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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 (40 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
139.1.b.a	$139$	$1$	139.b	139.b	$2$	$1$	$1$	$0.069$	$\Q$	$D_{3}$	$\Q(\sqrt{-139}) $	None	✓	$2$	$0$	$0$	$0$	$-1$	$-1$		$1$		$q+q^{4}-q^{5}-q^{7}+q^{9}-q^{11}-q^{13}+\cdots$
139.2.a.a	$139$	$2$	139.a	1.a	$1$	$1$	$1$	$1.110$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$1$	$2$	$-1$	$3$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+2q^{3}-q^{4}-q^{5}+2q^{6}+3q^{7}+\cdots$
139.2.a.b	$139$	$2$	139.a	1.a	$1$	$3$	$3$	$1.110$	$\Q(\zeta_{14})^+$	$_{}$	None	None	✓	$1$	$1$	$-2$	$-2$	$-8$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1-\beta _{2})q^{2}+(-\beta _{1}+\beta _{2})q^{3}+(\beta _{1}+\cdots)q^{4}+\cdots$
139.2.a.c	$139$	$2$	139.a	1.a	$1$	$7$	$7$	$1.110$	$\mathbb{Q}[x]/(x^{7} - \cdots)$	$_{}$	None	None	✓	$1$	$0$	$1$	$-2$	$11$	$-5$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+\beta _{6}q^{3}+(1+\beta _{1}-\beta _{3}+\beta _{5}+\cdots)q^{4}+\cdots$
139.2.c.a	$139$	$2$	139.c	139.c	$3$	$22$	$11$	$1.110$		$_{}$	None	None		$2$	$0$	$0$	$2$	$-2$	$-1$			$\mathrm{SU}(2)[C_{3}]$
139.2.e.a	$139$	$2$	139.e	139.e	$23$	$220$	$10$	$1.110$		$_{}$	None	None		$2$	$0$	$-20$	$-17$	$-19$	$-13$			$\mathrm{SU}(2)[C_{23}]$
139.2.g.a	$139$	$2$	139.g	139.g	$69$	$484$	$11$	$1.110$		$_{}$	None	None		$2$	$0$	$-46$	$-48$	$-44$	$-45$			$\mathrm{SU}(2)[C_{69}]$
139.3.b.a	$139$	$3$	139.b	139.b	$2$	$3$	$3$	$3.787$	3.3.3753.1	$_{}$	$\Q(\sqrt{-139}) $	None	✓	$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{U}(1)[D_{2}]$	$q+4q^{4}+(2\beta _{1}+\beta _{2})q^{5}+(-3\beta _{1}-\beta _{2})q^{7}+\cdots$
139.3.b.b	$139$	$3$	139.b	139.b	$2$	$20$	$20$	$3.787$	$\mathbb{Q}[x]/(x^{20} + \cdots)$	$_{}$	None	None		$2$	$0$	$0$	$0$	$-4$	$14$		$2^{10}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{2}-\beta _{9}q^{3}+(-3+\beta _{2})q^{4}-\beta _{4}q^{5}+\cdots$
139.3.d.a	$139$	$3$	139.d	139.d	$6$	$44$	$22$	$3.787$		$_{}$	None	None		$2$	$0$	$-3$	$-6$	$-2$	$3$			$\mathrm{SU}(2)[C_{6}]$
139.3.f.a	$139$	$3$	139.f	139.f	$46$	$506$	$23$	$3.787$		$_{}$	None	None		$2$	$0$	$-23$	$-23$	$-19$	$-37$			$\mathrm{SU}(2)[C_{46}]$
139.3.h.a	$139$	$3$	139.h	139.h	$138$	$968$	$22$	$3.787$		$_{}$	None	None		$2$	$0$	$-43$	$-40$	$-44$	$-49$			$\mathrm{SU}(2)[C_{138}]$
139.4.a.a	$139$	$4$	139.a	1.a	$1$	$2$	$2$	$8.201$	$\Q(\sqrt{2}) $	$_{}$	None	None	✓	$1$	$1$	$2$	$-4$	$10$	$-34$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1+2\beta )q^{2}+(-2-3\beta )q^{3}+(1+4\beta )q^{4}+\cdots$
139.4.a.b	$139$	$4$	139.a	1.a	$1$	$12$	$12$	$8.201$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	$_{}$	None	None	✓	$1$	$1$	$-9$	$-7$	$-67$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta _{1})q^{2}+(-1-\beta _{9})q^{3}+(4+\cdots)q^{4}+\cdots$
139.4.a.c	$139$	$4$	139.a	1.a	$1$	$20$	$20$	$8.201$	$\mathbb{Q}[x]/(x^{20} - \cdots)$	$_{}$	None	None	✓	$1$	$0$	$7$	$7$	$63$	$8$	$+$	$2^{4}$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+\beta _{6}q^{3}+(5+\beta _{2})q^{4}+(3-\beta _{5}+\cdots)q^{5}+\cdots$
139.4.c.a	$139$	$4$	139.c	139.c	$3$	$68$	$34$	$8.201$		$_{}$	None	None		$2$	$0$	$-3$	$-5$	$3$	$-37$			$\mathrm{SU}(2)[C_{3}]$
139.4.e.a	$139$	$4$	139.e	139.e	$23$	$748$	$34$	$8.201$		$_{}$	None	None		$2$	$0$	$-23$	$-19$	$-29$	$3$			$\mathrm{SU}(2)[C_{23}]$
139.4.g.a	$139$	$4$	139.g	139.g	$69$	$1496$	$34$	$8.201$		$_{}$	None	None		$2$	$0$	$-43$	$-41$	$-49$	$-9$			$\mathrm{SU}(2)[C_{69}]$
139.5.b.a	$139$	$5$	139.b	139.b	$2$	$3$	$3$	$14.368$	3.3.3753.1	$_{}$	$\Q(\sqrt{-139}) $	None	✓	$2$	$0$	$0$	$0$	$0$	$0$		$3$	$\mathrm{U}(1)[D_{2}]$	$q+2^{4}q^{4}+(3\beta _{1}-5\beta _{2})q^{5}+(7\beta _{1}-4\beta _{2})q^{7}+\cdots$
139.5.b.b	$139$	$5$	139.b	139.b	$2$	$42$	$42$	$14.368$		$_{}$	None	None		$2$	$0$	$0$	$0$	$16$	$-82$			$\mathrm{SU}(2)[C_{2}]$
139.5.d.a	$139$	$5$	139.d	139.d	$6$	$92$	$46$	$14.368$		$_{}$	None	None		$2$	$0$	$-3$	$-12$	$8$	$11$			$\mathrm{SU}(2)[C_{6}]$
139.5.f.a	$139$	$5$	139.f	139.f	$46$	$990$	$45$	$14.368$		$_{}$	None	None		$2$	$0$	$-23$	$-23$	$-39$	$59$			$\mathrm{SU}(2)[C_{46}]$
139.5.h.a	$139$	$5$	139.h	139.h	$138$	$2024$	$46$	$14.368$		$_{}$	None	None		$2$	$0$	$-43$	$-34$	$-54$	$-57$			$\mathrm{SU}(2)[C_{138}]$
139.6.a.a	$139$	$6$	139.a	1.a	$1$	$26$	$26$	$22.293$		$_{}$	None	None	✓	$1$	$1$	$-17$	$-26$	$-312$	$-136$	$+$		$\mathrm{SU}(2)$
139.6.a.b	$139$	$6$	139.a	1.a	$1$	$32$	$32$	$22.293$		$_{}$	None	None	✓	$1$	$0$	$11$	$28$	$288$	$158$	$-$		$\mathrm{SU}(2)$
139.7.b.a	$139$	$7$	139.b	139.b	$2$	$1$	$1$	$31.978$	$\Q$	$_{}$	$\Q(\sqrt{-139}) $	None	✓	$2$	$0$	$0$	$0$	$111$	$-565$		$1$	$\mathrm{U}(1)[D_{2}]$	$q+2^{6}q^{4}+111q^{5}-565q^{7}+3^{6}q^{9}+\cdots$
139.7.b.b	$139$	$7$	139.b	139.b	$2$	$2$	$2$	$31.978$	$\Q(\sqrt{417}) $	$_{}$	$\Q(\sqrt{-139}) $	None	✓	$2$	$0$	$0$	$0$	$-111$	$565$		$1$	$\mathrm{U}(1)[D_{2}]$	$q+2^{6}q^{4}+(-46-19\beta )q^{5}+(266+33\beta )q^{7}+\cdots$
139.7.b.c	$139$	$7$	139.b	139.b	$2$	$66$	$66$	$31.978$		$_{}$	None	None		$2$	$0$	$0$	$0$	$-114$	$-546$			$\mathrm{SU}(2)[C_{2}]$
139.8.a.a	$139$	$8$	139.a	1.a	$1$	$37$	$37$	$43.422$		$_{}$	None	None	✓	$1$	$1$	$-25$	$-68$	$-1502$	$-698$	$-$		$\mathrm{SU}(2)$
139.8.a.b	$139$	$8$	139.a	1.a	$1$	$43$	$43$	$43.422$		$_{}$	None	None	✓	$1$	$0$	$31$	$94$	$1498$	$1360$	$+$		$\mathrm{SU}(2)$
139.9.b.a	$139$	$9$	139.b	139.b	$2$	$3$	$3$	$56.626$	3.3.3753.1	$_{}$	$\Q(\sqrt{-139}) $	None	✓	$2$	$0$	$0$	$0$	$0$	$0$		$3$	$\mathrm{U}(1)[D_{2}]$	$q+2^{8}q^{4}+(-\beta _{1}+236\beta _{2})q^{5}+(222\beta _{1}+\cdots)q^{7}+\cdots$
139.9.b.b	$139$	$9$	139.b	139.b	$2$	$90$	$90$	$56.626$		$_{}$	None	None		$2$	$0$	$0$	$0$	$556$	$-3122$			$\mathrm{SU}(2)[C_{2}]$
139.10.a.a	$139$	$10$	139.a	1.a	$1$	$49$	$49$	$71.590$		$_{}$	None	None	✓	$1$	$1$	$-65$	$-317$	$-7217$	$-9680$	$+$		$\mathrm{SU}(2)$
139.10.a.b	$139$	$10$	139.a	1.a	$1$	$55$	$55$	$71.590$		$_{}$	None	None	✓	$1$	$0$	$47$	$169$	$7783$	$4726$	$-$		$\mathrm{SU}(2)$
139.12.a.a	$139$	$12$	139.a	1.a	$1$	$60$	$60$	$106.800$		$_{}$	None	None	✓	$1$	$1$	$-73$	$-476$	$-44862$	$-51474$	$-$		$\mathrm{SU}(2)$
139.12.a.b	$139$	$12$	139.a	1.a	$1$	$66$	$66$	$106.800$		$_{}$	None	None	✓	$1$	$0$	$151$	$982$	$30138$	$49368$	$+$		$\mathrm{SU}(2)$
139.14.a.a	$139$	$14$	139.a	1.a	$1$	$72$	$72$	$149.051$		$_{}$	None	None	✓	$1$	$1$	$-257$	$-2786$	$-171822$	$-153816$	$+$		$\mathrm{SU}(2)$
139.14.a.b	$139$	$14$	139.a	1.a	$1$	$78$	$78$	$149.051$		$_{}$	None	None	✓	$1$	$0$	$191$	$1588$	$203178$	$552078$	$-$		$\mathrm{SU}(2)$
139.16.a.a	$139$	$16$	139.a	1.a	$1$	$83$	$83$	$198.344$		$_{}$	None	None	✓	$1$	$1$	$-601$	$-5843$	$-1067447$	$-4880938$	$-$		$\mathrm{SU}(2)$
139.16.a.b	$139$	$16$	139.a	1.a	$1$	$89$	$89$	$198.344$		$_{}$	None	None	✓	$1$	$0$	$295$	$7279$	$807553$	$60320$	$+$		$\mathrm{SU}(2)$

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Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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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.