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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 (40 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	113	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
7232.2.a.a	$7232$	$2$	7232.a	1.a	$1$	$1$	$1$	$57.748$	$\Q$	None	✓				113.2.a.a	$1$	$2$	$0$	$-2$	$-2$	$0$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{3}-2q^{5}+q^{9}-2q^{13}+4q^{15}+\cdots$
7232.2.a.b	$7232$	$2$	7232.a	1.a	$1$	$1$	$1$	$57.748$	$\Q$	None	✓				3616.2.a.a	$1$	$1$	$0$	$-2$	$0$	$0$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{3}+q^{9}+2q^{13}-2q^{17}+6q^{19}+\cdots$
7232.2.a.c	$7232$	$2$	7232.a	1.a	$1$	$1$	$1$	$57.748$	$\Q$	None	✓				226.2.a.a	$1$	$1$	$0$	$-2$	$4$	$0$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{3}+4q^{5}+q^{9}-4q^{11}+2q^{13}+\cdots$
7232.2.a.d	$7232$	$2$	7232.a	1.a	$1$	$1$	$1$	$57.748$	$\Q$	None	✓				904.2.a.a	$1$	$2$	$0$	$0$	$0$	$-4$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-4q^{7}-3q^{9}-4q^{11}-6q^{13}-2q^{17}+\cdots$
7232.2.a.e	$7232$	$2$	7232.a	1.a	$1$	$1$	$1$	$57.748$	$\Q$	None	✓				904.2.a.a	$1$	$1$	$0$	$0$	$0$	$4$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+4q^{7}-3q^{9}+4q^{11}-6q^{13}-2q^{17}+\cdots$
7232.2.a.f	$7232$	$2$	7232.a	1.a	$1$	$1$	$1$	$57.748$	$\Q$	None	✓				113.2.a.a	$1$	$1$	$0$	$2$	$-2$	$0$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+2q^{3}-2q^{5}+q^{9}-2q^{13}-4q^{15}+\cdots$
7232.2.a.g	$7232$	$2$	7232.a	1.a	$1$	$1$	$1$	$57.748$	$\Q$	None	✓				3616.2.a.a	$1$	$1$	$0$	$2$	$0$	$0$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+2q^{3}+q^{9}+2q^{13}-2q^{17}-6q^{19}+\cdots$
7232.2.a.h	$7232$	$2$	7232.a	1.a	$1$	$1$	$1$	$57.748$	$\Q$	None	✓				226.2.a.a	$1$	$0$	$0$	$2$	$4$	$0$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{3}+4q^{5}+q^{9}+4q^{11}+2q^{13}+\cdots$
7232.2.a.i	$7232$	$2$	7232.a	1.a	$1$	$2$	$2$	$57.748$	$\Q(\sqrt{3}) $	None	✓				226.2.a.c	$1$	$0$	$0$	$-2$	$-4$	$0$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta )q^{3}-2q^{5}+(1-2\beta )q^{9}+\cdots$
7232.2.a.j	$7232$	$2$	7232.a	1.a	$1$	$2$	$2$	$57.748$	$\Q(\sqrt{3}) $	None	✓				113.2.a.b	$1$	$0$	$0$	$-2$	$0$	$8$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta )q^{3}-2\beta q^{5}+4q^{7}+(1-2\beta )q^{9}+\cdots$
7232.2.a.k	$7232$	$2$	7232.a	1.a	$1$	$2$	$2$	$57.748$	$\Q(\sqrt{2}) $	None	✓				226.2.a.b	$1$	$1$	$0$	$0$	$4$	$-4$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{3}+(2-\beta )q^{5}+(-2+2\beta )q^{7}+\cdots$
7232.2.a.l	$7232$	$2$	7232.a	1.a	$1$	$2$	$2$	$57.748$	$\Q(\sqrt{2}) $	None	✓				226.2.a.b	$1$	$0$	$0$	$0$	$4$	$4$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{3}+(2+\beta )q^{5}+(2+2\beta )q^{7}-q^{9}+\cdots$
7232.2.a.m	$7232$	$2$	7232.a	1.a	$1$	$2$	$2$	$57.748$	$\Q(\sqrt{3}) $	None	✓				226.2.a.c	$1$	$1$	$0$	$2$	$-4$	$0$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+(1+\beta )q^{3}-2q^{5}+(1+2\beta )q^{9}+(2+\cdots)q^{11}+\cdots$
7232.2.a.n	$7232$	$2$	7232.a	1.a	$1$	$2$	$2$	$57.748$	$\Q(\sqrt{3}) $	None	✓				113.2.a.b	$1$	$1$	$0$	$2$	$0$	$-8$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+(1+\beta )q^{3}+2\beta q^{5}-4q^{7}+(1+2\beta )q^{9}+\cdots$
7232.2.a.o	$7232$	$2$	7232.a	1.a	$1$	$3$	$3$	$57.748$	$\Q(\zeta_{14})^+$	None	✓				113.2.a.c	$1$	$0$	$0$	$-5$	$1$	$10$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+(-2-\beta _{2})q^{3}+(-1+2\beta _{1}-2\beta _{2})q^{5}+\cdots$
7232.2.a.p	$7232$	$2$	7232.a	1.a	$1$	$3$	$3$	$57.748$	$\Q(\zeta_{18})^+$	None	✓				452.2.a.a	$1$	$1$	$0$	$-3$	$3$	$0$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1-\beta _{1})q^{3}+q^{5}+(-2\beta _{1}+\beta _{2})q^{7}+\cdots$
7232.2.a.q	$7232$	$2$	7232.a	1.a	$1$	$3$	$3$	$57.748$	3.3.321.1	None	✓				113.2.a.d	$1$	$1$	$0$	$-1$	$3$	$-6$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{3}+q^{5}+(-2-\beta _{1}-\beta _{2})q^{7}+\cdots$
7232.2.a.r	$7232$	$2$	7232.a	1.a	$1$	$3$	$3$	$57.748$	3.3.321.1	None	✓				113.2.a.d	$1$	$0$	$0$	$1$	$3$	$6$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{3}+q^{5}+(2+\beta _{1}+\beta _{2})q^{7}+(\beta _{1}+\cdots)q^{9}+\cdots$
7232.2.a.s	$7232$	$2$	7232.a	1.a	$1$	$3$	$3$	$57.748$	$\Q(\zeta_{18})^+$	None	✓				452.2.a.a	$1$	$0$	$0$	$3$	$3$	$0$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1+\beta _{1})q^{3}+q^{5}+(2\beta _{1}-\beta _{2})q^{7}+\cdots$
7232.2.a.t	$7232$	$2$	7232.a	1.a	$1$	$3$	$3$	$57.748$	$\Q(\zeta_{14})^+$	None	✓				113.2.a.c	$1$	$1$	$0$	$5$	$1$	$-10$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+(2-\beta _{1})q^{3}+(1+2\beta _{2})q^{5}+(-3+\beta _{2})q^{7}+\cdots$
7232.2.a.u	$7232$	$2$	7232.a	1.a	$1$	$4$	$4$	$57.748$	$\Q(\zeta_{20})^+$	None	✓				226.2.a.d	$1$	$1$	$0$	$-2$	$-4$	$-4$	$+$	$+$	$+$	$2$	$\mathrm{SU}(2)$	$q+(-1-\beta _{1}+\beta _{2}-\beta _{3})q^{3}+(-1+\beta _{1}+\cdots)q^{5}+\cdots$
7232.2.a.v	$7232$	$2$	7232.a	1.a	$1$	$4$	$4$	$57.748$	$\Q(\zeta_{20})^+$	None	✓				226.2.a.d	$1$	$0$	$0$	$2$	$-4$	$4$	$-$	$+$	$-$	$2$	$\mathrm{SU}(2)$	$q+(1+\beta _{1}-\beta _{2}+\beta _{3})q^{3}+(-1+\beta _{1}+\cdots)q^{5}+\cdots$
7232.2.a.w	$7232$	$2$	7232.a	1.a	$1$	$5$	$5$	$57.748$	5.5.138136.1	None	✓				904.2.a.b	$1$	$1$	$0$	$-1$	$5$	$-2$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{3}+(1+\beta _{1}-\beta _{3})q^{5}+(-\beta _{1}+\cdots)q^{7}+\cdots$
7232.2.a.x	$7232$	$2$	7232.a	1.a	$1$	$5$	$5$	$57.748$	5.5.138136.1	None	✓				904.2.a.b	$1$	$0$	$0$	$1$	$5$	$2$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{3}+(1+\beta _{1}-\beta _{3})q^{5}+(\beta _{1}+\beta _{4})q^{7}+\cdots$
7232.2.a.y	$7232$	$2$	7232.a	1.a	$1$	$6$	$6$	$57.748$	6.6.18810196.1	None	✓				904.2.a.c	$1$	$1$	$0$	$-7$	$5$	$-2$	$-$	$-$	$+$	$2$	$\mathrm{SU}(2)$	$q+(-1+\beta _{1})q^{3}+(1-\beta _{4})q^{5}+(\beta _{2}+\beta _{4}+\cdots)q^{7}+\cdots$
7232.2.a.z	$7232$	$2$	7232.a	1.a	$1$	$6$	$6$	$57.748$	6.6.18810196.1	None	✓				904.2.a.c	$1$	$0$	$0$	$7$	$5$	$2$	$+$	$-$	$-$	$2$	$\mathrm{SU}(2)$	$q+(1-\beta _{1})q^{3}+(1-\beta _{4})q^{5}+(-\beta _{2}-\beta _{4}+\cdots)q^{7}+\cdots$
7232.2.a.ba	$7232$	$2$	7232.a	1.a	$1$	$7$	$7$	$57.748$	$\mathbb{Q}[x]/(x^{7} - \cdots)$	None	✓				904.2.a.d	$1$	$1$	$0$	$-7$	$-3$	$2$	$+$	$+$	$+$	$2$	$\mathrm{SU}(2)$	$q+(-1+\beta _{4})q^{3}+\beta _{1}q^{5}+(-\beta _{2}+\beta _{3}+\cdots)q^{7}+\cdots$
7232.2.a.bb	$7232$	$2$	7232.a	1.a	$1$	$7$	$7$	$57.748$	$\mathbb{Q}[x]/(x^{7} - \cdots)$	None	✓				452.2.a.b	$1$	$1$	$0$	$-3$	$-3$	$0$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{3}-\beta _{2}q^{5}-\beta _{6}q^{7}+(1+\beta _{1}+\cdots)q^{9}+\cdots$
7232.2.a.bc	$7232$	$2$	7232.a	1.a	$1$	$7$	$7$	$57.748$	$\mathbb{Q}[x]/(x^{7} - \cdots)$	None	✓				452.2.a.b	$1$	$0$	$0$	$3$	$-3$	$0$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{3}-\beta _{2}q^{5}+\beta _{6}q^{7}+(1+\beta _{1}+\cdots)q^{9}+\cdots$
7232.2.a.bd	$7232$	$2$	7232.a	1.a	$1$	$7$	$7$	$57.748$	$\mathbb{Q}[x]/(x^{7} - \cdots)$	None	✓				904.2.a.d	$1$	$0$	$0$	$7$	$-3$	$-2$	$-$	$+$	$-$	$2$	$\mathrm{SU}(2)$	$q+(1-\beta _{4})q^{3}+\beta _{1}q^{5}+(\beta _{2}-\beta _{3}+\beta _{5}+\cdots)q^{7}+\cdots$
7232.2.a.be	$7232$	$2$	7232.a	1.a	$1$	$8$	$8$	$57.748$	8.8.$\cdots$.2	None	✓				3616.2.a.c	$2$	$1$	$0$	$0$	$6$	$0$	$-$	$-$	$+$	$2$	$\mathrm{SU}(2)$	$q-\beta _{3}q^{3}+(\beta _{1}-\beta _{5})q^{5}-\beta _{7}q^{7}-\beta _{2}q^{9}+\cdots$
7232.2.a.bf	$7232$	$2$	7232.a	1.a	$1$	$9$	$9$	$57.748$	$\mathbb{Q}[x]/(x^{9} - \cdots)$	None	✓				904.2.a.e	$1$	$1$	$0$	$-3$	$-9$	$-2$	$-$	$-$	$+$	$2^{4}$	$\mathrm{SU}(2)$	$q-\beta _{4}q^{3}+(-1-\beta _{2})q^{5}+\beta _{6}q^{7}+(1+\cdots)q^{9}+\cdots$
7232.2.a.bg	$7232$	$2$	7232.a	1.a	$1$	$9$	$9$	$57.748$	$\mathbb{Q}[x]/(x^{9} - \cdots)$	None	✓				904.2.a.e	$1$	$0$	$0$	$3$	$-9$	$2$	$+$	$-$	$-$	$2^{4}$	$\mathrm{SU}(2)$	$q+\beta _{4}q^{3}+(-1-\beta _{2})q^{5}-\beta _{6}q^{7}+(1+\cdots)q^{9}+\cdots$
7232.2.a.bh	$7232$	$2$	7232.a	1.a	$1$	$12$	$12$	$57.748$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	None	✓				3616.2.a.d	$1$	$1$	$0$	$-4$	$-2$	$6$	$+$	$+$	$+$	$2^{6}$	$\mathrm{SU}(2)$	$q-\beta _{10}q^{3}+\beta _{4}q^{5}-\beta _{9}q^{7}+(\beta _{5}-\beta _{6}+\cdots)q^{9}+\cdots$
7232.2.a.bi	$7232$	$2$	7232.a	1.a	$1$	$12$	$12$	$57.748$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	None	✓				3616.2.a.d	$1$	$1$	$0$	$4$	$-2$	$-6$	$+$	$+$	$+$	$2^{6}$	$\mathrm{SU}(2)$	$q+\beta _{10}q^{3}+\beta _{4}q^{5}+\beta _{9}q^{7}+(\beta _{5}-\beta _{6}+\cdots)q^{9}+\cdots$
7232.2.a.bj	$7232$	$2$	7232.a	1.a	$1$	$14$	$14$	$57.748$	$\mathbb{Q}[x]/(x^{14} - \cdots)$	None	✓		✓		3616.2.a.g	$2$	$1$	$0$	$0$	$-14$	$0$	$-$	$-$	$+$	$2^{9}$	$\mathrm{SU}(2)$	$q-\beta _{8}q^{3}+(-1-\beta _{3})q^{5}-\beta _{9}q^{7}+(1+\cdots)q^{9}+\cdots$
7232.2.a.bk	$7232$	$2$	7232.a	1.a	$1$	$14$	$14$	$57.748$	$\mathbb{Q}[x]/(x^{14} - \cdots)$	None	✓				3616.2.a.f	$2$	$0$	$0$	$0$	$14$	$0$	$-$	$+$	$-$	$2^{4}$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{3}+(1+\beta _{9})q^{5}-\beta _{7}q^{7}+(-\beta _{2}+\cdots)q^{9}+\cdots$
7232.2.a.bl	$7232$	$2$	7232.a	1.a	$1$	$16$	$16$	$57.748$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	None	✓				3616.2.a.h	$1$	$0$	$0$	$-6$	$4$	$2$	$+$	$-$	$-$	$2^{8}$	$\mathrm{SU}(2)$	$q-\beta _{10}q^{3}-\beta _{11}q^{5}+\beta _{5}q^{7}+(1+\beta _{10}+\cdots)q^{9}+\cdots$
7232.2.a.bm	$7232$	$2$	7232.a	1.a	$1$	$16$	$16$	$57.748$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	None	✓				3616.2.a.h	$1$	$0$	$0$	$6$	$4$	$-2$	$+$	$-$	$-$	$2^{8}$	$\mathrm{SU}(2)$	$q+\beta _{10}q^{3}-\beta _{11}q^{5}-\beta _{5}q^{7}+(1+\beta _{10}+\cdots)q^{9}+\cdots$
7232.2.a.bn	$7232$	$2$	7232.a	1.a	$1$	$18$	$18$	$57.748$	$\mathbb{Q}[x]/(x^{18} - \cdots)$	None	✓		✓		3616.2.a.j	$2$	$0$	$0$	$0$	$-10$	$0$	$-$	$+$	$-$	$2^{10}\cdot 5$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{3}+(-1-\beta _{8})q^{5}+\beta _{13}q^{7}+\cdots$

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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.