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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 (35 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
17.2.a.a	$17$	$2$	17.a	1.a	$1$	$1$	$1$	$0.136$	$\Q$	None	✓	$1$	$0$	$-1$	$0$	$-2$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{4}-2q^{5}+4q^{7}+3q^{8}-3q^{9}+\cdots$
17.2.d.a	$17$	$2$	17.d	17.d	$8$	$4$	$1$	$0.136$	$\Q(\zeta_{8})$	None		$2$	$0$	$-4$	$-4$	$0$	$-4$		$1$	$\mathrm{SU}(2)[C_{8}]$	$q+(-1+\zeta_{8}^{2}-\zeta_{8}^{3})q^{2}+(-1-\zeta_{8}+\cdots)q^{3}+\cdots$
17.3.e.a	$17$	$3$	17.e	17.e	$16$	$8$	$1$	$0.463$	$\Q(\zeta_{16})$	None		$2$	$0$	$-8$	$-8$	$16$	$8$		$1$	$\mathrm{SU}(2)[C_{16}]$	$q+(-1+\zeta_{16}+\zeta_{16}^{2}-\zeta_{16}^{4}-\zeta_{16}^{5}+\cdots)q^{2}+\cdots$
17.3.e.b	$17$	$3$	17.e	17.e	$16$	$8$	$1$	$0.463$	$\Q(\zeta_{16})$	None		$2$	$0$	$0$	$0$	$-24$	$-16$		$1$	$\mathrm{SU}(2)[C_{16}]$	$q+(-\zeta_{16}^{2}+\zeta_{16}^{4}+\zeta_{16}^{7})q^{2}+(2\zeta_{16}^{2}+\cdots)q^{3}+\cdots$
17.4.a.a	$17$	$4$	17.a	1.a	$1$	$1$	$1$	$1.003$	$\Q$	None	✓	$1$	$1$	$-3$	$-8$	$6$	$-28$	$-$	$1$	$\mathrm{SU}(2)$	$q-3q^{2}-8q^{3}+q^{4}+6q^{5}+24q^{6}+\cdots$
17.4.a.b	$17$	$4$	17.a	1.a	$1$	$3$	$3$	$1.003$	3.3.2636.1	None	✓	$1$	$0$	$1$	$4$	$-8$	$22$	$+$	$1$	$\mathrm{SU}(2)$	$q+(\beta _{1}-\beta _{2})q^{2}+(2-\beta _{1}+2\beta _{2})q^{3}+\cdots$
17.4.b.a	$17$	$4$	17.b	17.b	$2$	$4$	$4$	$1.003$	4.0.4669632.2	None		$2$	$0$	$-2$	$0$	$0$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q+(-1+\beta _{2})q^{2}+\beta _{1}q^{3}+(1-\beta _{2})q^{4}+\cdots$
17.4.c.a	$17$	$4$	17.c	17.c	$4$	$8$	$4$	$1.003$	$\mathbb{Q}[x]/(x^{8} + \cdots)$	None		$2$	$0$	$0$	$0$	$14$	$2$		$2^{2}$	$\mathrm{SU}(2)[C_{4}]$	$q+(\beta _{1}-\beta _{3})q^{2}+\beta _{4}q^{3}+(-5-\beta _{2}+\cdots)q^{4}+\cdots$
17.4.d.a	$17$	$4$	17.d	17.d	$8$	$12$	$3$	$1.003$	$\mathbb{Q}[x]/(x^{12} + \cdots)$	None		$2$	$0$	$-4$	$-4$	$-20$	$-4$		$2$	$\mathrm{SU}(2)[C_{8}]$	$q+(-\beta _{3}-\beta _{10})q^{2}+\beta _{8}q^{3}+(-\beta _{1}+\cdots)q^{4}+\cdots$
17.5.e.a	$17$	$5$	17.e	17.e	$16$	$40$	$5$	$1.757$		None		$2$	$0$	$-8$	$-8$	$-8$	$-8$			$\mathrm{SU}(2)[C_{16}]$
17.6.a.a	$17$	$6$	17.a	1.a	$1$	$1$	$1$	$2.727$	$\Q$	None	✓	$1$	$1$	$-6$	$10$	$-72$	$-196$	$+$	$1$	$\mathrm{SU}(2)$	$q-6q^{2}+10q^{3}+4q^{4}-72q^{5}-60q^{6}+\cdots$
17.6.a.b	$17$	$6$	17.a	1.a	$1$	$1$	$1$	$2.727$	$\Q$	None	✓	$1$	$1$	$1$	$-18$	$-16$	$28$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-18q^{3}-31q^{4}-2^{4}q^{5}-18q^{6}+\cdots$
17.6.a.c	$17$	$6$	17.a	1.a	$1$	$4$	$4$	$2.727$	4.4.5416116.1	None	✓	$1$	$0$	$3$	$28$	$80$	$284$	$-$	$2^{3}$	$\mathrm{SU}(2)$	$q+(1+\beta _{1})q^{2}+(7+\beta _{1}-\beta _{3})q^{3}+(18+\cdots)q^{4}+\cdots$
17.6.b.a	$17$	$6$	17.b	17.b	$2$	$6$	$6$	$2.727$	$\mathbb{Q}[x]/(x^{6} + \cdots)$	None		$2$	$0$	$-2$	$0$	$0$	$0$		$2^{6}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{4}q^{2}-\beta _{1}q^{3}+(14+\beta _{5})q^{4}+(\beta _{1}+\cdots)q^{5}+\cdots$
17.6.c.a	$17$	$6$	17.c	17.c	$4$	$12$	$6$	$2.727$	$\mathbb{Q}[x]/(x^{12} + \cdots)$	None		$2$	$0$	$0$	$-24$	$-40$	$-120$		$2^{7}$	$\mathrm{SU}(2)[C_{4}]$	$q+(\beta _{1}+\beta _{3})q^{2}+(-2-2\beta _{3}-\beta _{8})q^{3}+\cdots$
17.6.d.a	$17$	$6$	17.d	17.d	$8$	$28$	$7$	$2.727$		None		$2$	$0$	$-4$	$-4$	$40$	$-4$			$\mathrm{SU}(2)[C_{8}]$
17.7.e.a	$17$	$7$	17.e	17.e	$16$	$64$	$8$	$3.911$		None		$2$	$0$	$-8$	$-8$	$-8$	$-8$			$\mathrm{SU}(2)[C_{16}]$
17.8.a.a	$17$	$8$	17.a	1.a	$1$	$1$	$1$	$5.311$	$\Q$	None	✓	$1$	$1$	$-2$	$18$	$-10$	$-902$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{2}+18q^{3}-124q^{4}-10q^{5}+\cdots$
17.8.a.b	$17$	$8$	17.a	1.a	$1$	$3$	$3$	$5.311$	3.3.694349.1	None	✓	$1$	$1$	$1$	$-86$	$-198$	$-1558$	$-$	$2$	$\mathrm{SU}(2)$	$q+\beta _{2}q^{2}+(-28-\beta _{1}-2\beta _{2})q^{3}+(78+\cdots)q^{4}+\cdots$
17.8.a.c	$17$	$8$	17.a	1.a	$1$	$6$	$6$	$5.311$	$\mathbb{Q}[x]/(x^{6} - \cdots)$	None	✓	$1$	$0$	$15$	$40$	$-184$	$2064$	$+$	$2^{4}\cdot 3$	$\mathrm{SU}(2)$	$q+(2+\beta _{1})q^{2}+(6+\beta _{1}+\beta _{4})q^{3}+(78+\cdots)q^{4}+\cdots$
17.8.b.a	$17$	$8$	17.b	17.b	$2$	$10$	$10$	$5.311$	$\mathbb{Q}[x]/(x^{10} + \cdots)$	None		$2$	$0$	$-18$	$0$	$0$	$0$		$2^{13}\cdot 3^{4}$	$\mathrm{SU}(2)[C_{2}]$	$q+(-2+\beta _{2})q^{2}+\beta _{1}q^{3}+(69-2\beta _{2}+\cdots)q^{4}+\cdots$
17.8.c.a	$17$	$8$	17.c	17.c	$4$	$20$	$10$	$5.311$	$\mathbb{Q}[x]/(x^{20} + \cdots)$	None		$2$	$0$	$0$	$24$	$384$	$392$		$2^{21}\cdot 17^{2}$	$\mathrm{SU}(2)[C_{4}]$	$q+\beta _{1}q^{2}+(1-\beta _{6}+\beta _{8})q^{3}+(-2^{6}+\cdots)q^{4}+\cdots$
17.8.d.a	$17$	$8$	17.d	17.d	$8$	$36$	$9$	$5.311$		None		$2$	$0$	$-4$	$-4$	$0$	$-4$			$\mathrm{SU}(2)[C_{8}]$
17.9.e.a	$17$	$9$	17.e	17.e	$16$	$88$	$11$	$6.925$		None		$2$	$0$	$-8$	$-8$	$-8$	$-8$			$\mathrm{SU}(2)[C_{16}]$
17.10.a.a	$17$	$10$	17.a	1.a	$1$	$5$	$5$	$8.756$	$\mathbb{Q}[x]/(x^{5} - \cdots)$	None	✓	$1$	$1$	$-33$	$-236$	$1480$	$-13202$	$+$	$2^{2}\cdot 3$	$\mathrm{SU}(2)$	$q+(-7+\beta _{1})q^{2}+(-48+2\beta _{1}+\beta _{4})q^{3}+\cdots$
17.10.a.b	$17$	$10$	17.a	1.a	$1$	$7$	$7$	$8.756$	$\mathbb{Q}[x]/(x^{7} - \cdots)$	None	✓	$1$	$0$	$-1$	$88$	$1362$	$9388$	$-$	$2^{10}\cdot 3^{4}$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+(12+2\beta _{1}-\beta _{4})q^{3}+(341+\cdots)q^{4}+\cdots$
17.10.b.a	$17$	$10$	17.b	17.b	$2$	$12$	$12$	$8.756$	$\mathbb{Q}[x]/(x^{12} + \cdots)$	None		$2$	$0$	$30$	$0$	$0$	$0$		$2^{17}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+(2+\beta _{2})q^{2}+\beta _{1}q^{3}+(154+4\beta _{2}+\cdots)q^{4}+\cdots$
17.10.c.a	$17$	$10$	17.c	17.c	$4$	$24$	$12$	$8.756$		None		$2$	$0$	$0$	$144$	$-1710$	$3810$			$\mathrm{SU}(2)[C_{4}]$
17.10.d.a	$17$	$10$	17.d	17.d	$8$	$52$	$13$	$8.756$		None		$2$	$0$	$-4$	$-4$	$-1140$	$-4$			$\mathrm{SU}(2)[C_{8}]$
17.11.e.a	$17$	$11$	17.e	17.e	$16$	$112$	$14$	$10.801$		None		$2$	$0$	$-8$	$-8$	$-8$	$-8$			$\mathrm{SU}(2)[C_{16}]$
17.12.a.a	$17$	$12$	17.a	1.a	$1$	$6$	$6$	$13.062$	$\mathbb{Q}[x]/(x^{6} - \cdots)$	None	✓	$1$	$1$	$-9$	$-476$	$-12884$	$-23436$	$-$	$2^{8}\cdot 3$	$\mathrm{SU}(2)$	$q+(-2+\beta _{1})q^{2}+(-79+\beta _{2})q^{3}+(767+\cdots)q^{4}+\cdots$
17.12.a.b	$17$	$12$	17.a	1.a	$1$	$8$	$8$	$13.062$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	None	✓	$1$	$0$	$55$	$496$	$8592$	$95288$	$+$	$2^{8}\cdot 3$	$\mathrm{SU}(2)$	$q+(7-\beta _{1})q^{2}+(62-\beta _{1}+\beta _{3})q^{3}+(1344+\cdots)q^{4}+\cdots$
17.12.b.a	$17$	$12$	17.b	17.b	$2$	$16$	$16$	$13.062$	$\mathbb{Q}[x]/(x^{16} + \cdots)$	None		$2$	$0$	$-2$	$0$	$0$	$0$		$2^{29}\cdot 3^{4}\cdot 17^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{2}q^{2}+\beta _{1}q^{3}+(1271+\beta _{3})q^{4}+\cdots$
17.12.c.a	$17$	$12$	17.c	17.c	$4$	$32$	$16$	$13.062$		None		$2$	$0$	$0$	$-528$	$-15496$	$-38368$			$\mathrm{SU}(2)[C_{4}]$
17.12.d.a	$17$	$12$	17.d	17.d	$8$	$60$	$15$	$13.062$		None		$2$	$0$	$-4$	$-4$	$10120$	$-4$			$\mathrm{SU}(2)[C_{8}]$

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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.