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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 (1-50 of 123 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*	$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$	3	5	7	13	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
20475.2.a.a	$20475$	$2$	20475.a	1.a	$1$	$1$	$1$	$163.494$	$\Q$	None	✓	?				$-1$		$-2$	$0$	$0$	$-1$	$-$	$+$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{2}+2q^{4}-q^{7}+2q^{11}-q^{13}+\cdots$
20475.2.a.b	$20475$	$2$	20475.a	1.a	$1$	$1$	$1$	$163.494$	$\Q$	None	✓	?				$-1$		$-2$	$0$	$0$	$1$	$-$	$-$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{2}+2q^{4}+q^{7}-4q^{11}+q^{13}+\cdots$
20475.2.a.c	$20475$	$2$	20475.a	1.a	$1$	$1$	$1$	$163.494$	$\Q$	None	✓	?				$-1$		$-2$	$0$	$0$	$1$	$-$	$+$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{2}+2q^{4}+q^{7}+6q^{11}+q^{13}+\cdots$
20475.2.a.d	$20475$	$2$	20475.a	1.a	$1$	$1$	$1$	$163.494$	$\Q$	None	✓	?				$-1$		$-1$	$0$	$0$	$-1$	$-$	$+$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{4}-q^{7}+3q^{8}-4q^{11}-q^{13}+\cdots$
20475.2.a.e	$20475$	$2$	20475.a	1.a	$1$	$1$	$1$	$163.494$	$\Q$	None	✓	?				$-1$		$-1$	$0$	$0$	$-1$	$-$	$-$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{4}-q^{7}+3q^{8}+q^{13}+q^{14}+\cdots$
20475.2.a.f	$20475$	$2$	20475.a	1.a	$1$	$1$	$1$	$163.494$	$\Q$	None	✓	?				$-1$		$-1$	$0$	$0$	$-1$	$+$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{4}-q^{7}+3q^{8}+q^{13}+q^{14}+\cdots$
20475.2.a.g	$20475$	$2$	20475.a	1.a	$1$	$1$	$1$	$163.494$	$\Q$	None	✓	?				$-1$		$-1$	$0$	$0$	$-1$	$+$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{4}-q^{7}+3q^{8}+2q^{11}-q^{13}+\cdots$
20475.2.a.h	$20475$	$2$	20475.a	1.a	$1$	$1$	$1$	$163.494$	$\Q$	None	✓	?				$-1$		$-1$	$0$	$0$	$-1$	$-$	$+$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{4}-q^{7}+3q^{8}+4q^{11}+q^{13}+\cdots$
20475.2.a.i	$20475$	$2$	20475.a	1.a	$1$	$1$	$1$	$163.494$	$\Q$	None	✓	?				$-1$		$-1$	$0$	$0$	$-1$	$+$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{4}-q^{7}+3q^{8}+4q^{11}+q^{13}+\cdots$
20475.2.a.j	$20475$	$2$	20475.a	1.a	$1$	$1$	$1$	$163.494$	$\Q$	None	✓	?				$-1$		$-1$	$0$	$0$	$-1$	$-$	$-$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{4}-q^{7}+3q^{8}+6q^{11}+q^{13}+\cdots$
20475.2.a.k	$20475$	$2$	20475.a	1.a	$1$	$1$	$1$	$163.494$	$\Q$	None	✓	?				$-1$		$-1$	$0$	$0$	$1$	$+$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{4}+q^{7}+3q^{8}-6q^{11}+q^{13}+\cdots$
20475.2.a.l	$20475$	$2$	20475.a	1.a	$1$	$1$	$1$	$163.494$	$\Q$	None	✓	?				$-1$		$-1$	$0$	$0$	$1$	$-$	$-$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{4}+q^{7}+3q^{8}-6q^{11}+q^{13}+\cdots$
20475.2.a.m	$20475$	$2$	20475.a	1.a	$1$	$1$	$1$	$163.494$	$\Q$	None	✓	?				$-1$		$-1$	$0$	$0$	$1$	$+$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{4}+q^{7}+3q^{8}-4q^{11}-q^{13}+\cdots$
20475.2.a.n	$20475$	$2$	20475.a	1.a	$1$	$1$	$1$	$163.494$	$\Q$	None	✓	?				$-1$		$-1$	$0$	$0$	$1$	$-$	$+$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{4}+q^{7}+3q^{8}-q^{13}-q^{14}+\cdots$
20475.2.a.o	$20475$	$2$	20475.a	1.a	$1$	$1$	$1$	$163.494$	$\Q$	None	✓	?				$-1$		$-1$	$0$	$0$	$1$	$+$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{4}+q^{7}+3q^{8}-q^{13}-q^{14}+\cdots$
20475.2.a.p	$20475$	$2$	20475.a	1.a	$1$	$1$	$1$	$163.494$	$\Q$	None	✓	?				$-1$		$-1$	$0$	$0$	$1$	$+$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{4}+q^{7}+3q^{8}+q^{13}-q^{14}+\cdots$
20475.2.a.q	$20475$	$2$	20475.a	1.a	$1$	$1$	$1$	$163.494$	$\Q$	None	✓	?				$-1$		$-1$	$0$	$0$	$1$	$+$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{4}+q^{7}+3q^{8}+6q^{11}-q^{13}+\cdots$
20475.2.a.r	$20475$	$2$	20475.a	1.a	$1$	$1$	$1$	$163.494$	$\Q$	None	✓	?				$-1$		$0$	$0$	$0$	$-1$	$-$	$+$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{4}-q^{7}-q^{13}+4q^{16}-6q^{17}+\cdots$
20475.2.a.s	$20475$	$2$	20475.a	1.a	$1$	$1$	$1$	$163.494$	$\Q$	None	✓	?				$-1$		$1$	$0$	$0$	$-1$	$-$	$-$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{4}-q^{7}-3q^{8}-6q^{11}-q^{13}+\cdots$
20475.2.a.t	$20475$	$2$	20475.a	1.a	$1$	$1$	$1$	$163.494$	$\Q$	None	✓	?				$-1$		$1$	$0$	$0$	$-1$	$+$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{4}-q^{7}-3q^{8}-4q^{11}+q^{13}+\cdots$
20475.2.a.u	$20475$	$2$	20475.a	1.a	$1$	$1$	$1$	$163.494$	$\Q$	None	✓	?				$-1$		$1$	$0$	$0$	$-1$	$+$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{4}-q^{7}-3q^{8}-2q^{11}-q^{13}+\cdots$
20475.2.a.v	$20475$	$2$	20475.a	1.a	$1$	$1$	$1$	$163.494$	$\Q$	None	✓	?				$-1$		$1$	$0$	$0$	$-1$	$-$	$+$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{4}-q^{7}-3q^{8}-q^{13}-q^{14}+\cdots$
20475.2.a.w	$20475$	$2$	20475.a	1.a	$1$	$1$	$1$	$163.494$	$\Q$	None	✓	?				$-1$		$1$	$0$	$0$	$-1$	$+$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{4}-q^{7}-3q^{8}+q^{13}-q^{14}+\cdots$
20475.2.a.x	$20475$	$2$	20475.a	1.a	$1$	$1$	$1$	$163.494$	$\Q$	None	✓	?				$-1$		$1$	$0$	$0$	$1$	$+$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{4}+q^{7}-3q^{8}-6q^{11}-q^{13}+\cdots$
20475.2.a.y	$20475$	$2$	20475.a	1.a	$1$	$1$	$1$	$163.494$	$\Q$	None	✓	?				$-1$		$1$	$0$	$0$	$1$	$-$	$+$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{4}+q^{7}-3q^{8}-4q^{11}-q^{13}+\cdots$
20475.2.a.z	$20475$	$2$	20475.a	1.a	$1$	$1$	$1$	$163.494$	$\Q$	None	✓	?				$-1$		$1$	$0$	$0$	$1$	$-$	$+$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{4}+q^{7}-3q^{8}-4q^{11}+q^{13}+\cdots$
20475.2.a.ba	$20475$	$2$	20475.a	1.a	$1$	$1$	$1$	$163.494$	$\Q$	None	✓	?				$-1$		$1$	$0$	$0$	$1$	$+$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{4}+q^{7}-3q^{8}-q^{13}+q^{14}+\cdots$
20475.2.a.bb	$20475$	$2$	20475.a	1.a	$1$	$1$	$1$	$163.494$	$\Q$	None	✓	?				$-1$		$1$	$0$	$0$	$1$	$-$	$+$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{4}+q^{7}-3q^{8}-q^{13}+q^{14}+\cdots$
20475.2.a.bc	$20475$	$2$	20475.a	1.a	$1$	$1$	$1$	$163.494$	$\Q$	None	✓	?				$-1$		$1$	$0$	$0$	$1$	$-$	$-$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{4}+q^{7}-3q^{8}-q^{13}+q^{14}+\cdots$
20475.2.a.bd	$20475$	$2$	20475.a	1.a	$1$	$1$	$1$	$163.494$	$\Q$	None	✓	?				$-1$		$1$	$0$	$0$	$1$	$+$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{4}+q^{7}-3q^{8}+q^{13}+q^{14}+\cdots$
20475.2.a.be	$20475$	$2$	20475.a	1.a	$1$	$1$	$1$	$163.494$	$\Q$	None	✓	?				$-1$		$1$	$0$	$0$	$1$	$-$	$+$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{4}+q^{7}-3q^{8}+q^{13}+q^{14}+\cdots$
20475.2.a.bf	$20475$	$2$	20475.a	1.a	$1$	$1$	$1$	$163.494$	$\Q$	None	✓	?				$-1$		$1$	$0$	$0$	$1$	$+$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{4}+q^{7}-3q^{8}+4q^{11}-q^{13}+\cdots$
20475.2.a.bg	$20475$	$2$	20475.a	1.a	$1$	$1$	$1$	$163.494$	$\Q$	None	✓	?				$-1$		$1$	$0$	$0$	$1$	$-$	$-$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{4}+q^{7}-3q^{8}+6q^{11}-q^{13}+\cdots$
20475.2.a.bh	$20475$	$2$	20475.a	1.a	$1$	$1$	$1$	$163.494$	$\Q$	None	✓	?				$-1$		$1$	$0$	$0$	$1$	$+$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{4}+q^{7}-3q^{8}+6q^{11}+q^{13}+\cdots$
20475.2.a.bi	$20475$	$2$	20475.a	1.a	$1$	$1$	$1$	$163.494$	$\Q$	None	✓	?				$-1$		$2$	$0$	$0$	$-1$	$-$	$+$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{2}+2q^{4}-q^{7}-4q^{11}-q^{13}+\cdots$
20475.2.a.bj	$20475$	$2$	20475.a	1.a	$1$	$1$	$1$	$163.494$	$\Q$	None	✓	?				$-1$		$2$	$0$	$0$	$1$	$-$	$+$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{2}+2q^{4}+q^{7}+2q^{11}+q^{13}+\cdots$
20475.2.a.bk	$20475$	$2$	20475.a	1.a	$1$	$2$	$2$	$163.494$	$\Q(\sqrt{5}) $	None	✓	?				$-1$		$-3$	$0$	$0$	$-2$	$-$	$+$	$+$	$+$	$-$		$\mathrm{SU}(2)$
20475.2.a.bl	$20475$	$2$	20475.a	1.a	$1$	$2$	$2$	$163.494$	$\Q(\sqrt{3}) $	None	✓	?				$-1$		$-2$	$0$	$0$	$-2$	$-$	$-$	$+$	$+$	$+$		$\mathrm{SU}(2)$
20475.2.a.bm	$20475$	$2$	20475.a	1.a	$1$	$2$	$2$	$163.494$	$\Q(\sqrt{5}) $	None	✓	?				$-1$		$-1$	$0$	$0$	$-2$	$-$	$+$	$+$	$-$	$+$		$\mathrm{SU}(2)$
20475.2.a.bn	$20475$	$2$	20475.a	1.a	$1$	$2$	$2$	$163.494$	$\Q(\sqrt{5}) $	None	✓	?				$-1$		$-1$	$0$	$0$	$-2$	$-$	$+$	$+$	$-$	$+$		$\mathrm{SU}(2)$
20475.2.a.bo	$20475$	$2$	20475.a	1.a	$1$	$2$	$2$	$163.494$	$\Q(\sqrt{5}) $	None	✓	?				$-1$		$-1$	$0$	$0$	$2$	$-$	$+$	$-$	$-$	$-$		$\mathrm{SU}(2)$
20475.2.a.bp	$20475$	$2$	20475.a	1.a	$1$	$2$	$2$	$163.494$	$\Q(\sqrt{5}) $	None	✓	?				$-1$		$-1$	$0$	$0$	$2$	$-$	$+$	$-$	$-$	$-$		$\mathrm{SU}(2)$
20475.2.a.bq	$20475$	$2$	20475.a	1.a	$1$	$2$	$2$	$163.494$	$\Q(\sqrt{13}) $	None	✓	?				$-1$		$-1$	$0$	$0$	$-2$	$-$	$+$	$+$	$-$	$+$		$\mathrm{SU}(2)$
20475.2.a.br	$20475$	$2$	20475.a	1.a	$1$	$2$	$2$	$163.494$	$\Q(\sqrt{2}) $	None	✓	?				$-1$		$0$	$0$	$0$	$-2$	$-$	$+$	$+$	$-$	$+$		$\mathrm{SU}(2)$
20475.2.a.bs	$20475$	$2$	20475.a	1.a	$1$	$2$	$2$	$163.494$	$\Q(\sqrt{5}) $	None	✓	?				$-1$		$1$	$0$	$0$	$-2$	$-$	$-$	$+$	$+$	$+$		$\mathrm{SU}(2)$
20475.2.a.bt	$20475$	$2$	20475.a	1.a	$1$	$2$	$2$	$163.494$	$\Q(\sqrt{5}) $	None	✓	?				$-1$		$1$	$0$	$0$	$-2$	$-$	$+$	$+$	$+$	$-$		$\mathrm{SU}(2)$
20475.2.a.bu	$20475$	$2$	20475.a	1.a	$1$	$2$	$2$	$163.494$	$\Q(\sqrt{13}) $	None	✓	?				$-1$		$1$	$0$	$0$	$-2$	$-$	$+$	$+$	$+$	$-$		$\mathrm{SU}(2)$
20475.2.a.bv	$20475$	$2$	20475.a	1.a	$1$	$2$	$2$	$163.494$	$\Q(\sqrt{13}) $	None	✓	?				$-1$		$1$	$0$	$0$	$2$	$-$	$+$	$-$	$+$	$+$		$\mathrm{SU}(2)$
20475.2.a.bw	$20475$	$2$	20475.a	1.a	$1$	$2$	$2$	$163.494$	$\Q(\sqrt{2}) $	None	✓	?				$-1$		$2$	$0$	$0$	$-2$	$-$	$+$	$+$	$-$	$+$		$\mathrm{SU}(2)$
20475.2.a.bx	$20475$	$2$	20475.a	1.a	$1$	$2$	$2$	$163.494$	$\Q(\sqrt{3}) $	None	✓	?				$-1$		$2$	$0$	$0$	$2$	$-$	$+$	$-$	$-$	$-$		$\mathrm{SU}(2)$

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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.