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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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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
106.2.a.a	$106$	$2$	106.a	1.a	$1$	$1$	$1$	$0.846$	$\Q$	None	✓	$1$	$1$	$-1$	$-1$	$-4$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}-4q^{5}+q^{6}-q^{8}+\cdots$
106.2.a.b	$106$	$2$	106.a	1.a	$1$	$1$	$1$	$0.846$	$\Q$	None	✓	$1$	$0$	$-1$	$2$	$1$	$-2$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+2q^{3}+q^{4}+q^{5}-2q^{6}-2q^{7}+\cdots$
106.2.a.c	$106$	$2$	106.a	1.a	$1$	$1$	$1$	$0.846$	$\Q$	None	✓	$1$	$0$	$1$	$-2$	$3$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-2q^{3}+q^{4}+3q^{5}-2q^{6}+2q^{7}+\cdots$
106.2.a.d	$106$	$2$	106.a	1.a	$1$	$1$	$1$	$0.846$	$\Q$	None	✓	$1$	$0$	$1$	$1$	$0$	$-4$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}+q^{6}-4q^{7}+q^{8}+\cdots$
106.2.b.a	$106$	$2$	106.b	53.b	$2$	$2$	$2$	$0.846$	$\Q(\sqrt{-1}) $	None		$2$	$0$	$0$	$0$	$0$	$-4$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+iq^{2}+iq^{3}-q^{4}+2iq^{5}-q^{6}+\cdots$
106.2.b.b	$106$	$2$	106.b	53.b	$2$	$2$	$2$	$0.846$	$\Q(\sqrt{-1}) $	None		$2$	$0$	$0$	$0$	$0$	$8$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+iq^{2}-2iq^{3}-q^{4}-iq^{5}+2q^{6}+\cdots$
106.2.d.a	$106$	$2$	106.d	53.d	$13$	$24$	$2$	$0.846$		None		$2$	$0$	$2$	$-1$	$3$	$2$			$\mathrm{SU}(2)[C_{13}]$
106.2.d.b	$106$	$2$	106.d	53.d	$13$	$36$	$3$	$0.846$		None		$2$	$0$	$-3$	$-3$	$-9$	$-6$			$\mathrm{SU}(2)[C_{13}]$
106.2.e.a	$106$	$2$	106.e	53.e	$26$	$48$	$4$	$0.846$		None		$2$	$0$	$0$	$0$	$0$	$-4$			$\mathrm{SU}(2)[C_{26}]$
106.3.c.a	$106$	$3$	106.c	53.c	$4$	$8$	$4$	$2.888$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	None		$2$	$0$	$-8$	$2$	$10$	$0$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+(-1+\beta _{4})q^{2}+\beta _{1}q^{3}-2\beta _{4}q^{4}+\cdots$
106.3.c.b	$106$	$3$	106.c	53.c	$4$	$10$	$5$	$2.888$	$\mathbb{Q}[x]/(x^{10} - \cdots)$	None		$2$	$0$	$10$	$2$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+(1-\beta _{2})q^{2}-\beta _{3}q^{3}-2\beta _{2}q^{4}+\beta _{8}q^{5}+\cdots$
106.3.f.a	$106$	$3$	106.f	53.f	$52$	$96$	$4$	$2.888$		None		$2$	$0$	$8$	$-2$	$-10$	$0$			$\mathrm{SU}(2)[C_{52}]$
106.3.f.b	$106$	$3$	106.f	53.f	$52$	$120$	$5$	$2.888$		None		$2$	$0$	$-10$	$-2$	$0$	$0$			$\mathrm{SU}(2)[C_{52}]$
106.4.a.a	$106$	$4$	106.a	1.a	$1$	$2$	$2$	$6.254$	$\Q(\sqrt{3}) $	None	✓	$1$	$1$	$4$	$-8$	$-16$	$-28$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{2}+(-4+\beta )q^{3}+4q^{4}+(-8+\cdots)q^{5}+\cdots$
106.4.a.b	$106$	$4$	106.a	1.a	$1$	$3$	$3$	$6.254$	3.3.10164.1	None	✓	$1$	$1$	$-6$	$-5$	$-6$	$8$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{2}+(-1-\beta _{1}+\beta _{2})q^{3}+4q^{4}+\cdots$
106.4.a.c	$106$	$4$	106.a	1.a	$1$	$3$	$3$	$6.254$	3.3.14408.1	None	✓	$1$	$0$	$-6$	$4$	$19$	$-6$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{2}+(1+\beta _{1}+\beta _{2})q^{3}+4q^{4}+(6+\cdots)q^{5}+\cdots$
106.4.a.d	$106$	$4$	106.a	1.a	$1$	$5$	$5$	$6.254$	$\mathbb{Q}[x]/(x^{5} - \cdots)$	None	✓	$1$	$0$	$10$	$1$	$29$	$14$	$+$	$1$	$\mathrm{SU}(2)$	$q+2q^{2}+\beta _{1}q^{3}+4q^{4}+(6-\beta _{3})q^{5}+\cdots$
106.4.b.a	$106$	$4$	106.b	53.b	$2$	$2$	$2$	$6.254$	$\Q(\sqrt{-1}) $	None		$2$	$1$	$0$	$0$	$0$	$-52$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+2iq^{2}+7iq^{3}-4q^{4}-18iq^{5}+\cdots$
106.4.b.b	$106$	$4$	106.b	53.b	$2$	$2$	$2$	$6.254$	$\Q(\sqrt{-1}) $	None		$2$	$0$	$0$	$0$	$0$	$8$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+2iq^{2}-2iq^{3}-4q^{4}-3iq^{5}+4q^{6}+\cdots$
106.4.b.c	$106$	$4$	106.b	53.b	$2$	$10$	$10$	$6.254$	$\mathbb{Q}[x]/(x^{10} + \cdots)$	None		$2$	$0$	$0$	$0$	$0$	$32$		$2^{8}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{3}q^{2}+\beta _{1}q^{3}-4q^{4}+(-4\beta _{3}-\beta _{7}+\cdots)q^{5}+\cdots$
106.4.d.a	$106$	$4$	106.d	53.d	$13$	$72$	$6$	$6.254$		None		$2$	$0$	$12$	$1$	$-13$	$-2$			$\mathrm{SU}(2)[C_{13}]$
106.4.d.b	$106$	$4$	106.d	53.d	$13$	$84$	$7$	$6.254$		None		$2$	$0$	$-14$	$7$	$-13$	$14$			$\mathrm{SU}(2)[C_{13}]$
106.4.e.a	$106$	$4$	106.e	53.e	$26$	$168$	$14$	$6.254$		None		$2$	$0$	$0$	$0$	$0$	$12$			$\mathrm{SU}(2)[C_{26}]$
106.5.c.a	$106$	$5$	106.c	53.c	$4$	$18$	$9$	$10.957$	$\mathbb{Q}[x]/(x^{18} - \cdots)$	None		$2$	$0$	$-36$	$-10$	$-64$	$0$		$2^{3}$	$\mathrm{SU}(2)[C_{4}]$	$q+(-2+2\beta _{2})q^{2}+(-1+\beta _{1}+\beta _{2}+\cdots)q^{3}+\cdots$
106.5.c.b	$106$	$5$	106.c	53.c	$4$	$18$	$9$	$10.957$	$\mathbb{Q}[x]/(x^{18} - \cdots)$	None		$2$	$0$	$36$	$-10$	$16$	$0$		$2^{3}\cdot 5^{2}$	$\mathrm{SU}(2)[C_{4}]$	$q+(2+2\beta _{3})q^{2}+(-1+\beta _{1}-\beta _{3})q^{3}+\cdots$
106.5.f.a	$106$	$5$	106.f	53.f	$52$	$216$	$9$	$10.957$		None		$2$	$0$	$-36$	$10$	$-16$	$0$			$\mathrm{SU}(2)[C_{52}]$
106.5.f.b	$106$	$5$	106.f	53.f	$52$	$216$	$9$	$10.957$		None		$2$	$0$	$36$	$10$	$64$	$0$			$\mathrm{SU}(2)[C_{52}]$
106.6.a.a	$106$	$6$	106.a	1.a	$1$	$4$	$4$	$17.001$	$\mathbb{Q}[x]/(x^{4} - \cdots)$	None	✓	$1$	$1$	$16$	$-8$	$-136$	$-210$	$+$	$2$	$\mathrm{SU}(2)$	$q+4q^{2}+(-2+\beta _{3})q^{3}+2^{4}q^{4}+(-35+\cdots)q^{5}+\cdots$
106.6.a.b	$106$	$6$	106.a	1.a	$1$	$6$	$6$	$17.001$	$\mathbb{Q}[x]/(x^{6} - \cdots)$	None	✓	$1$	$1$	$-24$	$-17$	$-86$	$74$	$+$	$2^{2}$	$\mathrm{SU}(2)$	$q-4q^{2}+(-3+\beta _{1})q^{3}+2^{4}q^{4}+(-15+\cdots)q^{5}+\cdots$
106.6.a.c	$106$	$6$	106.a	1.a	$1$	$6$	$6$	$17.001$	$\mathbb{Q}[x]/(x^{6} - \cdots)$	None	✓	$1$	$0$	$-24$	$10$	$39$	$-24$	$-$	$2$	$\mathrm{SU}(2)$	$q-4q^{2}+(2-\beta _{1})q^{3}+2^{4}q^{4}+(6+\beta _{1}+\cdots)q^{5}+\cdots$
106.6.a.d	$106$	$6$	106.a	1.a	$1$	$7$	$7$	$17.001$	$\mathbb{Q}[x]/(x^{7} - \cdots)$	None	✓	$1$	$0$	$28$	$19$	$89$	$84$	$-$	$2^{2}$	$\mathrm{SU}(2)$	$q+4q^{2}+(3-\beta _{1})q^{3}+2^{4}q^{4}+(13-2\beta _{1}+\cdots)q^{5}+\cdots$
106.6.b.a	$106$	$6$	106.b	53.b	$2$	$22$	$22$	$17.001$		None		$2$	$0$	$0$	$0$	$0$	$-76$			$\mathrm{SU}(2)[C_{2}]$
106.6.d.a	$106$	$6$	106.d	53.d	$13$	$132$	$11$	$17.001$		None		$2$	$0$	$-44$	$-11$	$47$	$126$			$\mathrm{SU}(2)[C_{13}]$
106.6.d.b	$106$	$6$	106.d	53.d	$13$	$144$	$12$	$17.001$		None		$2$	$0$	$48$	$7$	$47$	$-50$			$\mathrm{SU}(2)[C_{13}]$
106.6.e.a	$106$	$6$	106.e	53.e	$26$	$264$	$22$	$17.001$		None		$2$	$0$	$0$	$0$	$0$	$76$			$\mathrm{SU}(2)[C_{26}]$
106.7.c.a	$106$	$7$	106.c	53.c	$4$	$26$	$13$	$24.386$		None		$2$	$0$	$104$	$32$	$-350$	$0$			$\mathrm{SU}(2)[C_{4}]$
106.7.c.b	$106$	$7$	106.c	53.c	$4$	$28$	$14$	$24.386$		None		$2$	$0$	$-112$	$32$	$40$	$0$			$\mathrm{SU}(2)[C_{4}]$
106.8.a.a	$106$	$8$	106.a	1.a	$1$	$6$	$6$	$33.113$	$\mathbb{Q}[x]/(x^{6} - \cdots)$	None	✓	$1$	$1$	$48$	$-41$	$-501$	$-298$	$-$	$2^{6}\cdot 3$	$\mathrm{SU}(2)$	$q+8q^{2}+(-7-\beta _{4})q^{3}+2^{6}q^{4}+(-84+\cdots)q^{5}+\cdots$
106.8.a.b	$106$	$8$	106.a	1.a	$1$	$7$	$7$	$33.113$	$\mathbb{Q}[x]/(x^{7} - \cdots)$	None	✓	$1$	$1$	$-56$	$-26$	$-251$	$-730$	$-$	$2^{5}\cdot 3^{3}$	$\mathrm{SU}(2)$	$q-8q^{2}+(-4+\beta _{2})q^{3}+2^{6}q^{4}+(-6^{2}+\cdots)q^{5}+\cdots$
106.8.a.c	$106$	$8$	106.a	1.a	$1$	$7$	$7$	$33.113$	$\mathbb{Q}[x]/(x^{7} - \cdots)$	None	✓	$1$	$0$	$-56$	$55$	$374$	$-1416$	$+$	$2^{7}$	$\mathrm{SU}(2)$	$q-8q^{2}+(8-\beta _{1})q^{3}+2^{6}q^{4}+(54-\beta _{1}+\cdots)q^{5}+\cdots$
106.8.a.d	$106$	$8$	106.a	1.a	$1$	$9$	$9$	$33.113$	$\mathbb{Q}[x]/(x^{9} - \cdots)$	None	✓	$1$	$0$	$72$	$40$	$624$	$1760$	$+$	$2^{6}\cdot 3^{2}$	$\mathrm{SU}(2)$	$q+8q^{2}+(4+\beta _{1})q^{3}+2^{6}q^{4}+(70-\beta _{1}+\cdots)q^{5}+\cdots$
106.8.b.a	$106$	$8$	106.b	53.b	$2$	$32$	$32$	$33.113$		None		$2$	$0$	$0$	$0$	$0$	$1348$			$\mathrm{SU}(2)[C_{2}]$
106.9.c.a	$106$	$9$	106.c	53.c	$4$	$36$	$18$	$43.182$		None		$2$	$0$	$-288$	$-70$	$-14$	$0$			$\mathrm{SU}(2)[C_{4}]$
106.9.c.b	$106$	$9$	106.c	53.c	$4$	$36$	$18$	$43.182$		None		$2$	$0$	$288$	$-70$	$1106$	$0$			$\mathrm{SU}(2)[C_{4}]$
106.10.a.a	$106$	$10$	106.a	1.a	$1$	$8$	$8$	$54.594$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	None	✓	$1$	$1$	$128$	$1$	$-2841$	$-9576$	$+$	$2^{7}\cdot 3$	$\mathrm{SU}(2)$	$q+2^{4}q^{2}+\beta _{1}q^{3}+2^{8}q^{4}+(-355+\cdots)q^{5}+\cdots$
106.10.a.b	$106$	$10$	106.a	1.a	$1$	$10$	$10$	$54.594$	$\mathbb{Q}[x]/(x^{10} - \cdots)$	None	✓	$1$	$1$	$-160$	$-236$	$-1591$	$848$	$+$	$2^{10}\cdot 3\cdot 7$	$\mathrm{SU}(2)$	$q-2^{4}q^{2}+(-24+\beta _{1})q^{3}+2^{8}q^{4}+\cdots$
106.10.a.c	$106$	$10$	106.a	1.a	$1$	$10$	$10$	$54.594$	$\mathbb{Q}[x]/(x^{10} - \cdots)$	None	✓	$1$	$0$	$-160$	$7$	$1534$	$-3954$	$-$	$2^{8}\cdot 3^{3}$	$\mathrm{SU}(2)$	$q-2^{4}q^{2}+(1-\beta _{1})q^{3}+2^{8}q^{4}+(154+\cdots)q^{5}+\cdots$
106.10.a.d	$106$	$10$	106.a	1.a	$1$	$11$	$11$	$54.594$	$\mathbb{Q}[x]/(x^{11} - \cdots)$	None	✓	$1$	$0$	$176$	$244$	$2784$	$4830$	$-$	$2^{11}\cdot 3^{3}$	$\mathrm{SU}(2)$	$q+2^{4}q^{2}+(22+\beta _{1})q^{3}+2^{8}q^{4}+(253+\cdots)q^{5}+\cdots$
106.10.b.a	$106$	$10$	106.b	53.b	$2$	$40$	$40$	$54.594$		None		$2$	$0$	$0$	$0$	$0$	$-9756$			$\mathrm{SU}(2)[C_{2}]$
106.11.c.a	$106$	$11$	106.c	53.c	$4$	$44$	$22$	$67.348$		None		$2$	$0$	$-704$	$62$	$3690$	$0$			$\mathrm{SU}(2)[C_{4}]$

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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.