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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 231 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
49.2.a.a	$49$	$2$	49.a	1.a	$1$	$1$	$1$	$0.391$	$\Q$	$\Q(\sqrt{-7}) $	✓	$2$	$0$	$1$	$0$	$0$	$0$	$-$	$1$	$N(\mathrm{U}(1))$	$q+q^{2}-q^{4}-3q^{8}-3q^{9}+4q^{11}+\cdots$
49.2.c.a	$49$	$2$	49.c	7.c	$3$	$2$	$1$	$0.391$	$\Q(\sqrt{-3}) $	$\Q(\sqrt{-7}) $		$4$	$0$	$-1$	$0$	$0$	$0$		$1$	$\mathrm{U}(1)[D_{3}]$	$q-\zeta_{6}q^{2}+(1-\zeta_{6})q^{4}-3q^{8}+3\zeta_{6}q^{9}+\cdots$
49.2.e.a	$49$	$2$	49.e	49.e	$7$	$6$	$1$	$0.391$	$\Q(\zeta_{14})$	None		$2$	$0$	$-3$	$-3$	$6$	$7$		$1$	$\mathrm{SU}(2)[C_{7}]$	$q+(-1+\zeta_{14}-\zeta_{14}^{4}+\zeta_{14}^{5})q^{2}+\cdots$
49.2.e.b	$49$	$2$	49.e	49.e	$7$	$12$	$2$	$0.391$	$\Q(\zeta_{21})$	None		$2$	$0$	$-2$	$0$	$-7$	$-7$		$7$	$\mathrm{SU}(2)[C_{7}]$	$q+(\zeta_{21}^{2}+\zeta_{21}^{4}-\zeta_{21}^{5}-\zeta_{21}^{9}+\zeta_{21}^{11})q^{2}+\cdots$
49.2.g.a	$49$	$2$	49.g	49.g	$21$	$48$	$4$	$0.391$		None		$2$	$0$	$-13$	$-14$	$-14$	$-14$			$\mathrm{SU}(2)[C_{21}]$
49.3.b.a	$49$	$3$	49.b	7.b	$2$	$4$	$4$	$1.335$	4.0.2048.2	None		$2$	$0$	$4$	$0$	$0$	$0$		$7$	$\mathrm{SU}(2)[C_{2}]$	$q+(1+\beta _{2})q^{2}-\beta _{3}q^{3}+(-1+2\beta _{2}+\cdots)q^{4}+\cdots$
49.3.d.a	$49$	$3$	49.d	7.d	$6$	$2$	$1$	$1.335$	$\Q(\sqrt{-3}) $	$\Q(\sqrt{-7}) $		$4$	$0$	$3$	$0$	$0$	$0$		$1$	$\mathrm{U}(1)[D_{6}]$	$q+3\zeta_{6}q^{2}+(-5+5\zeta_{6})q^{4}-3q^{8}+\cdots$
49.3.d.b	$49$	$3$	49.d	7.d	$6$	$8$	$4$	$1.335$	8.0.339738624.1	None		$4$	$0$	$-4$	$0$	$0$	$0$		$7^{2}$	$\mathrm{SU}(2)[C_{6}]$	$q+(\beta _{4}-\beta _{5})q^{2}+\beta _{1}q^{3}+(1+2\beta _{2}+\beta _{4}+\cdots)q^{4}+\cdots$
49.3.f.a	$49$	$3$	49.f	49.f	$14$	$54$	$9$	$1.335$		None		$2$	$0$	$-5$	$-7$	$-7$	$0$			$\mathrm{SU}(2)[C_{14}]$
49.3.h.a	$49$	$3$	49.h	49.h	$42$	$96$	$8$	$1.335$		None		$2$	$0$	$-13$	$-14$	$-14$	$-14$			$\mathrm{SU}(2)[C_{42}]$
49.4.a.a	$49$	$4$	49.a	1.a	$1$	$1$	$1$	$2.891$	$\Q$	$\Q(\sqrt{-7}) $	✓	$2$	$1$	$-5$	$0$	$0$	$0$	$-$	$1$	$N(\mathrm{U}(1))$	$q-5q^{2}+17q^{4}-45q^{8}-3^{3}q^{9}-68q^{11}+\cdots$
49.4.a.b	$49$	$4$	49.a	1.a	$1$	$1$	$1$	$2.891$	$\Q$	None	✓	$1$	$1$	$-1$	$2$	$-16$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+2q^{3}-7q^{4}-2^{4}q^{5}-2q^{6}+\cdots$
49.4.a.c	$49$	$4$	49.a	1.a	$1$	$1$	$1$	$2.891$	$\Q$	None	✓	$1$	$1$	$2$	$-7$	$-7$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{2}-7q^{3}-4q^{4}-7q^{5}-14q^{6}+\cdots$
49.4.a.d	$49$	$4$	49.a	1.a	$1$	$1$	$1$	$2.891$	$\Q$	None	✓	$1$	$0$	$2$	$7$	$7$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+2q^{2}+7q^{3}-4q^{4}+7q^{5}+14q^{6}+\cdots$
49.4.a.e	$49$	$4$	49.a	1.a	$1$	$4$	$4$	$2.891$	$\Q(\sqrt{2}, \sqrt{65})$	None	✓	$2$	$0$	$2$	$0$	$0$	$0$	$+$	$7$	$\mathrm{SU}(2)$	$q+(1+\beta _{1})q^{2}+\beta _{2}q^{3}+(9+\beta _{1})q^{4}+\cdots$
49.4.c.a	$49$	$4$	49.c	7.c	$3$	$2$	$1$	$2.891$	$\Q(\sqrt{-3}) $	None		$2$	$0$	$-2$	$7$	$7$	$0$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q-2\zeta_{6}q^{2}+(7-7\zeta_{6})q^{3}+(4-4\zeta_{6})q^{4}+\cdots$
49.4.c.b	$49$	$4$	49.c	7.c	$3$	$2$	$1$	$2.891$	$\Q(\sqrt{-3}) $	None		$2$	$0$	$1$	$-2$	$16$	$0$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+\zeta_{6}q^{2}+(-2+2\zeta_{6})q^{3}+(7-7\zeta_{6})q^{4}+\cdots$
49.4.c.c	$49$	$4$	49.c	7.c	$3$	$2$	$1$	$2.891$	$\Q(\sqrt{-3}) $	None		$2$	$0$	$1$	$2$	$-16$	$0$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+\zeta_{6}q^{2}+(2-2\zeta_{6})q^{3}+(7-7\zeta_{6})q^{4}+\cdots$
49.4.c.d	$49$	$4$	49.c	7.c	$3$	$2$	$1$	$2.891$	$\Q(\sqrt{-3}) $	$\Q(\sqrt{-7}) $		$4$	$0$	$5$	$0$	$0$	$0$		$1$	$\mathrm{U}(1)[D_{3}]$	$q+5\zeta_{6}q^{2}+(-17+17\zeta_{6})q^{4}-45q^{8}+\cdots$
49.4.c.e	$49$	$4$	49.c	7.c	$3$	$8$	$4$	$2.891$	8.0.$\cdots$.19	None		$4$	$0$	$-2$	$0$	$0$	$0$		$7^{2}$	$\mathrm{SU}(2)[C_{3}]$	$q+(-1+\beta _{2}-\beta _{6})q^{2}+\beta _{3}q^{3}+(-8+\cdots)q^{4}+\cdots$
49.4.e.a	$49$	$4$	49.e	49.e	$7$	$78$	$13$	$2.891$		None		$2$	$0$	$-5$	$-5$	$-23$	$0$			$\mathrm{SU}(2)[C_{7}]$
49.4.g.a	$49$	$4$	49.g	49.g	$21$	$156$	$13$	$2.891$		None		$2$	$0$	$-13$	$-7$	$-7$	$-42$			$\mathrm{SU}(2)[C_{21}]$
49.5.b.a	$49$	$5$	49.b	7.b	$2$	$4$	$4$	$5.065$	$\Q(\sqrt{-3}, \sqrt{22})$	None		$2$	$0$	$8$	$0$	$0$	$0$		$2^{2}\cdot 7$	$\mathrm{SU}(2)[C_{2}]$	$q+(2+\beta _{1})q^{2}+\beta _{2}q^{3}+(10+4\beta _{1})q^{4}+\cdots$
49.5.b.b	$49$	$5$	49.b	7.b	$2$	$8$	$8$	$5.065$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	None		$2$	$0$	$-12$	$0$	$0$	$0$		$7^{6}$	$\mathrm{SU}(2)[C_{2}]$	$q+(-2-\beta _{2})q^{2}-\beta _{3}q^{3}+(8+\beta _{1}+3\beta _{2}+\cdots)q^{4}+\cdots$
49.5.d.a	$49$	$5$	49.d	7.d	$6$	$2$	$1$	$5.065$	$\Q(\sqrt{-3}) $	$\Q(\sqrt{-7}) $		$4$	$0$	$-1$	$0$	$0$	$0$		$1$	$\mathrm{U}(1)[D_{6}]$	$q-\zeta_{6}q^{2}+(15-15\zeta_{6})q^{4}-31q^{8}+\cdots$
49.5.d.b	$49$	$5$	49.d	7.d	$6$	$4$	$2$	$5.065$	$\Q(\sqrt{-3}, \sqrt{22})$	None		$2$	$0$	$-4$	$-6$	$30$	$0$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q+(-2+\beta _{1}-2\beta _{2})q^{2}+(-2+\beta _{1}+\cdots)q^{3}+\cdots$
49.5.d.c	$49$	$5$	49.d	7.d	$6$	$16$	$8$	$5.065$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	None		$4$	$0$	$12$	$0$	$0$	$0$		$7^{12}$	$\mathrm{SU}(2)[C_{6}]$	$q+(1+\beta _{2}+\beta _{12})q^{2}+\beta _{5}q^{3}+(5\beta _{2}+\cdots)q^{4}+\cdots$
49.5.f.a	$49$	$5$	49.f	49.f	$14$	$102$	$17$	$5.065$		None		$2$	$0$	$-5$	$-7$	$-7$	$-56$			$\mathrm{SU}(2)[C_{14}]$
49.5.h.a	$49$	$5$	49.h	49.h	$42$	$216$	$18$	$5.065$		None		$2$	$0$	$-13$	$-20$	$16$	$-14$			$\mathrm{SU}(2)[C_{42}]$
49.6.a.a	$49$	$6$	49.a	1.a	$1$	$1$	$1$	$7.859$	$\Q$	None	✓	$1$	$0$	$-10$	$14$	$56$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q-10q^{2}+14q^{3}+68q^{4}+56q^{5}+\cdots$
49.6.a.b	$49$	$6$	49.a	1.a	$1$	$1$	$1$	$7.859$	$\Q$	$\Q(\sqrt{-7}) $	✓	$2$	$0$	$11$	$0$	$0$	$0$	$-$	$1$	$N(\mathrm{U}(1))$	$q+11q^{2}+89q^{4}+627q^{8}-3^{5}q^{9}+\cdots$
49.6.a.c	$49$	$6$	49.a	1.a	$1$	$2$	$2$	$7.859$	$\Q(\sqrt{39}) $	None	✓	$2$	$0$	$-4$	$0$	$0$	$0$	$-$	$2^{2}$	$\mathrm{SU}(2)$	$q-2q^{2}+\beta q^{3}-28q^{4}+3\beta q^{5}-2\beta q^{6}+\cdots$
49.6.a.d	$49$	$6$	49.a	1.a	$1$	$2$	$2$	$7.859$	$\Q(\sqrt{37}) $	None	✓	$1$	$1$	$2$	$-8$	$-38$	$0$	$+$	$2$	$\mathrm{SU}(2)$	$q+(1+\beta )q^{2}+(-4-\beta )q^{3}+(6+2\beta )q^{4}+\cdots$
49.6.a.e	$49$	$6$	49.a	1.a	$1$	$2$	$2$	$7.859$	$\Q(\sqrt{37}) $	None	✓	$1$	$0$	$2$	$8$	$38$	$0$	$-$	$2$	$\mathrm{SU}(2)$	$q+(1+\beta )q^{2}+(4+\beta )q^{3}+(6+2\beta )q^{4}+\cdots$
49.6.a.f	$49$	$6$	49.a	1.a	$1$	$2$	$2$	$7.859$	$\Q(\sqrt{57}) $	None	✓	$1$	$0$	$9$	$6$	$18$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+(5-\beta )q^{2}+(6-6\beta )q^{3}+(7-9\beta )q^{4}+\cdots$
49.6.a.g	$49$	$6$	49.a	1.a	$1$	$4$	$4$	$7.859$	$\Q(\sqrt{2}, \sqrt{113})$	None	✓	$2$	$1$	$-10$	$0$	$0$	$0$	$+$	$7$	$\mathrm{SU}(2)$	$q+(-2+\beta _{1})q^{2}+(2\beta _{2}-\beta _{3})q^{3}-5\beta _{1}q^{4}+\cdots$
49.6.c.a	$49$	$6$	49.c	7.c	$3$	$2$	$1$	$7.859$	$\Q(\sqrt{-3}) $	$\Q(\sqrt{-7}) $		$4$	$0$	$-11$	$0$	$0$	$0$		$1$	$\mathrm{U}(1)[D_{3}]$	$q-11\zeta_{6}q^{2}+(-89+89\zeta_{6})q^{4}+627q^{8}+\cdots$
49.6.c.b	$49$	$6$	49.c	7.c	$3$	$2$	$1$	$7.859$	$\Q(\sqrt{-3}) $	None		$2$	$0$	$10$	$-14$	$-56$	$0$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+10\zeta_{6}q^{2}+(-14+14\zeta_{6})q^{3}+(-68+\cdots)q^{4}+\cdots$
49.6.c.c	$49$	$6$	49.c	7.c	$3$	$2$	$1$	$7.859$	$\Q(\sqrt{-3}) $	None		$2$	$0$	$10$	$14$	$56$	$0$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+10\zeta_{6}q^{2}+(14-14\zeta_{6})q^{3}+(-68+\cdots)q^{4}+\cdots$
49.6.c.d	$49$	$6$	49.c	7.c	$3$	$4$	$2$	$7.859$	$\Q(\sqrt{-3}, \sqrt{-19})$	None		$2$	$0$	$-9$	$-6$	$-18$	$0$		$3$	$\mathrm{SU}(2)[C_{3}]$	$q+(5\beta _{1}+\beta _{2}-\beta _{3})q^{2}+(-6-6\beta _{1}+\cdots)q^{3}+\cdots$
49.6.c.e	$49$	$6$	49.c	7.c	$3$	$4$	$2$	$7.859$	$\Q(\sqrt{-3}, \sqrt{-19})$	None		$2$	$0$	$-9$	$6$	$18$	$0$		$3$	$\mathrm{SU}(2)[C_{3}]$	$q+(5\beta _{1}+\beta _{2}-\beta _{3})q^{2}+(6+6\beta _{1}-6\beta _{3})q^{3}+\cdots$
49.6.c.f	$49$	$6$	49.c	7.c	$3$	$4$	$2$	$7.859$	$\Q(\sqrt{-3}, \sqrt{37})$	None		$2$	$0$	$-2$	$-8$	$-38$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{3}]$	$q+(-\beta _{1}-\beta _{2})q^{2}+(-4+4\beta _{1}+\beta _{2}+\cdots)q^{3}+\cdots$
49.6.c.g	$49$	$6$	49.c	7.c	$3$	$4$	$2$	$7.859$	$\Q(\sqrt{-3}, \sqrt{-13})$	None		$4$	$0$	$4$	$0$	$0$	$0$		$2^{4}\cdot 3$	$\mathrm{SU}(2)[C_{3}]$	$q+(2-2\beta _{1})q^{2}+\beta _{2}q^{3}+28\beta _{1}q^{4}+\cdots$
49.6.c.h	$49$	$6$	49.c	7.c	$3$	$8$	$4$	$7.859$	8.0.$\cdots$.19	None		$4$	$0$	$10$	$0$	$0$	$0$		$7^{2}$	$\mathrm{SU}(2)[C_{3}]$	$q+(3-2\beta _{1}-\beta _{3}-\beta _{6})q^{2}+(-2\beta _{2}+\cdots)q^{3}+\cdots$
49.6.e.a	$49$	$6$	49.e	49.e	$7$	$138$	$23$	$7.859$		None		$2$	$0$	$-5$	$13$	$67$	$-56$			$\mathrm{SU}(2)[C_{7}]$
49.6.g.a	$49$	$6$	49.g	49.g	$21$	$264$	$22$	$7.859$		None		$2$	$0$	$-13$	$-22$	$-52$	$154$			$\mathrm{SU}(2)[C_{21}]$
49.7.b.a	$49$	$7$	49.b	7.b	$2$	$2$	$2$	$11.273$	$\Q(\sqrt{-3}) $	None		$2$	$0$	$-24$	$0$	$0$	$0$		$2\cdot 7$	$\mathrm{SU}(2)[C_{2}]$	$q-12q^{2}-\zeta_{6}q^{3}+80q^{4}-15\zeta_{6}q^{5}+\cdots$
49.7.b.b	$49$	$7$	49.b	7.b	$2$	$4$	$4$	$11.273$	$\Q(\sqrt{2}, \sqrt{-3})$	None		$2$	$0$	$16$	$0$	$0$	$0$		$2^{2}\cdot 3\cdot 7$	$\mathrm{SU}(2)[C_{2}]$	$q+(4+\beta _{1})q^{2}+(6\beta _{2}-\beta _{3})q^{3}+(-30+\cdots)q^{4}+\cdots$
49.7.b.c	$49$	$7$	49.b	7.b	$2$	$12$	$12$	$11.273$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	None		$2$	$0$	$20$	$0$	$0$	$0$		$2\cdot 7^{15}$	$\mathrm{SU}(2)[C_{2}]$	$q+(2-\beta _{1})q^{2}+\beta _{3}q^{3}+(47-\beta _{1}-\beta _{5}+\cdots)q^{4}+\cdots$
49.7.d.a	$49$	$7$	49.d	7.d	$6$	$2$	$1$	$11.273$	$\Q(\sqrt{-3}) $	$\Q(\sqrt{-7}) $		$4$	$0$	$-9$	$0$	$0$	$0$		$1$	$\mathrm{U}(1)[D_{6}]$	$q-9\zeta_{6}q^{2}+(-17+17\zeta_{6})q^{4}-423q^{8}+\cdots$

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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.