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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 (45 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				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*	$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$	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	✓	$2$	$0$	$0$	$0$	$-1$	$-1$	$1$		$q+q^{4}-q^{5}-q^{7}+q^{9}-q^{11}-q^{13}+\cdots$
556.1.c.a	$556$	$1$	556.c	139.b	$2$	$3$	$3$	$0.277$	$\Q(\zeta_{18})^+$	$D_{9}$	$\Q(\sqrt{-139}) $	None	✓	$2$	$0$	$0$	$0$	$0$	$0$	$1$		$q-\beta _{1}q^{5}+\beta _{2}q^{7}+q^{9}+(\beta _{1}-\beta _{2})q^{11}+\cdots$
695.1.d.b	$695$	$1$	695.d	695.d	$2$	$1$	$1$	$0.347$	$\Q$	$D_{2}$	$\Q(\sqrt{-139}) $, $\Q(\sqrt{-695}) $	$\Q(\sqrt{5}) $	✓	$4$	$0$	$0$	$0$	$1$	$0$	$1$		$q-q^{4}+q^{5}-q^{9}+2q^{11}+q^{16}-q^{20}+\cdots$
695.1.d.d	$695$	$1$	695.d	695.d	$2$	$2$	$2$	$0.347$	$\Q(\sqrt{-3}) $	$D_{6}$	$\Q(\sqrt{-139}) $	None		$4$	$0$	$0$	$0$	$-1$	$0$	$1$		$q-q^{4}+\zeta_{6}^{2}q^{5}+(-\zeta_{6}-\zeta_{6}^{2})q^{7}+\cdots$
973.1.r.b	$973$	$1$	973.r	973.r	$6$	$6$	$3$	$0.486$	$\Q(\zeta_{18})$	$D_{9}$	$\Q(\sqrt{-139}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q-\zeta_{18}^{3}q^{4}+(\zeta_{18}^{4}+\zeta_{18}^{8})q^{5}-\zeta_{18}^{5}q^{7}+\cdots$
1251.1.c.a	$1251$	$1$	1251.c	139.b	$2$	$1$	$1$	$0.624$	$\Q$	$D_{2}$	$\Q(\sqrt{-3}) $, $\Q(\sqrt{-139}) $	$\Q(\sqrt{417}) $	✓	$4$	$0$	$0$	$0$	$0$	$2$	$1$		$q+q^{4}+2q^{7}-2q^{13}+q^{16}-q^{25}+\cdots$
1251.1.c.b	$1251$	$1$	1251.c	139.b	$2$	$1$	$1$	$0.624$	$\Q$	$D_{3}$	$\Q(\sqrt{-139}) $	None	✓	$2$	$0$	$0$	$0$	$1$	$-1$	$1$		$q+q^{4}+q^{5}-q^{7}+q^{11}-q^{13}+q^{16}+\cdots$
1251.1.c.c	$1251$	$1$	1251.c	139.b	$2$	$2$	$2$	$0.624$	$\Q(\sqrt{3}) $	$D_{6}$	$\Q(\sqrt{-139}) $	None	✓	$4$	$0$	$0$	$0$	$0$	$-2$	$1$		$q+q^{4}-\beta q^{5}-q^{7}+\beta q^{11}+q^{13}+\cdots$
1529.1.l.a	$1529$	$1$	1529.l	1529.l	$10$	$4$	$1$	$0.763$	$\Q(\zeta_{10})$	$D_{5}$	$\Q(\sqrt{-139}) $	None		$4$	$0$	$0$	$0$	$-2$	$-2$	$1$		$q-\zeta_{10}^{3}q^{4}+(-\zeta_{10}^{3}+\zeta_{10}^{4})q^{5}+\cdots$
1529.1.l.b	$1529$	$1$	1529.l	1529.l	$10$	$8$	$2$	$0.763$	$\Q(\zeta_{15})$	$D_{15}$	$\Q(\sqrt{-139}) $	None		$4$	$0$	$0$	$0$	$2$	$2$	$1$		$q-\zeta_{30}^{9}q^{4}+(\zeta_{30}^{2}+\zeta_{30}^{4})q^{5}+\zeta_{30}^{9}q^{7}+\cdots$
1807.1.d.b	$1807$	$1$	1807.d	1807.d	$2$	$1$	$1$	$0.902$	$\Q$	$D_{2}$	$\Q(\sqrt{-139}) $, $\Q(\sqrt{-1807}) $	$\Q(\sqrt{13}) $	✓	$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q-q^{4}+q^{9}-q^{13}+q^{16}+q^{25}+2q^{29}+\cdots$
1807.1.d.d	$1807$	$1$	1807.d	1807.d	$2$	$2$	$2$	$0.902$	$\Q(\sqrt{-3}) $	$D_{6}$	$\Q(\sqrt{-139}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q-q^{4}+(\zeta_{6}+\zeta_{6}^{2})q^{5}+(\zeta_{6}+\zeta_{6}^{2})q^{7}+\cdots$
1807.1.n.a	$1807$	$1$	1807.n	1807.n	$6$	$6$	$3$	$0.902$	$\Q(\zeta_{18})$	$D_{18}$	$\Q(\sqrt{-139}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q-\zeta_{18}^{6}q^{4}+(\zeta_{18}^{4}+\zeta_{18}^{5})q^{5}+(\zeta_{18}^{4}+\cdots)q^{7}+\cdots$
1807.1.t.a	$1807$	$1$	1807.t	1807.t	$6$	$6$	$3$	$0.902$	$\Q(\zeta_{18})$	$D_{9}$	$\Q(\sqrt{-139}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q-\zeta_{18}^{3}q^{4}+(\zeta_{18}^{4}-\zeta_{18}^{5})q^{5}+(-\zeta_{18}+\cdots)q^{7}+\cdots$
2224.1.e.a	$2224$	$1$	2224.e	139.b	$2$	$1$	$1$	$1.110$	$\Q$	$D_{3}$	$\Q(\sqrt{-139}) $	None	✓	$2$	$0$	$0$	$0$	$-1$	$1$	$1$		$q-q^{5}+q^{7}+q^{9}+q^{11}-q^{13}-q^{29}+\cdots$
2224.1.e.b	$2224$	$1$	2224.e	139.b	$2$	$3$	$3$	$1.110$	$\Q(\zeta_{18})^+$	$D_{9}$	$\Q(\sqrt{-139}) $	None	✓	$2$	$0$	$0$	$0$	$0$	$0$	$1$		$q+(\beta _{1}-\beta _{2})q^{5}+\beta _{1}q^{7}+q^{9}-\beta _{2}q^{11}+\cdots$
2780.1.g.a	$2780$	$1$	2780.g	695.d	$2$	$6$	$6$	$1.387$	$\Q(\zeta_{18})$	$D_{18}$	$\Q(\sqrt{-139}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q-\zeta_{18}^{5}q^{5}+(-\zeta_{18}-\zeta_{18}^{8})q^{7}-q^{9}+\cdots$
3475.1.c.a	$3475$	$1$	3475.c	139.b	$2$	$1$	$1$	$1.734$	$\Q$	$D_{2}$	$\Q(\sqrt{-139}) $, $\Q(\sqrt{-695}) $	$\Q(\sqrt{5}) $	✓	$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q+q^{4}+q^{9}+2q^{11}+q^{16}-2q^{29}+\cdots$
3475.1.c.b	$3475$	$1$	3475.c	139.b	$2$	$1$	$1$	$1.734$	$\Q$	$D_{3}$	$\Q(\sqrt{-139}) $	None	✓	$2$	$0$	$0$	$0$	$0$	$1$	$1$		$q+q^{4}+q^{7}+q^{9}-q^{11}+q^{13}+q^{16}+\cdots$
3475.1.c.f	$3475$	$1$	3475.c	139.b	$2$	$2$	$2$	$1.734$	$\Q(\sqrt{3}) $	$D_{6}$	$\Q(\sqrt{-139}) $	None	✓	$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q+q^{4}-\beta q^{7}+q^{9}-q^{11}+\beta q^{13}+\cdots$
3475.1.d.a	$3475$	$1$	3475.d	695.d	$2$	$2$	$2$	$1.734$	$\Q(\sqrt{-1}) $	$D_{3}$	$\Q(\sqrt{-139}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q-q^{4}-iq^{7}-q^{9}-q^{11}+iq^{13}+\cdots$
3475.1.l.a	$3475$	$1$	3475.l	3475.l	$10$	$4$	$1$	$1.734$	$\Q(\zeta_{10})$	$D_{10}$	$\Q(\sqrt{-139}) $	None		$4$	$0$	$0$	$0$	$-1$	$0$	$1$		$q-\zeta_{10}^{2}q^{4}+\zeta_{10}^{2}q^{5}+(-\zeta_{10}-\zeta_{10}^{4}+\cdots)q^{7}+\cdots$
3475.1.l.b	$3475$	$1$	3475.l	3475.l	$10$	$8$	$2$	$1.734$	$\Q(\zeta_{15})$	$D_{30}$	$\Q(\sqrt{-139}) $	None		$4$	$0$	$0$	$0$	$1$	$0$	$1$		$q-\zeta_{30}^{6}q^{4}-\zeta_{30}^{11}q^{5}+(-\zeta_{30}^{2}+\cdots)q^{7}+\cdots$
3475.1.n.a	$3475$	$1$	3475.n	3475.n	$10$	$4$	$1$	$1.734$	$\Q(\zeta_{10})$	$D_{5}$	$\Q(\sqrt{-139}) $	None		$4$	$0$	$0$	$0$	$-1$	$-2$	$1$		$q-\zeta_{10}q^{4}-\zeta_{10}q^{5}+(\zeta_{10}^{2}-\zeta_{10}^{3}+\cdots)q^{7}+\cdots$
3475.1.n.b	$3475$	$1$	3475.n	3475.n	$10$	$8$	$2$	$1.734$	$\Q(\zeta_{15})$	$D_{15}$	$\Q(\sqrt{-139}) $	None		$4$	$0$	$0$	$0$	$1$	$2$	$1$		$q-\zeta_{30}^{3}q^{4}+\zeta_{30}^{8}q^{5}+(\zeta_{30}^{4}-\zeta_{30}^{11}+\cdots)q^{7}+\cdots$
3892.1.bc.a	$3892$	$1$	3892.bc	973.r	$6$	$2$	$1$	$1.942$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-139}) $	None		$4$	$0$	$0$	$0$	$-2$	$2$	$1$		$q+\zeta_{6}^{2}q^{5}+q^{7}+\zeta_{6}^{2}q^{9}-\zeta_{6}q^{11}+\cdots$
3892.1.bc.b	$3892$	$1$	3892.bc	973.r	$6$	$2$	$1$	$1.942$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-139}) $	None		$4$	$0$	$0$	$0$	$1$	$-1$	$1$		$q-\zeta_{6}^{2}q^{5}+\zeta_{6}^{2}q^{7}+\zeta_{6}^{2}q^{9}+\zeta_{6}q^{11}+\cdots$
3892.1.bc.c	$3892$	$1$	3892.bc	973.r	$6$	$2$	$1$	$1.942$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-139}) $	None		$4$	$0$	$0$	$0$	$1$	$-1$	$1$		$q-\zeta_{6}^{2}q^{5}-\zeta_{6}q^{7}+\zeta_{6}^{2}q^{9}+\zeta_{6}q^{11}+\cdots$
3892.1.bc.e	$3892$	$1$	3892.bc	973.r	$6$	$6$	$3$	$1.942$	$\Q(\zeta_{18})$	$D_{9}$	$\Q(\sqrt{-139}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q+(-\zeta_{18}^{7}+\zeta_{18}^{8})q^{5}+\zeta_{18}^{8}q^{7}+\cdots$
139.3.b.a	$139$	$3$	139.b	139.b	$2$	$3$	$3$	$3.787$	3.3.3753.1	$_{}$	$\Q(\sqrt{-139}) $	None	✓	$2$	$0$	$0$	$0$	$0$	$0$	$1$	$\mathrm{U}(1)[D_{2}]$	$q+4q^{4}+(2\beta _{1}+\beta _{2})q^{5}+(-3\beta _{1}-\beta _{2})q^{7}+\cdots$
695.2.g.a	$695$	$2$	695.g	695.g	$4$	$12$	$6$	$5.550$	$\mathbb{Q}[x]/(x^{12} + \cdots)$	$_{}$	$\Q(\sqrt{-139}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$5$	$\mathrm{U}(1)[D_{4}]$	$q-2\beta _{2}q^{4}+\beta _{4}q^{5}+(-\beta _{8}-\beta _{10})q^{7}+\cdots$
973.2.c.a	$973$	$2$	973.c	973.c	$2$	$6$	$6$	$7.769$	6.0.1957816251.1	$_{}$	$\Q(\sqrt{-139}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$	$\mathrm{U}(1)[D_{2}]$	$q+2q^{4}+(-\beta _{1}+\beta _{2})q^{5}+\beta _{3}q^{7}-3q^{9}+\cdots$
973.2.o.c	$973$	$2$	973.o	973.o	$6$	$12$	$6$	$7.769$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	$_{}$	$\Q(\sqrt{-139}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$7$	$\mathrm{U}(1)[D_{6}]$	$q-2\beta _{2}q^{4}+(-\beta _{6}+\beta _{7})q^{5}+(-\beta _{1}+\cdots)q^{7}+\cdots$
1251.2.d.a	$1251$	$2$	1251.d	417.d	$2$	$12$	$12$	$9.989$	$\mathbb{Q}[x]/(x^{12} + \cdots)$	$_{}$	$\Q(\sqrt{-139}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$3^{5}$	$\mathrm{U}(1)[D_{2}]$	$q-2q^{4}-\beta _{1}q^{5}+\beta _{4}q^{7}+\beta _{3}q^{11}+\cdots$
139.5.b.a	$139$	$5$	139.b	139.b	$2$	$3$	$3$	$14.368$	3.3.3753.1	$_{}$	$\Q(\sqrt{-139}) $	None	✓	$2$	$0$	$0$	$0$	$0$	$0$	$3$	$\mathrm{U}(1)[D_{2}]$	$q+2^{4}q^{4}+(3\beta _{1}-5\beta _{2})q^{5}+(7\beta _{1}-4\beta _{2})q^{7}+\cdots$
556.3.c.a	$556$	$3$	556.c	139.b	$2$	$6$	$6$	$15.150$	6.6.$\cdots$.2	$_{}$	$\Q(\sqrt{-139}) $	None	✓	$2$	$0$	$0$	$0$	$0$	$0$	$2^{3}$	$\mathrm{U}(1)[D_{2}]$	$q+(\beta _{4}-\beta _{5})q^{5}+(\beta _{2}+\beta _{3}+\beta _{4}-\beta _{5})q^{7}+\cdots$
2224.2.h.a	$2224$	$2$	2224.h	556.d	$2$	$6$	$6$	$17.759$	6.0.1957816251.1	$_{}$	$\Q(\sqrt{-139}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$2^{3}$	$\mathrm{U}(1)[D_{2}]$	$q+\beta _{2}q^{5}-\beta _{4}q^{7}-3q^{9}+(-\beta _{1}-\beta _{4}+\cdots)q^{11}+\cdots$
2224.2.h.b	$2224$	$2$	2224.h	556.d	$2$	$12$	$12$	$17.759$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	$_{}$	$\Q(\sqrt{-139}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$2^{10}$	$\mathrm{U}(1)[D_{2}]$	$q-\beta _{6}q^{5}+\beta _{8}q^{7}-3q^{9}+\beta _{4}q^{11}+\cdots$
3892.2.g.b	$3892$	$2$	3892.g	973.c	$2$	$12$	$12$	$31.078$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	$_{}$	$\Q(\sqrt{-139}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$2^{3}$	$\mathrm{U}(1)[D_{2}]$	$q+(-\beta _{5}-\beta _{6})q^{5}-\beta _{11}q^{7}-3q^{9}+\cdots$
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	✓	$2$	$0$	$0$	$0$	$-111$	$565$	$1$	$\mathrm{U}(1)[D_{2}]$	$q+2^{6}q^{4}+(-46-19\beta )q^{5}+(266+33\beta )q^{7}+\cdots$
5004.2.e.a	$5004$	$2$	5004.e	417.d	$2$	$24$	$24$	$39.957$		$_{}$	$\Q(\sqrt{-139}) $	None		$4$	$0$	$0$	$0$	$0$	$0$		$\mathrm{U}(1)[D_{2}]$
139.9.b.a	$139$	$9$	139.b	139.b	$2$	$3$	$3$	$56.626$	3.3.3753.1	$_{}$	$\Q(\sqrt{-139}) $	None	✓	$2$	$0$	$0$	$0$	$0$	$0$	$3$	$\mathrm{U}(1)[D_{2}]$	$q+2^{8}q^{4}+(-\beta _{1}+236\beta _{2})q^{5}+(222\beta _{1}+\cdots)q^{7}+\cdots$
556.5.c.a	$556$	$5$	556.c	139.b	$2$	$6$	$6$	$57.474$	6.6.$\cdots$.2	$_{}$	$\Q(\sqrt{-139}) $	None	✓	$2$	$0$	$0$	$0$	$0$	$0$	$2^{4}\cdot 3^{3}$	$\mathrm{U}(1)[D_{2}]$	$q+(\beta _{2}-3\beta _{4})q^{5}+(-5\beta _{2}+5\beta _{3}+2\beta _{4}+\cdots)q^{7}+\cdots$
556.7.c.a	$556$	$7$	556.c	139.b	$2$	$6$	$6$	$127.910$	6.6.$\cdots$.1	$_{}$	$\Q(\sqrt{-139}) $	None	✓	$2$	$0$	$0$	$0$	$0$	$0$	$2^{9}$	$\mathrm{U}(1)[D_{2}]$	$q+(-19\beta _{2}+\beta _{3}+19\beta _{5})q^{5}+(5^{2}\beta _{3}+\cdots)q^{7}+\cdots$

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Elliptic curves over $\Q$
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Genus 2 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.