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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 (23 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*	$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$	2	3	7	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
1344.4.a.a	$1344$	$4$	1344.a	1.a	$1$	$1$	$1$	$79.299$	$\Q$	None	✓	$1$	$1$	$0$	$-3$	$-18$	$-7$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-3q^{3}-18q^{5}-7q^{7}+9q^{9}-72q^{11}+\cdots$
1344.4.a.c	$1344$	$4$	1344.a	1.a	$1$	$1$	$1$	$79.299$	$\Q$	None	✓	$1$	$1$	$0$	$-3$	$-6$	$-7$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-3q^{3}-6q^{5}-7q^{7}+9q^{9}-4q^{11}+\cdots$
1344.4.a.d	$1344$	$4$	1344.a	1.a	$1$	$1$	$1$	$79.299$	$\Q$	None	✓	$1$	$1$	$0$	$-3$	$-6$	$-7$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-3q^{3}-6q^{5}-7q^{7}+9q^{9}+6^{2}q^{11}+\cdots$
1344.4.a.h	$1344$	$4$	1344.a	1.a	$1$	$1$	$1$	$79.299$	$\Q$	None	✓	$1$	$1$	$0$	$-3$	$2$	$-7$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-3q^{3}+2q^{5}-7q^{7}+9q^{9}+12q^{11}+\cdots$
1344.4.a.j	$1344$	$4$	1344.a	1.a	$1$	$1$	$1$	$79.299$	$\Q$	None	✓	$1$	$1$	$0$	$-3$	$10$	$-7$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-3q^{3}+10q^{5}-7q^{7}+9q^{9}-12q^{11}+\cdots$
1344.4.a.l	$1344$	$4$	1344.a	1.a	$1$	$1$	$1$	$79.299$	$\Q$	None	✓	$1$	$1$	$0$	$-3$	$16$	$7$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-3q^{3}+2^{4}q^{5}+7q^{7}+9q^{9}+18q^{11}+\cdots$
1344.4.a.n	$1344$	$4$	1344.a	1.a	$1$	$1$	$1$	$79.299$	$\Q$	None	✓	$1$	$1$	$0$	$-3$	$18$	$-7$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-3q^{3}+18q^{5}-7q^{7}+9q^{9}-6^{2}q^{11}+\cdots$
1344.4.a.p	$1344$	$4$	1344.a	1.a	$1$	$1$	$1$	$79.299$	$\Q$	None	✓	$1$	$1$	$0$	$3$	$-14$	$7$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+3q^{3}-14q^{5}+7q^{7}+9q^{9}+4q^{11}+\cdots$
1344.4.a.r	$1344$	$4$	1344.a	1.a	$1$	$1$	$1$	$79.299$	$\Q$	None	✓	$1$	$1$	$0$	$3$	$-6$	$7$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+3q^{3}-6q^{5}+7q^{7}+9q^{9}+4q^{11}+\cdots$
1344.4.a.s	$1344$	$4$	1344.a	1.a	$1$	$1$	$1$	$79.299$	$\Q$	None	✓	$1$	$1$	$0$	$3$	$-4$	$-7$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+3q^{3}-4q^{5}-7q^{7}+9q^{9}+26q^{11}+\cdots$
1344.4.a.t	$1344$	$4$	1344.a	1.a	$1$	$1$	$1$	$79.299$	$\Q$	None	✓	$1$	$1$	$0$	$3$	$-2$	$7$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+3q^{3}-2q^{5}+7q^{7}+9q^{9}-8q^{11}+\cdots$
1344.4.a.v	$1344$	$4$	1344.a	1.a	$1$	$1$	$1$	$79.299$	$\Q$	None	✓	$1$	$1$	$0$	$3$	$2$	$7$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+3q^{3}+2q^{5}+7q^{7}+9q^{9}+52q^{11}+\cdots$
1344.4.a.w	$1344$	$4$	1344.a	1.a	$1$	$1$	$1$	$79.299$	$\Q$	None	✓	$1$	$1$	$0$	$3$	$4$	$-7$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+3q^{3}+4q^{5}-7q^{7}+9q^{9}-62q^{11}+\cdots$
1344.4.a.x	$1344$	$4$	1344.a	1.a	$1$	$1$	$1$	$79.299$	$\Q$	None	✓	$1$	$1$	$0$	$3$	$10$	$7$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+3q^{3}+10q^{5}+7q^{7}+9q^{9}-52q^{11}+\cdots$
1344.4.a.bc	$1344$	$4$	1344.a	1.a	$1$	$2$	$2$	$79.299$	$\Q(\sqrt{43}) $	None	✓	$1$	$1$	$0$	$-6$	$-16$	$-14$	$-$	$+$	$+$	$-$	$2$	$\mathrm{SU}(2)$	$q-3q^{3}+(-8+\beta )q^{5}-7q^{7}+9q^{9}+\cdots$
1344.4.a.bd	$1344$	$4$	1344.a	1.a	$1$	$2$	$2$	$79.299$	$\Q(\sqrt{177}) $	None	✓	$1$	$1$	$0$	$-6$	$-14$	$14$	$+$	$+$	$-$	$-$	$2$	$\mathrm{SU}(2)$	$q-3q^{3}+(-7-\beta )q^{5}+7q^{7}+9q^{9}+\cdots$
1344.4.a.be	$1344$	$4$	1344.a	1.a	$1$	$2$	$2$	$79.299$	$\Q(\sqrt{137}) $	None	✓	$1$	$1$	$0$	$-6$	$-10$	$14$	$+$	$+$	$-$	$-$	$2$	$\mathrm{SU}(2)$	$q-3q^{3}+(-5-\beta )q^{5}+7q^{7}+9q^{9}+\cdots$
1344.4.a.bg	$1344$	$4$	1344.a	1.a	$1$	$2$	$2$	$79.299$	$\Q(\sqrt{57}) $	None	✓	$1$	$1$	$0$	$-6$	$-6$	$14$	$+$	$+$	$-$	$-$	$2$	$\mathrm{SU}(2)$	$q-3q^{3}+(-3-\beta )q^{5}+7q^{7}+9q^{9}+\cdots$
1344.4.a.bj	$1344$	$4$	1344.a	1.a	$1$	$2$	$2$	$79.299$	$\Q(\sqrt{17}) $	None	✓	$1$	$1$	$0$	$-6$	$10$	$14$	$+$	$+$	$-$	$-$	$2$	$\mathrm{SU}(2)$	$q-3q^{3}+(5-\beta )q^{5}+7q^{7}+9q^{9}+(11+\cdots)q^{11}+\cdots$
1344.4.a.bk	$1344$	$4$	1344.a	1.a	$1$	$2$	$2$	$79.299$	$\Q(\sqrt{43}) $	None	✓	$1$	$1$	$0$	$6$	$-16$	$14$	$-$	$-$	$-$	$-$	$2$	$\mathrm{SU}(2)$	$q+3q^{3}+(-8+\beta )q^{5}+7q^{7}+9q^{9}+\cdots$
1344.4.a.bm	$1344$	$4$	1344.a	1.a	$1$	$2$	$2$	$79.299$	$\Q(\sqrt{137}) $	None	✓	$1$	$1$	$0$	$6$	$-10$	$-14$	$+$	$-$	$+$	$-$	$2$	$\mathrm{SU}(2)$	$q+3q^{3}+(-5-\beta )q^{5}-7q^{7}+9q^{9}+\cdots$
1344.4.a.bq	$1344$	$4$	1344.a	1.a	$1$	$2$	$2$	$79.299$	$\Q(\sqrt{337}) $	None	✓	$1$	$1$	$0$	$6$	$6$	$-14$	$+$	$-$	$+$	$-$	$2$	$\mathrm{SU}(2)$	$q+3q^{3}+(3+\beta )q^{5}-7q^{7}+9q^{9}+(-13+\cdots)q^{11}+\cdots$
1344.4.a.br	$1344$	$4$	1344.a	1.a	$1$	$2$	$2$	$79.299$	$\Q(\sqrt{17}) $	None	✓	$1$	$1$	$0$	$6$	$10$	$-14$	$+$	$-$	$+$	$-$	$2$	$\mathrm{SU}(2)$	$q+3q^{3}+(5-\beta )q^{5}-7q^{7}+9q^{9}+(-11+\cdots)q^{11}+\cdots$

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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.