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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	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
2093.1.bc.a	$2093$	$1$	2093.bc	2093.ac	$6$	$4$	$2$	$1.045$	$\Q(\zeta_{12})$	$A_{4}$	None	None		$4$	$0$	$0$	$4$	$0$	$0$		$1$		$q+q^{3}+\zeta_{12}^{2}q^{4}+\zeta_{12}^{5}q^{5}-\zeta_{12}^{5}q^{7}+\cdots$
2093.1.bg.a	$2093$	$1$	2093.bg	2093.ag	$6$	$2$	$1$	$1.045$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-299}) $	None		$4$	$0$	$0$	$1$	$-2$	$2$		$1$		$q+\zeta_{6}q^{3}-\zeta_{6}q^{4}+\zeta_{6}^{2}q^{5}+q^{7}+\zeta_{6}q^{11}+\cdots$
2093.1.bg.b	$2093$	$1$	2093.bg	2093.ag	$6$	$2$	$1$	$1.045$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-299}) $	None		$4$	$0$	$0$	$1$	$2$	$-2$		$1$		$q+\zeta_{6}q^{3}-\zeta_{6}q^{4}-\zeta_{6}^{2}q^{5}-q^{7}-\zeta_{6}q^{11}+\cdots$
2093.1.bg.c	$2093$	$1$	2093.bg	2093.ag	$6$	$4$	$2$	$1.045$	$\Q(\zeta_{12})$	$D_{6}$	$\Q(\sqrt{-299}) $	None		$8$	$0$	$0$	$-2$	$0$	$0$		$1$		$q+\zeta_{12}^{4}q^{3}+\zeta_{12}^{4}q^{4}-\zeta_{12}^{3}q^{7}+\cdots$
2093.1.bg.d	$2093$	$1$	2093.bg	2093.ag	$6$	$8$	$4$	$1.045$	$\Q(\zeta_{24})$	$D_{12}$	$\Q(\sqrt{-299}) $	None		$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q+(-\zeta_{24}^{6}-\zeta_{24}^{10})q^{3}+\zeta_{24}^{8}q^{4}+\cdots$
2093.1.bp.a	$2093$	$1$	2093.bp	2093.ap	$6$	$4$	$2$	$1.045$	$\Q(\zeta_{12})$	$A_{4}$	None	None		$4$	$0$	$0$	$-2$	$0$	$0$		$1$		$q+\zeta_{12}^{4}q^{3}-q^{4}-\zeta_{12}q^{5}-\zeta_{12}^{3}q^{7}+\cdots$
2093.1.co.a	$2093$	$1$	2093.co	2093.bo	$22$	$10$	$1$	$1.045$	$\Q(\zeta_{22})$	$D_{11}$	$\Q(\sqrt{-91}) $	None		$4$	$0$	$0$	$0$	$-9$	$1$		$1$		$q+\zeta_{22}^{8}q^{4}+(-1-\zeta_{22}^{4})q^{5}+\zeta_{22}^{5}q^{7}+\cdots$
2093.1.co.b	$2093$	$1$	2093.co	2093.bo	$22$	$10$	$1$	$1.045$	$\Q(\zeta_{22})$	$D_{11}$	$\Q(\sqrt{-91}) $	None		$4$	$0$	$0$	$0$	$9$	$-1$		$1$		$q+\zeta_{22}^{8}q^{4}+(1+\zeta_{22}^{4})q^{5}-\zeta_{22}^{5}q^{7}+\cdots$
2093.2.a.a	$2093$	$2$	2093.a	1.a	$1$	$1$	$1$	$16.713$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$-2$	$-1$	$-3$	$1$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{2}-q^{3}+2q^{4}-3q^{5}+2q^{6}+\cdots$
2093.2.a.b	$2093$	$2$	2093.a	1.a	$1$	$1$	$1$	$16.713$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$-2$	$-1$	$1$	$1$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{2}-q^{3}+2q^{4}+q^{5}+2q^{6}+q^{7}+\cdots$
2093.2.a.c	$2093$	$2$	2093.a	1.a	$1$	$1$	$1$	$16.713$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$-2$	$3$	$3$	$-1$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{2}+3q^{3}+2q^{4}+3q^{5}-6q^{6}+\cdots$
2093.2.a.d	$2093$	$2$	2093.a	1.a	$1$	$1$	$1$	$16.713$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$-1$	$2$	$0$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+2q^{3}-q^{4}-2q^{6}+q^{7}+3q^{8}+\cdots$
2093.2.a.e	$2093$	$2$	2093.a	1.a	$1$	$1$	$1$	$16.713$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$0$	$-2$	$0$	$1$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{3}-2q^{4}+q^{7}+q^{9}-3q^{11}+\cdots$
2093.2.a.f	$2093$	$2$	2093.a	1.a	$1$	$1$	$1$	$16.713$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$0$	$-1$	$1$	$-1$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-2q^{4}+q^{5}-q^{7}-2q^{9}+5q^{11}+\cdots$
2093.2.a.g	$2093$	$2$	2093.a	1.a	$1$	$1$	$1$	$16.713$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$0$	$1$	$-3$	$1$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-2q^{4}-3q^{5}+q^{7}-2q^{9}+3q^{11}+\cdots$
2093.2.a.h	$2093$	$2$	2093.a	1.a	$1$	$1$	$1$	$16.713$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$0$	$1$	$3$	$1$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-2q^{4}+3q^{5}+q^{7}-2q^{9}-3q^{11}+\cdots$
2093.2.a.i	$2093$	$2$	2093.a	1.a	$1$	$1$	$1$	$16.713$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$0$	$2$	$-4$	$-1$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{3}-2q^{4}-4q^{5}-q^{7}+q^{9}-5q^{11}+\cdots$
2093.2.a.j	$2093$	$2$	2093.a	1.a	$1$	$1$	$1$	$16.713$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$2$	$2$	$2$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{2}+2q^{3}+2q^{4}+2q^{5}+4q^{6}+\cdots$
2093.2.a.k	$2093$	$2$	2093.a	1.a	$1$	$2$	$2$	$16.713$	$\Q(\sqrt{2}) $	$_{}$	None	None	✓	$1$	$1$	$0$	$-2$	$-2$	$2$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{2}+(-1-\beta )q^{3}+(-1+2\beta )q^{5}+\cdots$
2093.2.a.l	$2093$	$2$	2093.a	1.a	$1$	$6$	$6$	$16.713$	6.6.52212317.1	$_{}$	None	None	✓	$1$	$1$	$-1$	$-5$	$-2$	$6$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+(-1-\beta _{4})q^{3}+(2+\beta _{2})q^{4}+\cdots$
2093.2.a.m	$2093$	$2$	2093.a	1.a	$1$	$11$	$11$	$16.713$	$\mathbb{Q}[x]/(x^{11} - \cdots)$	$_{}$	None	None	✓	$1$	$1$	$-1$	$-3$	$-4$	$-11$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+\beta _{5}q^{3}+(1+\beta _{2})q^{4}+\beta _{6}q^{5}+\cdots$
2093.2.a.n	$2093$	$2$	2093.a	1.a	$1$	$15$	$15$	$16.713$	$\mathbb{Q}[x]/(x^{15} - \cdots)$	$_{}$	None	None	✓	$1$	$1$	$1$	$-7$	$-10$	$15$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+\beta _{11}q^{3}+(1+\beta _{2})q^{4}+(-1+\cdots)q^{5}+\cdots$
2093.2.a.o	$2093$	$2$	2093.a	1.a	$1$	$16$	$16$	$16.713$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	$_{}$	None	None	✓	$1$	$1$	$-3$	$-4$	$7$	$-16$	$+$	$2^{2}$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}-\beta _{6}q^{3}+(1+\beta _{2})q^{4}-\beta _{8}q^{5}+\cdots$
2093.2.a.p	$2093$	$2$	2093.a	1.a	$1$	$16$	$16$	$16.713$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	$_{}$	None	None	✓	$1$	$0$	$3$	$4$	$3$	$16$	$-$	$2^{2}$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}-\beta _{7}q^{3}+(1+\beta _{2})q^{4}-\beta _{14}q^{5}+\cdots$
2093.2.a.q	$2093$	$2$	2093.a	1.a	$1$	$16$	$16$	$16.713$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	$_{}$	None	None	✓	$1$	$0$	$6$	$-1$	$0$	$-16$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}-\beta _{12}q^{3}+(1+\beta _{2})q^{4}+\beta _{6}q^{5}+\cdots$
2093.2.a.r	$2093$	$2$	2093.a	1.a	$1$	$19$	$19$	$16.713$	$\mathbb{Q}[x]/(x^{19} - \cdots)$	$_{}$	None	None	✓	$1$	$0$	$-1$	$8$	$5$	$19$	$-$	$2$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+\beta _{9}q^{3}+(1+\beta _{2})q^{4}-\beta _{8}q^{5}+\cdots$
2093.2.a.s	$2093$	$2$	2093.a	1.a	$1$	$20$	$20$	$16.713$	$\mathbb{Q}[x]/(x^{20} - \cdots)$	$_{}$	None	None	✓	$1$	$0$	$2$	$8$	$-3$	$-20$	$-$	$2^{4}$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+\beta _{8}q^{3}+(2+\beta _{2})q^{4}+\beta _{4}q^{5}+\cdots$
2093.4.a.a	$2093$	$4$	2093.a	1.a	$1$	$45$	$45$	$123.491$		$_{}$	None	None	✓	$1$	$1$	$-8$	$-38$	$-65$	$315$	$-$		$\mathrm{SU}(2)$
2093.4.a.b	$2093$	$4$	2093.a	1.a	$1$	$45$	$45$	$123.491$		$_{}$	None	None	✓	$1$	$1$	$-4$	$-26$	$35$	$-315$	$-$		$\mathrm{SU}(2)$
2093.4.a.c	$2093$	$4$	2093.a	1.a	$1$	$49$	$49$	$123.491$		$_{}$	None	None	✓	$1$	$1$	$-8$	$-2$	$-15$	$-343$	$-$		$\mathrm{SU}(2)$
2093.4.a.d	$2093$	$4$	2093.a	1.a	$1$	$49$	$49$	$123.491$		$_{}$	None	None	✓	$1$	$1$	$-4$	$-14$	$-15$	$343$	$-$		$\mathrm{SU}(2)$
2093.4.a.e	$2093$	$4$	2093.a	1.a	$1$	$50$	$50$	$123.491$		$_{}$	None	None	✓	$1$	$0$	$2$	$28$	$65$	$350$	$+$		$\mathrm{SU}(2)$
2093.4.a.f	$2093$	$4$	2093.a	1.a	$1$	$50$	$50$	$123.491$		$_{}$	None	None	✓	$1$	$0$	$6$	$16$	$-35$	$-350$	$+$		$\mathrm{SU}(2)$
2093.4.a.g	$2093$	$4$	2093.a	1.a	$1$	$54$	$54$	$123.491$		$_{}$	None	None	✓	$1$	$0$	$2$	$16$	$15$	$-378$	$+$		$\mathrm{SU}(2)$
2093.4.a.h	$2093$	$4$	2093.a	1.a	$1$	$54$	$54$	$123.491$		$_{}$	None	None	✓	$1$	$0$	$6$	$28$	$15$	$378$	$+$		$\mathrm{SU}(2)$

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Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
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.