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Level	Weight	Analytic conductor	Analytic rank	Dim.

Bad $p$	Char.	Primitive character	Character order	Is maximal/largest

Coefficient field	Self-twists	CM/RM discriminant	Inner twist count	Is self-dual

Coefficient ring index	Coefficient ring gens.	Is twist minimal	Projective image

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Results (25 matches)

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Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	Image	CM	RM	Self-dual	Twist minimal	Largest	Maximal	Minimal twist	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	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
1027.1.b.a	$1027$	$1$	1027.b	1027.b	$2$	$1$	$1$	$0.513$	$\Q$	$D_{2}$	$\Q(\sqrt{-79}) $, $\Q(\sqrt{-1027}) $	$\Q(\sqrt{13}) $	✓	✓			1027.1.b.a	$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q+q^{4}+q^{9}-q^{13}+q^{16}-2q^{23}+\cdots$
1027.1.b.b	$1027$	$1$	1027.b	1027.b	$2$	$4$	$4$	$0.513$	$\Q(\zeta_{10})$	$D_{10}$	$\Q(\sqrt{-79}) $	None		✓	✓		1027.1.b.b	$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q+(\zeta_{10}+\zeta_{10}^{4})q^{2}+(-1+\zeta_{10}^{2}-\zeta_{10}^{3}+\cdots)q^{4}+\cdots$
1027.1.o.a	$1027$	$1$	1027.o	1027.o	$6$	$2$	$1$	$0.513$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-79}) $	None		✓			1027.1.o.a	$4$	$0$	$1$	$0$	$-2$	$0$		$1$		$q-\zeta_{6}^{2}q^{2}-q^{5}+q^{8}-\zeta_{6}q^{9}+\zeta_{6}^{2}q^{10}+\cdots$
1027.1.o.b	$1027$	$1$	1027.o	1027.o	$6$	$8$	$4$	$0.513$	$\Q(\zeta_{15})$	$D_{15}$	$\Q(\sqrt{-79}) $	None		✓	✓		1027.1.o.b	$4$	$0$	$-1$	$0$	$2$	$0$		$1$		$q+(\zeta_{30}^{4}+\zeta_{30}^{6})q^{2}+(\zeta_{30}^{8}+\zeta_{30}^{10}+\cdots)q^{4}+\cdots$
1027.1.s.a	$1027$	$1$	1027.s	1027.s	$6$	$2$	$1$	$0.513$	$\Q(\sqrt{-3}) $	$D_{6}$	$\Q(\sqrt{-79}) $	None		✓			1027.1.s.a	$4$	$0$	$3$	$0$	$0$	$0$		$1$		$q+(1-\zeta_{6}^{2})q^{2}+(1-\zeta_{6}-\zeta_{6}^{2})q^{4}+\cdots$
1027.1.s.b	$1027$	$1$	1027.s	1027.s	$6$	$8$	$4$	$0.513$	$\Q(\zeta_{15})$	$D_{30}$	$\Q(\sqrt{-79}) $	None		✓	✓		1027.1.s.b	$4$	$0$	$-3$	$0$	$0$	$0$		$1$		$q+(-\zeta_{30}^{8}+\zeta_{30}^{12})q^{2}+(-\zeta_{30}+\zeta_{30}^{5}+\cdots)q^{4}+\cdots$
1027.1.u.a	$1027$	$1$	1027.u	1027.u	$6$	$2$	$1$	$0.513$	$\Q(\sqrt{-3}) $	$D_{6}$	None	$\Q(\sqrt{13}) $		✓	✓	✓	1027.1.u.a	$4$	$0$	$0$	$3$	$0$	$0$		$1$		$q+(1+\zeta_{6})q^{3}-\zeta_{6}q^{4}+(1+\zeta_{6}+\zeta_{6}^{2}+\cdots)q^{9}+\cdots$
1027.1.x.a	$1027$	$1$	1027.x	1027.x	$12$	$4$	$1$	$0.513$	$\Q(\zeta_{12})$	$S_{4}$	None	None		✓	✓	✓	1027.1.x.a	$4$	$0$	$0$	$-2$	$2$	$0$		$1$		$q+\zeta_{12}^{4}q^{3}-\zeta_{12}^{5}q^{4}+(\zeta_{12}^{2}-\zeta_{12}^{5}+\cdots)q^{5}+\cdots$
1027.2.a.a	$1027$	$2$	1027.a	1.a	$1$	$1$	$1$	$8.201$	$\Q$	$_{}$	None	None	✓	✓			1027.2.a.a	$1$	$1$	$0$	$-2$	$0$	$-1$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{3}-2q^{4}-q^{7}+q^{9}+6q^{11}+\cdots$
1027.2.a.b	$1027$	$2$	1027.a	1.a	$1$	$17$	$17$	$8.201$	$\mathbb{Q}[x]/(x^{17} - \cdots)$	$_{}$	None	None	✓	✓	✓		1027.2.a.b	$1$	$1$	$-10$	$-2$	$-21$	$-1$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta _{1})q^{2}-\beta _{15}q^{3}+(2-\beta _{1}+\cdots)q^{4}+\cdots$
1027.2.a.c	$1027$	$2$	1027.a	1.a	$1$	$18$	$18$	$8.201$	$\mathbb{Q}[x]/(x^{18} - \cdots)$	$_{}$	None	None	✓	✓	✓	✓	1027.2.a.c	$1$	$1$	$-6$	$-8$	$-7$	$-6$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+\beta _{3}q^{3}+(1+\beta _{2})q^{4}+\beta _{6}q^{5}+\cdots$
1027.2.a.d	$1027$	$2$	1027.a	1.a	$1$	$21$	$21$	$8.201$		$_{}$	None	None	✓	✓	✓	✓	1027.2.a.d	$1$	$0$	$9$	$4$	$17$	$8$	$-$		$\mathrm{SU}(2)$
1027.2.a.e	$1027$	$2$	1027.a	1.a	$1$	$22$	$22$	$8.201$		$_{}$	None	None	✓	✓	✓	✓	1027.2.a.e	$1$	$0$	$8$	$4$	$5$	$4$	$-$		$\mathrm{SU}(2)$
1027.2.c.a	$1027$	$2$	1027.c	13.b	$2$	$2$	$2$	$8.201$	$\Q(\sqrt{-1}) $	$_{}$	None	None		✓			1027.2.c.a	$2$	$1$	$0$	$-4$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+2 i q^{2}-2 q^{3}-2 q^{4}+2 i q^{5}+\cdots$
1027.2.c.b	$1027$	$2$	1027.c	13.b	$2$	$40$	$40$	$8.201$		$_{}$	None	None		✓			1027.2.c.b	$2$	$0$	$0$	$-6$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
1027.2.c.c	$1027$	$2$	1027.c	13.b	$2$	$48$	$48$	$8.201$		$_{}$	None	None		✓	✓		1027.2.c.c	$2$	$0$	$0$	$10$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
1027.4.a.a	$1027$	$4$	1027.a	1.a	$1$	$1$	$1$	$60.595$	$\Q$	$_{}$	None	None	✓	✓			1027.4.a.a	$1$	$1$	$3$	$-8$	$5$	$-3$	$-$	$1$	$\mathrm{SU}(2)$	$q+3q^{2}-8q^{3}+q^{4}+5q^{5}-24q^{6}+\cdots$
1027.4.a.b	$1027$	$4$	1027.a	1.a	$1$	$56$	$56$	$60.595$		$_{}$	None	None	✓	✓	✓		1027.4.a.b	$1$	$1$	$-21$	$-9$	$-100$	$-62$	$-$		$\mathrm{SU}(2)$
1027.4.a.c	$1027$	$4$	1027.a	1.a	$1$	$56$	$56$	$60.595$		$_{}$	None	None	✓	✓	✓	✓	1027.4.a.c	$1$	$1$	$-16$	$-17$	$-35$	$-37$	$-$		$\mathrm{SU}(2)$
1027.4.a.d	$1027$	$4$	1027.a	1.a	$1$	$60$	$60$	$60.595$		$_{}$	None	None	✓	✓	✓	✓	1027.4.a.d	$1$	$0$	$12$	$19$	$25$	$33$	$+$		$\mathrm{SU}(2)$
1027.4.a.e	$1027$	$4$	1027.a	1.a	$1$	$61$	$61$	$60.595$		$_{}$	None	None	✓	✓	✓	✓	1027.4.a.e	$1$	$0$	$26$	$19$	$125$	$61$	$+$		$\mathrm{SU}(2)$
1027.6.a.a	$1027$	$6$	1027.a	1.a	$1$	$95$	$95$	$164.714$		$_{}$	None	None	✓	✓	✓	✓	1027.6.a.a	$1$	$1$	$-52$	$-44$	$-607$	$-382$	$+$		$\mathrm{SU}(2)$
1027.6.a.b	$1027$	$6$	1027.a	1.a	$1$	$96$	$96$	$164.714$		$_{}$	None	None	✓	✓	✓	✓	1027.6.a.b	$1$	$1$	$-24$	$-44$	$-107$	$-186$	$+$		$\mathrm{SU}(2)$
1027.6.a.c	$1027$	$6$	1027.a	1.a	$1$	$99$	$99$	$164.714$		$_{}$	None	None	✓	✓	✓	✓	1027.6.a.c	$1$	$0$	$36$	$64$	$493$	$500$	$-$		$\mathrm{SU}(2)$
1027.6.a.d	$1027$	$6$	1027.a	1.a	$1$	$100$	$100$	$164.714$		$_{}$	None	None	✓	✓	✓	✓	1027.6.a.d	$1$	$0$	$32$	$64$	$193$	$304$	$-$		$\mathrm{SU}(2)$

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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.