zeta_{8})q^{5}+(\zeta_{8}+\cdots)q^{7}+\cdots$
68.2.i.a	$68$	$2$	68.i	68.i	$16$	$8$	$1$	$0.543$	$\Q(\zeta_{16})$	$_{}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{U}(1)[D_{16}]$	$q+(-\zeta_{16}+\zeta_{16}^{5})q^{2}-2\zeta_{16}^{6}q^{4}+\cdots$
68.2.i.b	$68$	$2$	68.i	68.i	$16$	$48$	$6$	$0.543$		$_{}$	None	None		$4$	$0$	$-8$	$0$	$-16$	$0$			$\mathrm{SU}(2)[C_{16}]$
68.3.c.a	$68$	$3$	68.c	4.b	$2$	$16$	$16$	$1.853$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	$_{}$	None	None		$2$	$0$	$-2$	$0$	$0$	$0$		$2^{21}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{3}q^{2}-\beta _{12}q^{3}+\beta _{10}q^{4}-\beta _{2}q^{5}+\cdots$
68.3.d.a	$68$	$3$	68.d	68.d	$2$	$2$	$2$	$1.853$	$\Q(\sqrt{34}) $	$_{}$	$\Q(\sqrt{-17}) $	None	✓	$4$	$0$	$-4$	$0$	$0$	$0$		$1$	$\mathrm{U}(1)[D_{2}]$	$q-2q^{2}+\beta q^{3}+4q^{4}-2\beta q^{6}-\beta q^{7}+\cdots$
68.3.d.b	$68$	$3$	68.d	68.d	$2$	$2$	$2$	$1.853$	$\Q(\sqrt{2}) $	$_{}$	$\Q(\sqrt{-17}) $	None	✓	$4$	$0$	$4$	$0$	$0$	$0$		$1$	$\mathrm{U}(1)[D_{2}]$	$q+2q^{2}+\beta q^{3}+4q^{4}+2\beta q^{6}-9\beta q^{7}+\cdots$
68.3.d.c	$68$	$3$	68.d	68.d	$2$	$12$	$12$	$1.853$	$\mathbb{Q}[x]/(x^{12} + \cdots)$	$_{}$	None	None		$4$	$0$	$-2$	$0$	$0$	$0$		$2^{15}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{1}q^{2}+\beta _{7}q^{3}+(-1-\beta _{3})q^{4}-\beta _{6}q^{5}+\cdots$
68.3.f.a	$68$	$3$	68.f	68.f	$4$	$32$	$16$	$1.853$		$_{}$	None	None		$4$	$0$	$0$	$0$	$-8$	$0$			$\mathrm{SU}(2)[C_{4}]$
68.3.g.a	$68$	$3$	68.g	68.g	$8$	$4$	$1$	$1.853$	$\Q(\zeta_{8})$	$_{}$	None	None		$2$	$0$	$0$	$0$	$-8$	$0$		$1$	$\mathrm{SU}(2)[C_{8}]$	$q-2\zeta_{8}^{2}q^{2}+(-2\zeta_{8}^{2}-2\zeta_{8}^{3})q^{3}+\cdots$
68.3.g.b	$68$	$3$	68.g	68.g	$8$	$4$	$1$	$1.853$	$\Q(\zeta_{8})$	$_{}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$0$	$0$	$-16$	$0$		$1$	$\mathrm{U}(1)[D_{8}]$	$q-2\zeta_{8}^{3}q^{2}-4\zeta_{8}^{2}q^{4}+(-4+4\zeta_{8}+\cdots)q^{5}+\cdots$
68.3.g.c	$68$	$3$	68.g	68.g	$8$	$4$	$1$	$1.853$	$\Q(\zeta_{8})$	$_{}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$0$	$0$	$16$	$0$		$1$	$\mathrm{U}(1)[D_{8}]$	$q+2\zeta_{8}^{3}q^{2}-4\zeta_{8}^{2}q^{4}+(4-4\zeta_{8}-3\zeta_{8}^{2}+\cdots)q^{5}+\cdots$
68.3.g.d	$68$	$3$	68.g	68.g	$8$	$4$	$1$	$1.853$	$\Q(\zeta_{8})$	$_{}$	None	None		$2$	$0$	$8$	$0$	$-8$	$0$		$1$	$\mathrm{SU}(2)[C_{8}]$	$q+2q^{2}+(2\zeta_{8}^{2}+2\zeta_{8}^{3})q^{3}+4q^{4}+\cdots$
68.3.g.e	$68$	$3$	68.g	68.g	$8$	$48$	$12$	$1.853$		$_{}$	None	None		$4$	$0$	$-12$	$0$	$8$	$0$			$\mathrm{SU}(2)[C_{8}]$
68.3.j.a	$68$	$3$	68.j	17.e	$16$	$24$	$3$	$1.853$		$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{16}]$
68.4.a.a	$68$	$4$	68.a	1.a	$1$	$1$	$1$	$4.012$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$0$	$-2$	$-8$	$-12$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{3}-8q^{5}-12q^{7}-23q^{9}-10q^{11}+\cdots$
68.4.a.b	$68$	$4$	68.a	1.a	$1$	$3$	$3$	$4.012$	3.3.1524.1	$_{}$	None	None	✓	$1$	$0$	$0$	$4$	$26$	$8$	$+$	$2^{3}$	$\mathrm{SU}(2)$	$q+(1+\beta _{2})q^{3}+(9-\beta _{1})q^{5}+(2+3\beta _{1}+\cdots)q^{7}+\cdots$
68.4.b.a	$68$	$4$	68.b	17.b	$2$	$4$	$4$	$4.012$	4.0.1499912.1	$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$0$		$2^{5}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{3}-\beta _{2}q^{5}+(\beta _{1}-\beta _{2})q^{7}+(-15+\cdots)q^{9}+\cdots$
68.4.e.a	$68$	$4$	68.e	17.c	$4$	$2$	$1$	$4.012$	$\Q(\sqrt{-1}) $	$_{}$	None	None		$2$	$1$	$0$	$-8$	$-2$	$-40$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+(-4-4i)q^{3}+(-1-i)q^{5}+(-20+\cdots)q^{7}+\cdots$
68.4.e.b	$68$	$4$	68.e	17.c	$4$	$6$	$3$	$4.012$	6.0.27793984.1	$_{}$	None	None		$2$	$0$	$0$	$6$	$0$	$44$		$2^{4}$	$\mathrm{SU}(2)[C_{4}]$	$q+(1+\beta _{2}+\beta _{3})q^{3}+(1-\beta _{2}+\beta _{3}-3\beta _{5})q^{5}+\cdots$
68.4.h.a	$68$	$4$	68.h	17.d	$8$	$20$	$5$	$4.012$	$\mathbb{Q}[x]/(x^{20} + \cdots)$	$_{}$	None	None		$2$	$0$	$0$	$0$	$-16$	$0$		$2^{17}$	$\mathrm{SU}(2)[C_{8}]$	$q+\beta _{6}q^{3}+(-1-\beta _{8}-\beta _{9}+\beta _{10}+\beta _{14}+\cdots)q^{5}+\cdots$
68.4.i.a	$68$	$4$	68.i	68.i	$16$	$8$	$1$	$4.012$	$\Q(\zeta_{16})$	$_{}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{U}(1)[D_{16}]$	$q+(2\zeta_{16}-2\zeta_{16}^{5})q^{2}-8\zeta_{16}^{6}q^{4}+\cdots$
68.4.i.b	$68$	$4$	68.i	68.i	$16$	$192$	$24$	$4.012$		$_{}$	None	None		$4$	$0$	$-8$	$0$	$-16$	$0$			$\mathrm{SU}(2)[C_{16}]$
68.5.c.a	$68$	$5$	68.c	4.b	$2$	$32$	$32$	$7.029$		$_{}$	None	None		$2$	$0$	$6$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
68.5.d.a	$68$	$5$	68.d	68.d	$2$	$1$	$1$	$7.029$	$\Q$	$_{}$	$\Q(\sqrt{-17}) $	None	✓	$2$	$0$	$4$	$-16$	$0$	$64$		$1$	$\mathrm{U}(1)[D_{2}]$	$q+4q^{2}-2^{4}q^{3}+2^{4}q^{4}-2^{6}q^{6}+2^{6}q^{7}+\cdots$
68.5.d.b	$68$	$5$	68.d	68.d	$2$	$1$	$1$	$7.029$	$\Q$	$_{}$	$\Q(\sqrt{-17}) $	None	✓	$2$	$0$	$4$	$16$	$0$	$-64$		$1$	$\mathrm{U}(1)[D_{2}]$	$q+4q^{2}+2^{4}q^{3}+2^{4}q^{4}+2^{6}q^{6}-2^{6}q^{7}+\cdots$
68.5.d.c	$68$	$5$	68.d	68.d	$2$	$2$	$2$	$7.029$	$\Q(\sqrt{17}) $	$_{}$	$\Q(\sqrt{-17}) $	None	✓	$4$	$0$	$-8$	$0$	$0$	$0$		$2^{2}$	$\mathrm{U}(1)[D_{2}]$	$q-4q^{2}-\beta q^{3}+2^{4}q^{4}+4\beta q^{6}-9\beta q^{7}+\cdots$
68.5.d.d	$68$	$5$	68.d	68.d	$2$	$2$	$2$	$7.029$	$\Q(\sqrt{-1}) $	$_{}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$8$	$0$	$0$	$0$		$2^{4}\cdot 3$	$\mathrm{U}(1)[D_{2}]$	$q+4q^{2}+2^{4}q^{4}+iq^{5}+2^{6}q^{8}-3^{4}q^{9}+\cdots$
68.5.d.e	$68$	$5$	68.d	68.d	$2$	$28$	$28$	$7.029$		$_{}$	None	None		$4$	$0$	$-10$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
68.5.f.a	$68$	$5$	68.f	68.f	$4$	$2$	$1$	$7.029$	$\Q(\sqrt{-1}) $	$_{}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$0$	$0$	$-34$	$0$		$1$	$\mathrm{U}(1)[D_{4}]$	$q-4iq^{2}-2^{4}q^{4}+(-17-17i)q^{5}+\cdots$
68.5.f.b	$68$	$5$	68.f	68.f	$4$	$2$	$1$	$7.029$	$\Q(\sqrt{-1}) $	$_{}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$0$	$0$	$62$	$0$		$1$	$\mathrm{U}(1)[D_{4}]$	$q-4iq^{2}-2^{4}q^{4}+(31+31i)q^{5}+2^{6}iq^{8}+\cdots$
68.5.f.c	$68$	$5$	68.f	68.f	$4$	$64$	$32$	$7.029$		$_{}$	None	None		$4$	$0$	$0$	$0$	$-8$	$0$			$\mathrm{SU}(2)[C_{4}]$
68.5.g.a	$68$	$5$	68.g	68.g	$8$	$136$	$34$	$7.029$		$_{}$	None	None		$4$	$0$	$-4$	$0$	$-8$	$0$			$\mathrm{SU}(2)[C_{8}]$
68.5.j.a	$68$	$5$	68.j	17.e	$16$	$48$	$6$	$7.029$		$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{16}]$
68.6.a.a	$68$	$6$	68.a	1.a	$1$	$2$	$2$	$10.906$	$\Q(\sqrt{13}) $	$_{}$	None	None	✓	$1$	$1$	$0$	$-8$	$-20$	$128$	$+$	$2^{3}$	$\mathrm{SU}(2)$	$q+(-4-\beta )q^{3}+(-10+2\beta )q^{5}+(2^{6}+\cdots)q^{7}+\cdots$
68.6.a.b	$68$	$6$	68.a	1.a	$1$	$4$	$4$	$10.906$	$\mathbb{Q}[x]/(x^{4} - \cdots)$	$_{}$	None	None	✓	$1$	$0$	$0$	$10$	$-88$	$166$	$-$	$2^{3}$	$\mathrm{SU}(2)$	$q+(2-\beta _{3})q^{3}+(-22+\beta _{1}-\beta _{2}-\beta _{3})q^{5}+\cdots$
68.6.b.a	$68$	$6$	68.b	17.b	$2$	$8$	$8$	$10.906$	$\mathbb{Q}[x]/(x^{8} + \cdots)$	$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$0$		$2^{13}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{3}+\beta _{4}q^{5}+(-2\beta _{1}-\beta _{6})q^{7}+\cdots$
68.6.e.a	$68$	$6$	68.e	17.c	$4$	$16$	$8$	$10.906$	$\mathbb{Q}[x]/(x^{16} + \cdots)$	$_{}$	None	None		$2$	$0$	$0$	$22$	$-44$	$-118$		$2^{21}$	$\mathrm{SU}(2)[C_{4}]$	$q+(1+\beta _{1}+\beta _{5})q^{3}+(-3-3\beta _{5}+\beta _{6}+\cdots)q^{5}+\cdots$
68.6.h.a	$68$	$6$	68.h	17.d	$8$	$28$	$7$	$10.906$		$_{}$	None	None		$2$	$0$	$0$	$0$	$44$	$0$			$\mathrm{SU}(2)[C_{8}]$
68.6.i.a	$68$	$6$	68.i	68.i	$16$	$8$	$1$	$10.906$	$\Q(\zeta_{16})$	$_{}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{U}(1)[D_{16}]$	$q+(4\zeta_{16}-4\zeta_{16}^{5})q^{2}-2^{5}\zeta_{16}^{6}q^{4}+\cdots$
68.6.i.b	$68$	$6$	68.i	68.i	$16$	$336$	$42$	$10.906$		$_{}$	None	None		$4$	$0$	$-8$	$0$	$-16$	$0$			$\mathrm{SU}(2)[C_{16}]$
68.7.c.a	$68$	$7$	68.c	4.b	$2$	$48$	$48$	$15.644$		$_{}$	None	None		$2$	$0$	$-10$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
68.7.d.a	$68$	$7$	68.d	68.d	$2$	$2$	$2$	$15.644$	$\Q(\sqrt{34}) $	$_{}$	$\Q(\sqrt{-17}) $	None	✓	$4$	$0$	$-16$	$0$	$0$	$0$		$1$	$\mathrm{U}(1)[D_{2}]$	$q-8q^{2}+7\beta q^{3}+2^{6}q^{4}-56\beta q^{6}+\cdots$
68.7.d.b	$68$	$7$	68.d	68.d	$2$	$2$	$2$	$15.644$	$\Q(\sqrt{2}) $	$_{}$	$\Q(\sqrt{-17}) $	None	✓	$4$	$0$	$16$	$0$	$0$	$0$		$5$	$\mathrm{U}(1)[D_{2}]$	$q+8q^{2}+5\beta q^{3}+2^{6}q^{4}+40\beta q^{6}+\cdots$
68.7.d.c	$68$	$7$	68.d	68.d	$2$	$48$	$48$	$15.644$		$_{}$	None	None		$4$	$0$	$-2$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
68.7.f.a	$68$	$7$	68.f	68.f	$4$	$104$	$52$	$15.644$		$_{}$	None	None		$4$	$0$	$0$	$0$	$-48$	$0$			$\mathrm{SU}(2)[C_{4}]$

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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.