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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 (20 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				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*	$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$	Coefficient ring index	Sato-Tate	$q$-expansion
1680.1.bb.a	$1680$	$1$	1680.bb	420.o	$2$	$1$	$1$	$0.838$	$\Q$	$D_{2}$	$\Q(\sqrt{-5}) $, $\Q(\sqrt{-105}) $	$\Q(\sqrt{21}) $	✓	$4$	$0$	$0$	$-1$	$-1$	$-1$	$1$		$q-q^{3}-q^{5}-q^{7}+q^{9}+q^{15}+q^{21}+\cdots$
1680.1.bb.b	$1680$	$1$	1680.bb	420.o	$2$	$1$	$1$	$0.838$	$\Q$	$D_{2}$	$\Q(\sqrt{-5}) $, $\Q(\sqrt{-105}) $	$\Q(\sqrt{21}) $	✓	$4$	$0$	$0$	$-1$	$1$	$1$	$1$		$q-q^{3}+q^{5}+q^{7}+q^{9}-q^{15}-q^{21}+\cdots$
1680.1.bb.c	$1680$	$1$	1680.bb	420.o	$2$	$1$	$1$	$0.838$	$\Q$	$D_{2}$	$\Q(\sqrt{-5}) $, $\Q(\sqrt{-105}) $	$\Q(\sqrt{21}) $	✓	$4$	$0$	$0$	$1$	$-1$	$1$	$1$		$q+q^{3}-q^{5}+q^{7}+q^{9}-q^{15}+q^{21}+\cdots$
1680.1.bb.d	$1680$	$1$	1680.bb	420.o	$2$	$1$	$1$	$0.838$	$\Q$	$D_{2}$	$\Q(\sqrt{-5}) $, $\Q(\sqrt{-105}) $	$\Q(\sqrt{21}) $	✓	$4$	$0$	$0$	$1$	$1$	$-1$	$1$		$q+q^{3}+q^{5}-q^{7}+q^{9}+q^{15}-q^{21}+\cdots$
3780.1.o.a	$3780$	$1$	3780.o	420.o	$2$	$1$	$1$	$1.886$	$\Q$	$D_{3}$	$\Q(\sqrt{-105}) $	None	✓	$2$	$0$	$-1$	$0$	$-1$	$-1$	$1$		$q-q^{2}+q^{4}-q^{5}-q^{7}-q^{8}+q^{10}+\cdots$
3780.1.o.b	$3780$	$1$	3780.o	420.o	$2$	$1$	$1$	$1.886$	$\Q$	$D_{3}$	$\Q(\sqrt{-105}) $	None	✓	$2$	$0$	$-1$	$0$	$-1$	$1$	$1$		$q-q^{2}+q^{4}-q^{5}+q^{7}-q^{8}+q^{10}+\cdots$
3780.1.o.c	$3780$	$1$	3780.o	420.o	$2$	$1$	$1$	$1.886$	$\Q$	$D_{3}$	$\Q(\sqrt{-105}) $	None	✓	$2$	$0$	$-1$	$0$	$1$	$-1$	$1$		$q-q^{2}+q^{4}+q^{5}-q^{7}-q^{8}-q^{10}+\cdots$
3780.1.o.d	$3780$	$1$	3780.o	420.o	$2$	$1$	$1$	$1.886$	$\Q$	$D_{3}$	$\Q(\sqrt{-105}) $	None	✓	$2$	$0$	$-1$	$0$	$1$	$1$	$1$		$q-q^{2}+q^{4}+q^{5}+q^{7}-q^{8}-q^{10}+\cdots$
3780.1.o.e	$3780$	$1$	3780.o	420.o	$2$	$1$	$1$	$1.886$	$\Q$	$D_{3}$	$\Q(\sqrt{-105}) $	None	✓	$2$	$0$	$1$	$0$	$-1$	$-1$	$1$		$q+q^{2}+q^{4}-q^{5}-q^{7}+q^{8}-q^{10}+\cdots$
3780.1.o.f	$3780$	$1$	3780.o	420.o	$2$	$1$	$1$	$1.886$	$\Q$	$D_{3}$	$\Q(\sqrt{-105}) $	None	✓	$2$	$0$	$1$	$0$	$-1$	$1$	$1$		$q+q^{2}+q^{4}-q^{5}+q^{7}+q^{8}-q^{10}+\cdots$
3780.1.o.g	$3780$	$1$	3780.o	420.o	$2$	$1$	$1$	$1.886$	$\Q$	$D_{3}$	$\Q(\sqrt{-105}) $	None	✓	$2$	$0$	$1$	$0$	$1$	$-1$	$1$		$q+q^{2}+q^{4}+q^{5}-q^{7}+q^{8}+q^{10}+\cdots$
3780.1.o.h	$3780$	$1$	3780.o	420.o	$2$	$1$	$1$	$1.886$	$\Q$	$D_{3}$	$\Q(\sqrt{-105}) $	None	✓	$2$	$0$	$1$	$0$	$1$	$1$	$1$		$q+q^{2}+q^{4}+q^{5}+q^{7}+q^{8}+q^{10}+\cdots$
420.3.o.a	$420$	$3$	420.o	420.o	$2$	$1$	$1$	$11.444$	$\Q$	$_{}$	$\Q(\sqrt{-105}) $	None	✓	$2$	$0$	$-2$	$-3$	$-5$	$-7$	$1$	$\mathrm{U}(1)[D_{2}]$	$q-2q^{2}-3q^{3}+4q^{4}-5q^{5}+6q^{6}+\cdots$
420.3.o.b	$420$	$3$	420.o	420.o	$2$	$1$	$1$	$11.444$	$\Q$	$_{}$	$\Q(\sqrt{-105}) $	None	✓	$2$	$0$	$-2$	$-3$	$5$	$7$	$1$	$\mathrm{U}(1)[D_{2}]$	$q-2q^{2}-3q^{3}+4q^{4}+5q^{5}+6q^{6}+\cdots$
420.3.o.c	$420$	$3$	420.o	420.o	$2$	$1$	$1$	$11.444$	$\Q$	$_{}$	$\Q(\sqrt{-105}) $	None	✓	$2$	$0$	$-2$	$3$	$-5$	$7$	$1$	$\mathrm{U}(1)[D_{2}]$	$q-2q^{2}+3q^{3}+4q^{4}-5q^{5}-6q^{6}+\cdots$
420.3.o.d	$420$	$3$	420.o	420.o	$2$	$1$	$1$	$11.444$	$\Q$	$_{}$	$\Q(\sqrt{-105}) $	None	✓	$2$	$0$	$-2$	$3$	$5$	$-7$	$1$	$\mathrm{U}(1)[D_{2}]$	$q-2q^{2}+3q^{3}+4q^{4}+5q^{5}-6q^{6}+\cdots$
420.3.o.e	$420$	$3$	420.o	420.o	$2$	$1$	$1$	$11.444$	$\Q$	$_{}$	$\Q(\sqrt{-105}) $	None	✓	$2$	$0$	$2$	$-3$	$-5$	$-7$	$1$	$\mathrm{U}(1)[D_{2}]$	$q+2q^{2}-3q^{3}+4q^{4}-5q^{5}-6q^{6}+\cdots$
420.3.o.f	$420$	$3$	420.o	420.o	$2$	$1$	$1$	$11.444$	$\Q$	$_{}$	$\Q(\sqrt{-105}) $	None	✓	$2$	$0$	$2$	$-3$	$5$	$7$	$1$	$\mathrm{U}(1)[D_{2}]$	$q+2q^{2}-3q^{3}+4q^{4}+5q^{5}-6q^{6}+\cdots$
420.3.o.g	$420$	$3$	420.o	420.o	$2$	$1$	$1$	$11.444$	$\Q$	$_{}$	$\Q(\sqrt{-105}) $	None	✓	$2$	$0$	$2$	$3$	$-5$	$7$	$1$	$\mathrm{U}(1)[D_{2}]$	$q+2q^{2}+3q^{3}+4q^{4}-5q^{5}+6q^{6}+\cdots$
420.3.o.h	$420$	$3$	420.o	420.o	$2$	$1$	$1$	$11.444$	$\Q$	$_{}$	$\Q(\sqrt{-105}) $	None	✓	$2$	$0$	$2$	$3$	$5$	$-7$	$1$	$\mathrm{U}(1)[D_{2}]$	$q+2q^{2}+3q^{3}+4q^{4}+5q^{5}+6q^{6}+\cdots$

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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.