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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 (43 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				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*	$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
3234.2.a.a	$3234$	$2$	3234.a	1.a	$1$	$1$	$1$	$25.824$	$\Q$	None	✓				462.2.i.a	$1$	$0$	$-1$	$-1$	$-3$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}-3q^{5}+q^{6}-q^{8}+\cdots$
3234.2.a.b	$3234$	$2$	3234.a	1.a	$1$	$1$	$1$	$25.824$	$\Q$	None	✓				462.2.a.d	$1$	$0$	$-1$	$-1$	$0$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}+q^{6}-q^{8}+q^{9}+\cdots$
3234.2.a.c	$3234$	$2$	3234.a	1.a	$1$	$1$	$1$	$25.824$	$\Q$	None	✓				462.2.i.d	$1$	$1$	$-1$	$-1$	$0$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}+q^{6}-q^{8}+q^{9}+\cdots$
3234.2.a.d	$3234$	$2$	3234.a	1.a	$1$	$1$	$1$	$25.824$	$\Q$	None	✓				66.2.a.a	$1$	$0$	$-1$	$-1$	$0$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}+q^{6}-q^{8}+q^{9}+\cdots$
3234.2.a.e	$3234$	$2$	3234.a	1.a	$1$	$1$	$1$	$25.824$	$\Q$	None	✓	✓			3234.2.a.e	$1$	$1$	$-1$	$-1$	$0$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}+q^{6}-q^{8}+q^{9}+\cdots$
3234.2.a.f	$3234$	$2$	3234.a	1.a	$1$	$1$	$1$	$25.824$	$\Q$	None	✓				462.2.i.b	$1$	$1$	$-1$	$-1$	$0$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}+q^{6}-q^{8}+q^{9}+\cdots$
3234.2.a.g	$3234$	$2$	3234.a	1.a	$1$	$1$	$1$	$25.824$	$\Q$	None	✓				462.2.i.c	$1$	$0$	$-1$	$-1$	$3$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}+3q^{5}+q^{6}-q^{8}+\cdots$
3234.2.a.h	$3234$	$2$	3234.a	1.a	$1$	$1$	$1$	$25.824$	$\Q$	None	✓				462.2.i.c	$1$	$0$	$-1$	$1$	$-3$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}-3q^{5}-q^{6}-q^{8}+\cdots$
3234.2.a.i	$3234$	$2$	3234.a	1.a	$1$	$1$	$1$	$25.824$	$\Q$	None	✓				462.2.a.c	$1$	$0$	$-1$	$1$	$-2$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}-2q^{5}-q^{6}-q^{8}+\cdots$
3234.2.a.j	$3234$	$2$	3234.a	1.a	$1$	$1$	$1$	$25.824$	$\Q$	None	✓				462.2.i.d	$1$	$1$	$-1$	$1$	$0$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}-q^{6}-q^{8}+q^{9}+\cdots$
3234.2.a.k	$3234$	$2$	3234.a	1.a	$1$	$1$	$1$	$25.824$	$\Q$	None	✓				462.2.a.b	$1$	$1$	$-1$	$1$	$0$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}-q^{6}-q^{8}+q^{9}+\cdots$
3234.2.a.l	$3234$	$2$	3234.a	1.a	$1$	$1$	$1$	$25.824$	$\Q$	None	✓				462.2.i.b	$1$	$1$	$-1$	$1$	$0$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}-q^{6}-q^{8}+q^{9}+\cdots$
3234.2.a.m	$3234$	$2$	3234.a	1.a	$1$	$1$	$1$	$25.824$	$\Q$	None	✓	✓			3234.2.a.e	$1$	$0$	$-1$	$1$	$0$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}-q^{6}-q^{8}+q^{9}+\cdots$
3234.2.a.n	$3234$	$2$	3234.a	1.a	$1$	$1$	$1$	$25.824$	$\Q$	None	✓				462.2.a.a	$1$	$0$	$-1$	$1$	$2$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}+2q^{5}-q^{6}-q^{8}+\cdots$
3234.2.a.o	$3234$	$2$	3234.a	1.a	$1$	$1$	$1$	$25.824$	$\Q$	None	✓				462.2.i.a	$1$	$0$	$-1$	$1$	$3$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}+3q^{5}-q^{6}-q^{8}+\cdots$
3234.2.a.p	$3234$	$2$	3234.a	1.a	$1$	$1$	$1$	$25.824$	$\Q$	None	✓				462.2.a.g	$1$	$0$	$1$	$-1$	$-2$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}-2q^{5}-q^{6}+q^{8}+\cdots$
3234.2.a.q	$3234$	$2$	3234.a	1.a	$1$	$1$	$1$	$25.824$	$\Q$	None	✓				462.2.a.f	$1$	$1$	$1$	$-1$	$0$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}-q^{6}+q^{8}+q^{9}+\cdots$
3234.2.a.r	$3234$	$2$	3234.a	1.a	$1$	$1$	$1$	$25.824$	$\Q$	None	✓	✓			3234.2.a.r	$1$	$0$	$1$	$-1$	$2$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}+2q^{5}-q^{6}+q^{8}+\cdots$
3234.2.a.s	$3234$	$2$	3234.a	1.a	$1$	$1$	$1$	$25.824$	$\Q$	None	✓				66.2.a.c	$1$	$0$	$1$	$-1$	$4$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}+4q^{5}-q^{6}+q^{8}+\cdots$
3234.2.a.t	$3234$	$2$	3234.a	1.a	$1$	$1$	$1$	$25.824$	$\Q$	None	✓				66.2.a.b	$1$	$0$	$1$	$1$	$-2$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}-2q^{5}+q^{6}+q^{8}+\cdots$
3234.2.a.u	$3234$	$2$	3234.a	1.a	$1$	$1$	$1$	$25.824$	$\Q$	None	✓	✓	✓	✓	3234.2.a.r	$1$	$1$	$1$	$1$	$-2$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}-2q^{5}+q^{6}+q^{8}+\cdots$
3234.2.a.v	$3234$	$2$	3234.a	1.a	$1$	$1$	$1$	$25.824$	$\Q$	None	✓				462.2.a.e	$1$	$0$	$1$	$1$	$4$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}+4q^{5}+q^{6}+q^{8}+\cdots$
3234.2.a.w	$3234$	$2$	3234.a	1.a	$1$	$2$	$2$	$25.824$	$\Q(\sqrt{7}) $	None	✓				462.2.i.e	$1$	$0$	$-2$	$-2$	$0$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}+\beta q^{5}+q^{6}-q^{8}+\cdots$
3234.2.a.x	$3234$	$2$	3234.a	1.a	$1$	$2$	$2$	$25.824$	$\Q(\sqrt{3}) $	None	✓		✓		462.2.a.h	$1$	$1$	$-2$	$-2$	$0$	$0$	$+$	$2$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}+\beta q^{5}+q^{6}-q^{8}+\cdots$
3234.2.a.y	$3234$	$2$	3234.a	1.a	$1$	$2$	$2$	$25.824$	$\Q(\sqrt{2}) $	None	✓	✓			3234.2.a.y	$1$	$0$	$-2$	$-2$	$0$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}+q^{6}-q^{8}+q^{9}+\cdots$
3234.2.a.z	$3234$	$2$	3234.a	1.a	$1$	$2$	$2$	$25.824$	$\Q(\sqrt{2}) $	None	✓	✓	✓		3234.2.a.y	$1$	$1$	$-2$	$2$	$0$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}-q^{6}-q^{8}+q^{9}+\cdots$
3234.2.a.ba	$3234$	$2$	3234.a	1.a	$1$	$2$	$2$	$25.824$	$\Q(\sqrt{7}) $	None	✓		✓		462.2.i.e	$1$	$0$	$-2$	$2$	$0$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}+\beta q^{5}-q^{6}-q^{8}+\cdots$
3234.2.a.bb	$3234$	$2$	3234.a	1.a	$1$	$2$	$2$	$25.824$	$\Q(\sqrt{5}) $	None	✓	✓	✓		3234.2.a.bb	$1$	$1$	$2$	$-2$	$-2$	$0$	$+$	$2$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}+(-1-\beta )q^{5}-q^{6}+\cdots$
3234.2.a.bc	$3234$	$2$	3234.a	1.a	$1$	$2$	$2$	$25.824$	$\Q(\sqrt{2}) $	None	✓	✓			3234.2.a.bc	$1$	$0$	$2$	$-2$	$4$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}+2q^{5}-q^{6}+q^{8}+\cdots$
3234.2.a.bd	$3234$	$2$	3234.a	1.a	$1$	$2$	$2$	$25.824$	$\Q(\sqrt{2}) $	None	✓	✓	✓	✓	3234.2.a.bc	$1$	$1$	$2$	$2$	$-4$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}-2q^{5}+q^{6}+q^{8}+\cdots$
3234.2.a.be	$3234$	$2$	3234.a	1.a	$1$	$2$	$2$	$25.824$	$\Q(\sqrt{5}) $	None	✓	✓			3234.2.a.bb	$1$	$0$	$2$	$2$	$2$	$0$	$-$	$2$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}+(1+\beta )q^{5}+q^{6}+\cdots$
3234.2.a.bf	$3234$	$2$	3234.a	1.a	$1$	$3$	$3$	$25.824$	3.3.2700.1	None	✓		✓		462.2.i.g	$1$	$0$	$3$	$-3$	$0$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}+\beta _{1}q^{5}-q^{6}+q^{8}+\cdots$
3234.2.a.bg	$3234$	$2$	3234.a	1.a	$1$	$3$	$3$	$25.824$	3.3.621.1	None	✓		✓		462.2.i.f	$1$	$0$	$3$	$-3$	$0$	$0$	$-$	$2$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}-\beta _{2}q^{5}-q^{6}+q^{8}+\cdots$
3234.2.a.bh	$3234$	$2$	3234.a	1.a	$1$	$3$	$3$	$25.824$	3.3.2700.1	None	✓		✓		462.2.i.g	$1$	$0$	$3$	$3$	$0$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}-\beta _{1}q^{5}+q^{6}+q^{8}+\cdots$
3234.2.a.bi	$3234$	$2$	3234.a	1.a	$1$	$3$	$3$	$25.824$	3.3.621.1	None	✓				462.2.i.f	$1$	$0$	$3$	$3$	$0$	$0$	$-$	$2$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}+\beta _{2}q^{5}+q^{6}+q^{8}+\cdots$
3234.2.a.bj	$3234$	$2$	3234.a	1.a	$1$	$4$	$4$	$25.824$	4.4.14336.1	None	✓	✓	✓		3234.2.a.bj	$1$	$1$	$-4$	$-4$	$0$	$0$	$+$	$2$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}+\beta _{2}q^{5}+q^{6}-q^{8}+\cdots$
3234.2.a.bk	$3234$	$2$	3234.a	1.a	$1$	$4$	$4$	$25.824$	4.4.14336.1	None	✓	✓	✓		3234.2.a.bj	$1$	$0$	$-4$	$4$	$0$	$0$	$-$	$2$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}+\beta _{2}q^{5}-q^{6}-q^{8}+\cdots$
3234.2.a.bl	$3234$	$2$	3234.a	1.a	$1$	$4$	$4$	$25.824$	4.4.4352.1	None	✓	✓	✓	✓	3234.2.a.bl	$1$	$1$	$4$	$-4$	$-4$	$0$	$+$	$2$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}+(-1-\beta _{3})q^{5}-q^{6}+\cdots$
3234.2.a.bm	$3234$	$2$	3234.a	1.a	$1$	$4$	$4$	$25.824$	4.4.4352.1	None	✓	✓	✓		3234.2.a.bl	$1$	$0$	$4$	$4$	$4$	$0$	$-$	$2$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}+(1+\beta _{3})q^{5}+q^{6}+\cdots$
3234.2.e.a	$3234$	$2$	3234.e	77.b	$2$	$16$	$16$	$25.824$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	None					462.2.p.a	$2$	$0$	$0$	$0$	$0$	$0$		$2^{6}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{12}q^{2}-\beta _{12}q^{3}-q^{4}+(-\beta _{11}+\cdots)q^{5}+\cdots$
3234.2.e.b	$3234$	$2$	3234.e	77.b	$2$	$16$	$16$	$25.824$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	None					462.2.p.a	$2$	$0$	$0$	$0$	$0$	$0$		$2^{6}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{12}q^{2}-\beta _{12}q^{3}-q^{4}+(-\beta _{11}+\cdots)q^{5}+\cdots$
3234.2.e.c	$3234$	$2$	3234.e	77.b	$2$	$24$	$24$	$25.824$		None		✓			3234.2.e.c	$2$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
3234.2.e.d	$3234$	$2$	3234.e	77.b	$2$	$24$	$24$	$25.824$		None		✓			3234.2.e.c	$2$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$

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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.