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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	11	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
1089.6.a.a	$1089$	$6$	1089.a	1.a	$1$	$1$	$1$	$174.658$	$\Q$	None	✓	$1$	$0$	$-9$	$0$	$-24$	$-72$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-9q^{2}+7^{2}q^{4}-24q^{5}-72q^{7}-153q^{8}+\cdots$
1089.6.a.e	$1089$	$6$	1089.a	1.a	$1$	$1$	$1$	$174.658$	$\Q$	$\Q(\sqrt{-11}) $	✓	$2$	$0$	$0$	$0$	$-57$	$0$	$-$	$+$	$-$	$1$	$N(\mathrm{U}(1))$	$q-2^{5}q^{4}-57q^{5}+2^{10}q^{16}+1824q^{20}+\cdots$
1089.6.a.f	$1089$	$6$	1089.a	1.a	$1$	$1$	$1$	$174.658$	$\Q$	$\Q(\sqrt{-3}) $	✓	$2$	$0$	$0$	$0$	$0$	$-25$	$+$	$-$	$-$	$1$	$N(\mathrm{U}(1))$	$q-2^{5}q^{4}-5^{2}q^{7}+1202q^{13}+2^{10}q^{16}+\cdots$
1089.6.a.g	$1089$	$6$	1089.a	1.a	$1$	$1$	$1$	$174.658$	$\Q$	$\Q(\sqrt{-3}) $	✓	$2$	$0$	$0$	$0$	$0$	$25$	$+$	$-$	$-$	$1$	$N(\mathrm{U}(1))$	$q-2^{5}q^{4}+5^{2}q^{7}-1202q^{13}+2^{10}q^{16}+\cdots$
1089.6.a.i	$1089$	$6$	1089.a	1.a	$1$	$1$	$1$	$174.658$	$\Q$	None	✓	$1$	$0$	$9$	$0$	$-24$	$72$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+9q^{2}+7^{2}q^{4}-24q^{5}+72q^{7}+153q^{8}+\cdots$
1089.6.a.l	$1089$	$6$	1089.a	1.a	$1$	$2$	$2$	$174.658$	$\Q(\sqrt{5}) $	None	✓	$2$	$0$	$0$	$0$	$196$	$0$	$-$	$+$	$-$	$2^{2}$	$\mathrm{SU}(2)$	$q-\beta q^{2}-12q^{4}+98q^{5}+53\beta q^{7}+\cdots$
1089.6.a.m	$1089$	$6$	1089.a	1.a	$1$	$2$	$2$	$174.658$	$\Q(\sqrt{38}) $	None	✓	$2$	$0$	$0$	$0$	$38$	$0$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{2}+6q^{4}+19q^{5}+8\beta q^{7}-26\beta q^{8}+\cdots$
1089.6.a.n	$1089$	$6$	1089.a	1.a	$1$	$2$	$2$	$174.658$	$\Q(\sqrt{3}) $	None	✓	$2$	$0$	$0$	$0$	$-48$	$0$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+4\beta q^{2}+2^{4}q^{4}-24q^{5}-\beta q^{7}-2^{6}\beta q^{8}+\cdots$
1089.6.a.w	$1089$	$6$	1089.a	1.a	$1$	$5$	$5$	$174.658$	$\mathbb{Q}[x]/(x^{5} - \cdots)$	None	✓	$1$	$0$	$-4$	$0$	$100$	$18$	$+$	$-$	$-$	$2^{5}\cdot 3^{2}$	$\mathrm{SU}(2)$	$q+(-1+\beta _{1})q^{2}+(21-3\beta _{1}+\beta _{4})q^{4}+\cdots$
1089.6.a.x	$1089$	$6$	1089.a	1.a	$1$	$5$	$5$	$174.658$	$\mathbb{Q}[x]/(x^{5} - \cdots)$	None	✓	$1$	$0$	$4$	$0$	$-100$	$18$	$+$	$-$	$-$	$2^{5}\cdot 3^{2}$	$\mathrm{SU}(2)$	$q+(1-\beta _{1})q^{2}+(21-3\beta _{1}+\beta _{4})q^{4}+\cdots$
1089.6.a.z	$1089$	$6$	1089.a	1.a	$1$	$6$	$6$	$174.658$	6.6.$\cdots$.1	None	✓	$2$	$0$	$0$	$0$	$50$	$0$	$-$	$+$	$-$	$2^{4}$	$\mathrm{SU}(2)$	$q+(-\beta _{1}+3\beta _{2})q^{2}+(14+\beta _{3}-7\beta _{4}+\cdots)q^{4}+\cdots$
1089.6.a.ba	$1089$	$6$	1089.a	1.a	$1$	$6$	$6$	$174.658$	$\mathbb{Q}[x]/(x^{6} - \cdots)$	None	✓	$2$	$0$	$0$	$0$	$48$	$0$	$-$	$+$	$-$	$2^{6}\cdot 3$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+(28+\beta _{2})q^{4}+(8+\beta _{2}+\beta _{4}+\cdots)q^{5}+\cdots$
1089.6.a.bd	$1089$	$6$	1089.a	1.a	$1$	$8$	$8$	$174.658$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	None	✓	$2$	$0$	$0$	$0$	$256$	$0$	$-$	$+$	$-$	$2^{4}\cdot 3\cdot 11$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+(19-2\beta _{2}+\beta _{6})q^{4}+(33+\cdots)q^{5}+\cdots$
1089.6.a.be	$1089$	$6$	1089.a	1.a	$1$	$8$	$8$	$174.658$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	None	✓	$2$	$0$	$0$	$0$	$0$	$-106$	$+$	$-$	$-$	$2^{4}\cdot 3^{4}$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+(5^{2}+\beta _{2})q^{4}+(-3\beta _{1}-\beta _{3}+\cdots)q^{5}+\cdots$
1089.6.a.bf	$1089$	$6$	1089.a	1.a	$1$	$8$	$8$	$174.658$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	None	✓	$2$	$0$	$0$	$0$	$0$	$106$	$+$	$-$	$-$	$2^{4}\cdot 3^{4}$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+(5^{2}+\beta _{2})q^{4}+(3\beta _{1}+\beta _{3}+\cdots)q^{5}+\cdots$
1089.6.a.bg	$1089$	$6$	1089.a	1.a	$1$	$8$	$8$	$174.658$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	None	✓	$1$	$0$	$8$	$0$	$-70$	$-292$	$-$	$+$	$-$	$2^{2}\cdot 11^{2}$	$\mathrm{SU}(2)$	$q+(1-\beta _{1})q^{2}+(11-\beta _{1}+\beta _{2})q^{4}+(-9+\cdots)q^{5}+\cdots$
1089.6.a.bh	$1089$	$6$	1089.a	1.a	$1$	$10$	$10$	$174.658$	$\mathbb{Q}[x]/(x^{10} - \cdots)$	None	✓	$1$	$0$	$-9$	$0$	$-11$	$470$	$-$	$+$	$-$	$2^{2}\cdot 11^{4}$	$\mathrm{SU}(2)$	$q+(-1+\beta _{1})q^{2}+(19-\beta _{1}+\beta _{2})q^{4}+\cdots$
1089.6.a.bj	$1089$	$6$	1089.a	1.a	$1$	$10$	$10$	$174.658$	$\mathbb{Q}[x]/(x^{10} - \cdots)$	None	✓	$2$	$0$	$0$	$0$	$-198$	$0$	$-$	$+$	$-$	$2^{6}\cdot 11^{4}$	$\mathrm{SU}(2)$	$q+\beta _{6}q^{2}+(18+\beta _{1})q^{4}+(-20-\beta _{1}+\cdots)q^{5}+\cdots$
1089.6.a.bk	$1089$	$6$	1089.a	1.a	$1$	$10$	$10$	$174.658$	$\mathbb{Q}[x]/(x^{10} - \cdots)$	None	✓	$1$	$0$	$7$	$0$	$33$	$78$	$-$	$+$	$-$	$2^{2}\cdot 11^{4}$	$\mathrm{SU}(2)$	$q+(1-\beta _{1})q^{2}+(15-\beta _{1}+\beta _{2}-\beta _{3}+\cdots)q^{4}+\cdots$
1089.6.a.bo	$1089$	$6$	1089.a	1.a	$1$	$20$	$20$	$174.658$	$\mathbb{Q}[x]/(x^{20} - \cdots)$	None	✓	$2$	$0$	$0$	$0$	$0$	$472$	$+$	$-$	$-$	$2^{8}\cdot 3^{8}\cdot 5^{2}\cdot 11^{9}\cdot 31^{2}$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+(15+\beta _{2})q^{4}+(\beta _{1}+\beta _{8})q^{5}+\cdots$

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Elliptic 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.