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Level	Weight	Analytic conductor	Analytic rank	Dim.

Bad $p$	Char.	Primitive character	Character order	Is maximal/largest

Coefficient field	Self-twists	CM/RM discriminant	Inner twist count	Is self-dual

Coefficient ring index	Coefficient ring gens.	Is twist minimal	Projective image

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Results (32 matches)

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Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Twist minimal	Largest	Maximal	Minimal twist	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	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$	2	3	11	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
7128.2.a.a	$7128$	$2$	7128.a	1.a	$1$	$1$	$1$	$56.917$	$\Q$	None	✓				792.2.q.c	$1$	$1$	$0$	$0$	$-3$	$-4$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-3q^{5}-4q^{7}-q^{11}+6q^{13}-4q^{17}+\cdots$
7128.2.a.b	$7128$	$2$	7128.a	1.a	$1$	$1$	$1$	$56.917$	$\Q$	None	✓	✓			7128.2.a.b	$1$	$1$	$0$	$0$	$-3$	$-4$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-3q^{5}-4q^{7}+q^{11}+3q^{13}+q^{17}+\cdots$
7128.2.a.c	$7128$	$2$	7128.a	1.a	$1$	$1$	$1$	$56.917$	$\Q$	None	✓				792.2.q.b	$1$	$1$	$0$	$0$	$-1$	$-2$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{5}-2q^{7}+q^{11}+6q^{17}-2q^{19}+\cdots$
7128.2.a.d	$7128$	$2$	7128.a	1.a	$1$	$1$	$1$	$56.917$	$\Q$	None	✓				792.2.q.a	$1$	$1$	$0$	$0$	$-1$	$0$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{5}+q^{11}+2q^{13}-6q^{17}+6q^{19}+\cdots$
7128.2.a.e	$7128$	$2$	7128.a	1.a	$1$	$1$	$1$	$56.917$	$\Q$	None	✓				792.2.q.b	$1$	$0$	$0$	$0$	$1$	$-2$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{5}-2q^{7}-q^{11}-6q^{17}-2q^{19}+\cdots$
7128.2.a.f	$7128$	$2$	7128.a	1.a	$1$	$1$	$1$	$56.917$	$\Q$	None	✓				792.2.q.a	$1$	$0$	$0$	$0$	$1$	$0$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{5}-q^{11}+2q^{13}+6q^{17}+6q^{19}+\cdots$
7128.2.a.g	$7128$	$2$	7128.a	1.a	$1$	$1$	$1$	$56.917$	$\Q$	None	✓	✓			7128.2.a.b	$1$	$1$	$0$	$0$	$3$	$-4$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+3q^{5}-4q^{7}-q^{11}+3q^{13}-q^{17}+\cdots$
7128.2.a.h	$7128$	$2$	7128.a	1.a	$1$	$1$	$1$	$56.917$	$\Q$	None	✓				792.2.q.c	$1$	$0$	$0$	$0$	$3$	$-4$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+3q^{5}-4q^{7}+q^{11}+6q^{13}+4q^{17}+\cdots$
7128.2.a.i	$7128$	$2$	7128.a	1.a	$1$	$2$	$2$	$56.917$	$\Q(\sqrt{3}) $	None	✓	✓			7128.2.a.i	$1$	$0$	$0$	$0$	$-6$	$-2$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-3q^{5}+(-1+\beta )q^{7}-q^{11}+3q^{13}+\cdots$
7128.2.a.j	$7128$	$2$	7128.a	1.a	$1$	$2$	$2$	$56.917$	$\Q(\sqrt{21}) $	None	✓	✓			7128.2.a.j	$1$	$1$	$0$	$0$	$-3$	$2$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1-\beta )q^{5}+q^{7}-q^{11}+(-1-\beta )q^{13}+\cdots$
7128.2.a.k	$7128$	$2$	7128.a	1.a	$1$	$2$	$2$	$56.917$	$\Q(\sqrt{3}) $	None	✓				792.2.q.d	$1$	$0$	$0$	$0$	$0$	$2$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{5}+(1+\beta )q^{7}-q^{11}+(3-\beta )q^{13}+\cdots$
7128.2.a.l	$7128$	$2$	7128.a	1.a	$1$	$2$	$2$	$56.917$	$\Q(\sqrt{3}) $	None	✓				792.2.q.d	$1$	$1$	$0$	$0$	$0$	$2$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{5}+(1-\beta )q^{7}+q^{11}+(3+\beta )q^{13}+\cdots$
7128.2.a.m	$7128$	$2$	7128.a	1.a	$1$	$2$	$2$	$56.917$	$\Q(\sqrt{21}) $	None	✓	✓			7128.2.a.j	$1$	$1$	$0$	$0$	$3$	$2$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+(1+\beta )q^{5}+q^{7}+q^{11}+(-1-\beta )q^{13}+\cdots$
7128.2.a.n	$7128$	$2$	7128.a	1.a	$1$	$2$	$2$	$56.917$	$\Q(\sqrt{3}) $	None	✓	✓			7128.2.a.i	$1$	$0$	$0$	$0$	$6$	$-2$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+3q^{5}+(-1-\beta )q^{7}+q^{11}+3q^{13}+\cdots$
7128.2.a.o	$7128$	$2$	7128.a	1.a	$1$	$3$	$3$	$56.917$	3.3.321.1	None	✓				792.2.q.e	$1$	$1$	$0$	$0$	$-1$	$-1$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta _{1}-\beta _{2})q^{5}-\beta _{1}q^{7}+q^{11}+\cdots$
7128.2.a.p	$7128$	$2$	7128.a	1.a	$1$	$3$	$3$	$56.917$	3.3.321.1	None	✓				792.2.q.e	$1$	$0$	$0$	$0$	$1$	$-1$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1-\beta _{1}+\beta _{2})q^{5}-\beta _{1}q^{7}-q^{11}+\cdots$
7128.2.a.q	$7128$	$2$	7128.a	1.a	$1$	$4$	$4$	$56.917$	4.4.25857.1	None	✓	✓			7128.2.a.q	$1$	$1$	$0$	$0$	$-1$	$-2$	$+$	$+$	$+$	$+$	$2$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{5}+(-\beta _{1}-\beta _{2})q^{7}-q^{11}+(-1+\cdots)q^{13}+\cdots$
7128.2.a.r	$7128$	$2$	7128.a	1.a	$1$	$4$	$4$	$56.917$	4.4.149949.1	None	✓	✓			7128.2.a.r	$1$	$0$	$0$	$0$	$0$	$2$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{2}q^{5}+\beta _{1}q^{7}-q^{11}+(2+\beta _{2})q^{13}+\cdots$
7128.2.a.s	$7128$	$2$	7128.a	1.a	$1$	$4$	$4$	$56.917$	4.4.149949.1	None	✓	✓			7128.2.a.r	$1$	$0$	$0$	$0$	$0$	$2$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta _{2}q^{5}+\beta _{1}q^{7}+q^{11}+(2+\beta _{2})q^{13}+\cdots$
7128.2.a.t	$7128$	$2$	7128.a	1.a	$1$	$4$	$4$	$56.917$	4.4.25857.1	None	✓	✓	✓		7128.2.a.q	$1$	$1$	$0$	$0$	$1$	$-2$	$-$	$+$	$-$	$+$	$2$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{5}+(-\beta _{1}-\beta _{2})q^{7}+q^{11}+(-1+\cdots)q^{13}+\cdots$
7128.2.a.u	$7128$	$2$	7128.a	1.a	$1$	$5$	$5$	$56.917$	5.5.13620681.1	None	✓	✓			7128.2.a.u	$1$	$0$	$0$	$0$	$-1$	$2$	$+$	$+$	$-$	$-$	$2$	$\mathrm{SU}(2)$	$q+\beta _{3}q^{5}+\beta _{2}q^{7}+q^{11}+\beta _{4}q^{13}+\cdots$
7128.2.a.v	$7128$	$2$	7128.a	1.a	$1$	$5$	$5$	$56.917$	5.5.13620681.1	None	✓	✓			7128.2.a.u	$1$	$0$	$0$	$0$	$1$	$2$	$-$	$+$	$+$	$-$	$2$	$\mathrm{SU}(2)$	$q-\beta _{3}q^{5}+\beta _{2}q^{7}-q^{11}+\beta _{4}q^{13}+\cdots$
7128.2.a.w	$7128$	$2$	7128.a	1.a	$1$	$6$	$6$	$56.917$	6.6.30796308.1	None	✓				792.2.q.f	$1$	$1$	$0$	$0$	$-4$	$5$	$-$	$-$	$+$	$+$	$2$	$\mathrm{SU}(2)$	$q+(-1+\beta _{1})q^{5}+(1-\beta _{4})q^{7}-q^{11}+\cdots$
7128.2.a.x	$7128$	$2$	7128.a	1.a	$1$	$6$	$6$	$56.917$	6.6.457285824.1	None	✓	✓			7128.2.a.x	$1$	$0$	$0$	$0$	$-4$	$6$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta _{1})q^{5}+(1+\beta _{3})q^{7}+q^{11}+\cdots$
7128.2.a.y	$7128$	$2$	7128.a	1.a	$1$	$6$	$6$	$56.917$	6.6.102147264.1	None	✓	✓			7128.2.a.y	$1$	$1$	$0$	$0$	$-2$	$-4$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{3}q^{5}+(-1+\beta _{1})q^{7}+q^{11}+(-1+\cdots)q^{13}+\cdots$
7128.2.a.z	$7128$	$2$	7128.a	1.a	$1$	$6$	$6$	$56.917$	6.6.102147264.1	None	✓	✓			7128.2.a.y	$1$	$1$	$0$	$0$	$2$	$-4$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta _{3}q^{5}+(-1+\beta _{1})q^{7}-q^{11}+(-1+\cdots)q^{13}+\cdots$
7128.2.a.ba	$7128$	$2$	7128.a	1.a	$1$	$6$	$6$	$56.917$	6.6.30796308.1	None	✓		✓		792.2.q.f	$1$	$0$	$0$	$0$	$4$	$5$	$+$	$+$	$-$	$-$	$2$	$\mathrm{SU}(2)$	$q+(1-\beta _{1})q^{5}+(1-\beta _{4})q^{7}+q^{11}+(-\beta _{1}+\cdots)q^{13}+\cdots$
7128.2.a.bb	$7128$	$2$	7128.a	1.a	$1$	$6$	$6$	$56.917$	6.6.457285824.1	None	✓	✓	✓		7128.2.a.x	$1$	$0$	$0$	$0$	$4$	$6$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1-\beta _{1})q^{5}+(1+\beta _{3})q^{7}-q^{11}+(-\beta _{1}+\cdots)q^{13}+\cdots$
7128.2.a.bc	$7128$	$2$	7128.a	1.a	$1$	$8$	$8$	$56.917$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	None	✓		✓		792.2.q.g	$1$	$1$	$0$	$0$	$-3$	$-5$	$+$	$-$	$-$	$+$	$2\cdot 3^{2}$	$\mathrm{SU}(2)$	$q+\beta _{2}q^{5}+(-1-\beta _{1})q^{7}+q^{11}+(-1+\cdots)q^{13}+\cdots$
7128.2.a.bd	$7128$	$2$	7128.a	1.a	$1$	$8$	$8$	$56.917$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	None	✓		✓		792.2.q.h	$1$	$0$	$0$	$0$	$-1$	$5$	$-$	$-$	$-$	$-$	$3$	$\mathrm{SU}(2)$	$q+\beta _{3}q^{5}+(1+\beta _{5})q^{7}+q^{11}+\beta _{2}q^{13}+\cdots$
7128.2.a.be	$7128$	$2$	7128.a	1.a	$1$	$8$	$8$	$56.917$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	None	✓		✓		792.2.q.h	$1$	$1$	$0$	$0$	$1$	$5$	$+$	$+$	$+$	$+$	$3$	$\mathrm{SU}(2)$	$q-\beta _{3}q^{5}+(1+\beta _{5})q^{7}-q^{11}+\beta _{2}q^{13}+\cdots$
7128.2.a.bf	$7128$	$2$	7128.a	1.a	$1$	$8$	$8$	$56.917$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	None	✓		✓		792.2.q.g	$1$	$0$	$0$	$0$	$3$	$-5$	$-$	$+$	$+$	$-$	$2\cdot 3^{2}$	$\mathrm{SU}(2)$	$q-\beta _{2}q^{5}+(-1-\beta _{1})q^{7}-q^{11}+(-1+\cdots)q^{13}+\cdots$

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