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Note: Search results may be incomplete due to uncomputed quantities: fricke_eigenval (110727 objects)

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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	CM	Self-dual	Inner twists	Rank*	Traces				A-L signs		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*	$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$	3	7	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
3969.2.a.b	$3969$	$2$	3969.a	1.a	$1$	$1$	$1$	$31.693$	$\Q$	None	✓	$1$	$0$	$-1$	$0$	$-1$	$0$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{4}-q^{5}+3q^{8}+q^{10}-2q^{11}+\cdots$
3969.2.a.c	$3969$	$2$	3969.a	1.a	$1$	$1$	$1$	$31.693$	$\Q$	None	✓	$1$	$0$	$-1$	$0$	$1$	$0$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{4}+q^{5}+3q^{8}-q^{10}-5q^{11}+\cdots$
3969.2.a.e	$3969$	$2$	3969.a	1.a	$1$	$1$	$1$	$31.693$	$\Q$	None	✓	$1$	$0$	$1$	$0$	$1$	$0$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{4}+q^{5}-3q^{8}+q^{10}+2q^{11}+\cdots$
3969.2.a.f	$3969$	$2$	3969.a	1.a	$1$	$1$	$1$	$31.693$	$\Q$	None	✓	$1$	$0$	$1$	$0$	$1$	$0$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{4}+q^{5}-3q^{8}+q^{10}+5q^{11}+\cdots$
3969.2.a.g	$3969$	$2$	3969.a	1.a	$1$	$2$	$2$	$31.693$	$\Q(\sqrt{15}) $	None	✓	$2$	$0$	$-2$	$0$	$0$	$0$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{4}+\beta q^{5}+3q^{8}-\beta q^{10}+\cdots$
3969.2.a.h	$3969$	$2$	3969.a	1.a	$1$	$2$	$2$	$31.693$	$\Q(\sqrt{21}) $	$\Q(\sqrt{-7}) $	✓	$2$	$0$	$-1$	$0$	$0$	$0$	$+$	$-$	$-$	$1$	$N(\mathrm{U}(1))$	$q-\beta q^{2}+(3+\beta )q^{4}+(-5-2\beta )q^{8}+\cdots$
3969.2.a.j	$3969$	$2$	3969.a	1.a	$1$	$2$	$2$	$31.693$	$\Q(\sqrt{21}) $	$\Q(\sqrt{-7}) $	✓	$2$	$0$	$1$	$0$	$0$	$0$	$+$	$-$	$-$	$1$	$N(\mathrm{U}(1))$	$q+\beta q^{2}+(3+\beta )q^{4}+(5+2\beta )q^{8}+(1+\cdots)q^{11}+\cdots$
3969.2.a.k	$3969$	$2$	3969.a	1.a	$1$	$2$	$2$	$31.693$	$\Q(\sqrt{15}) $	None	✓	$2$	$0$	$2$	$0$	$0$	$0$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{4}+\beta q^{5}-3q^{8}+\beta q^{10}+\cdots$
3969.2.a.m	$3969$	$2$	3969.a	1.a	$1$	$3$	$3$	$31.693$	3.3.321.1	None	✓	$1$	$0$	$-1$	$0$	$5$	$0$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+(1+\beta _{1}+\beta _{2})q^{4}+(2+\beta _{2})q^{5}+\cdots$
3969.2.a.n	$3969$	$2$	3969.a	1.a	$1$	$3$	$3$	$31.693$	3.3.621.1	None	✓	$1$	$0$	$0$	$0$	$-3$	$0$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+(2+\beta _{1}+\beta _{2})q^{4}+(-1-\beta _{2})q^{5}+\cdots$
3969.2.a.o	$3969$	$2$	3969.a	1.a	$1$	$3$	$3$	$31.693$	3.3.621.1	None	✓	$1$	$0$	$0$	$0$	$3$	$0$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+(2+\beta _{1}+\beta _{2})q^{4}+(1+\beta _{2})q^{5}+\cdots$
3969.2.a.q	$3969$	$2$	3969.a	1.a	$1$	$3$	$3$	$31.693$	$\Q(\zeta_{18})^+$	None	✓	$1$	$0$	$3$	$0$	$-3$	$0$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1-\beta _{1})q^{2}+(1-2\beta _{1}+\beta _{2})q^{4}+(-1+\cdots)q^{5}+\cdots$
3969.2.a.t	$3969$	$2$	3969.a	1.a	$1$	$4$	$4$	$31.693$	4.4.14013.1	None	✓	$1$	$0$	$-1$	$0$	$2$	$0$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+(1+\beta _{2})q^{4}+(1-\beta _{1}-\beta _{2}+\cdots)q^{5}+\cdots$
3969.2.a.w	$3969$	$2$	3969.a	1.a	$1$	$4$	$4$	$31.693$	4.4.14013.1	None	✓	$1$	$0$	$1$	$0$	$-2$	$0$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}+(-1+\beta _{1}+\beta _{2}+\cdots)q^{5}+\cdots$
3969.2.a.ba	$3969$	$2$	3969.a	1.a	$1$	$5$	$5$	$31.693$	5.5.574857.1	None	✓	$1$	$0$	$-2$	$0$	$4$	$0$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+(1+\beta _{2})q^{4}+(1+\beta _{4})q^{5}+\cdots$
3969.2.a.bc	$3969$	$2$	3969.a	1.a	$1$	$5$	$5$	$31.693$	5.5.574857.1	None	✓	$1$	$0$	$2$	$0$	$4$	$0$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}+(1+\beta _{4})q^{5}+\cdots$
3969.2.a.be	$3969$	$2$	3969.a	1.a	$1$	$6$	$6$	$31.693$	6.6.59351616.1	None	✓	$2$	$0$	$2$	$0$	$0$	$0$	$+$	$-$	$-$	$3$	$\mathrm{SU}(2)$	$q+\beta _{2}q^{2}+(1+\beta _{2}+\beta _{4})q^{4}+\beta _{1}q^{5}+\cdots$
3969.2.a.bg	$3969$	$2$	3969.a	1.a	$1$	$8$	$8$	$31.693$	8.8.$\cdots$.1	None	✓	$2$	$0$	$0$	$0$	$0$	$0$	$-$	$+$	$-$	$3$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}+(\beta _{1}-\beta _{3})q^{5}+\cdots$
3969.2.a.bi	$3969$	$2$	3969.a	1.a	$1$	$12$	$12$	$31.693$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	None	✓	$2$	$0$	$4$	$0$	$0$	$0$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{2}q^{2}+(1+\beta _{8})q^{4}-\beta _{10}q^{5}+(1+\cdots)q^{8}+\cdots$
3969.2.a.bj	$3969$	$2$	3969.a	1.a	$1$	$16$	$16$	$31.693$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	None	✓	$4$	$0$	$0$	$0$	$0$	$0$	$-$	$+$	$-$	$2^{6}$	$\mathrm{SU}(2)$	$q-\beta _{5}q^{2}+(2-\beta _{12})q^{4}+(\beta _{3}-\beta _{9})q^{5}+\cdots$

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Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
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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.