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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 (24 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	13	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
4368.2.a.b	$4368$	$2$	4368.a	1.a	$1$	$1$	$1$	$34.879$	$\Q$	None	✓	$1$	$0$	$0$	$-1$	$-2$	$-1$	$+$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-2q^{5}-q^{7}+q^{9}+4q^{11}+q^{13}+\cdots$
4368.2.a.d	$4368$	$2$	4368.a	1.a	$1$	$1$	$1$	$34.879$	$\Q$	None	✓	$1$	$0$	$0$	$-1$	$-2$	$1$	$-$	$+$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-2q^{5}+q^{7}+q^{9}+4q^{11}+q^{13}+\cdots$
4368.2.a.e	$4368$	$2$	4368.a	1.a	$1$	$1$	$1$	$34.879$	$\Q$	None	✓	$1$	$0$	$0$	$-1$	$-1$	$-1$	$-$	$+$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-q^{5}-q^{7}+q^{9}-5q^{11}-q^{13}+\cdots$
4368.2.a.g	$4368$	$2$	4368.a	1.a	$1$	$1$	$1$	$34.879$	$\Q$	None	✓	$1$	$0$	$0$	$-1$	$0$	$1$	$+$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+q^{7}+q^{9}+2q^{11}-q^{13}-2q^{17}+\cdots$
4368.2.a.k	$4368$	$2$	4368.a	1.a	$1$	$1$	$1$	$34.879$	$\Q$	None	✓	$1$	$0$	$0$	$-1$	$2$	$-1$	$-$	$+$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+2q^{5}-q^{7}+q^{9}+4q^{11}-q^{13}+\cdots$
4368.2.a.m	$4368$	$2$	4368.a	1.a	$1$	$1$	$1$	$34.879$	$\Q$	None	✓	$1$	$0$	$0$	$1$	$-3$	$-1$	$+$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-3q^{5}-q^{7}+q^{9}-6q^{11}-q^{13}+\cdots$
4368.2.a.n	$4368$	$2$	4368.a	1.a	$1$	$1$	$1$	$34.879$	$\Q$	None	✓	$1$	$0$	$0$	$1$	$-3$	$-1$	$+$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-3q^{5}-q^{7}+q^{9}+5q^{11}-q^{13}+\cdots$
4368.2.a.q	$4368$	$2$	4368.a	1.a	$1$	$1$	$1$	$34.879$	$\Q$	None	✓	$1$	$0$	$0$	$1$	$-1$	$-1$	$-$	$-$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-q^{5}-q^{7}+q^{9}+2q^{11}+q^{13}+\cdots$
4368.2.a.u	$4368$	$2$	4368.a	1.a	$1$	$1$	$1$	$34.879$	$\Q$	None	✓	$1$	$0$	$0$	$1$	$0$	$1$	$-$	$-$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+q^{7}+q^{9}+2q^{11}-q^{13}+4q^{17}+\cdots$
4368.2.a.x	$4368$	$2$	4368.a	1.a	$1$	$1$	$1$	$34.879$	$\Q$	None	✓	$1$	$0$	$0$	$1$	$2$	$-1$	$+$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+2q^{5}-q^{7}+q^{9}+4q^{11}-q^{13}+\cdots$
4368.2.a.y	$4368$	$2$	4368.a	1.a	$1$	$1$	$1$	$34.879$	$\Q$	None	✓	$1$	$0$	$0$	$1$	$2$	$1$	$+$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+2q^{5}+q^{7}+q^{9}+q^{13}+2q^{15}+\cdots$
4368.2.a.z	$4368$	$2$	4368.a	1.a	$1$	$1$	$1$	$34.879$	$\Q$	None	✓	$1$	$0$	$0$	$1$	$3$	$1$	$-$	$-$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+3q^{5}+q^{7}+q^{9}-q^{11}-q^{13}+\cdots$
4368.2.a.ba	$4368$	$2$	4368.a	1.a	$1$	$1$	$1$	$34.879$	$\Q$	None	✓	$1$	$0$	$0$	$1$	$4$	$-1$	$+$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+4q^{5}-q^{7}+q^{9}-6q^{11}-q^{13}+\cdots$
4368.2.a.bc	$4368$	$2$	4368.a	1.a	$1$	$2$	$2$	$34.879$	$\Q(\sqrt{33}) $	None	✓	$1$	$0$	$0$	$-2$	$1$	$-2$	$-$	$+$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+\beta q^{5}-q^{7}+q^{9}-2q^{11}-q^{13}+\cdots$
4368.2.a.bd	$4368$	$2$	4368.a	1.a	$1$	$2$	$2$	$34.879$	$\Q(\sqrt{33}) $	None	✓	$1$	$0$	$0$	$-2$	$1$	$2$	$+$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+\beta q^{5}+q^{7}+q^{9}+(2-\beta )q^{11}+\cdots$
4368.2.a.be	$4368$	$2$	4368.a	1.a	$1$	$2$	$2$	$34.879$	$\Q(\sqrt{17}) $	None	✓	$1$	$0$	$0$	$-2$	$3$	$2$	$-$	$+$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+(1+\beta )q^{5}+q^{7}+q^{9}+(-1+\cdots)q^{11}+\cdots$
4368.2.a.bf	$4368$	$2$	4368.a	1.a	$1$	$2$	$2$	$34.879$	$\Q(\sqrt{17}) $	None	✓	$1$	$0$	$0$	$2$	$-3$	$2$	$+$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+(-1-\beta )q^{5}+q^{7}+q^{9}+(2+\cdots)q^{11}+\cdots$
4368.2.a.bg	$4368$	$2$	4368.a	1.a	$1$	$2$	$2$	$34.879$	$\Q(\sqrt{41}) $	None	✓	$1$	$0$	$0$	$2$	$-1$	$-2$	$-$	$-$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-\beta q^{5}-q^{7}+q^{9}+(-2-\beta )q^{11}+\cdots$
4368.2.a.bk	$4368$	$2$	4368.a	1.a	$1$	$2$	$2$	$34.879$	$\Q(\sqrt{17}) $	None	✓	$1$	$0$	$0$	$2$	$1$	$-2$	$+$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+\beta q^{5}-q^{7}+q^{9}+2q^{11}-q^{13}+\cdots$
4368.2.a.bl	$4368$	$2$	4368.a	1.a	$1$	$2$	$2$	$34.879$	$\Q(\sqrt{5}) $	None	✓	$1$	$0$	$0$	$2$	$2$	$-2$	$-$	$-$	$+$	$-$	$-$	$2$	$\mathrm{SU}(2)$	$q+q^{3}+(1+\beta )q^{5}-q^{7}+q^{9}+(-1+\cdots)q^{11}+\cdots$
4368.2.a.bn	$4368$	$2$	4368.a	1.a	$1$	$3$	$3$	$34.879$	3.3.1373.1	None	✓	$1$	$0$	$0$	$-3$	$1$	$3$	$-$	$+$	$-$	$-$	$-$	$2$	$\mathrm{SU}(2)$	$q-q^{3}+\beta _{2}q^{5}+q^{7}+q^{9}-\beta _{1}q^{11}+\cdots$
4368.2.a.bp	$4368$	$2$	4368.a	1.a	$1$	$3$	$3$	$34.879$	3.3.316.1	None	✓	$1$	$0$	$0$	$-3$	$3$	$-3$	$+$	$+$	$+$	$-$	$-$	$2$	$\mathrm{SU}(2)$	$q-q^{3}+(1-\beta _{1})q^{5}-q^{7}+q^{9}+(-1+\cdots)q^{11}+\cdots$
4368.2.a.bq	$4368$	$2$	4368.a	1.a	$1$	$3$	$3$	$34.879$	3.3.316.1	None	✓	$1$	$0$	$0$	$3$	$-3$	$3$	$-$	$-$	$-$	$+$	$-$	$2$	$\mathrm{SU}(2)$	$q+q^{3}+(-1-\beta _{1})q^{5}+q^{7}+q^{9}+(1+\cdots)q^{11}+\cdots$
4368.2.a.bs	$4368$	$2$	4368.a	1.a	$1$	$4$	$4$	$34.879$	4.4.138892.1	None	✓	$1$	$0$	$0$	$4$	$2$	$4$	$+$	$-$	$-$	$-$	$-$	$2$	$\mathrm{SU}(2)$	$q+q^{3}+(1+\beta _{1})q^{5}+q^{7}+q^{9}+(1-\beta _{2}+\cdots)q^{11}+\cdots$

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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.