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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*	$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$	13	29	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
4901.2.a.a	$4901$	$2$	4901.a	1.a	$1$	$1$	$1$	$39.135$	$\Q$	None	✓	$1$	$1$	$-2$	$2$	$3$	$0$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{2}+2q^{3}+2q^{4}+3q^{5}-4q^{6}+\cdots$
4901.2.a.b	$4901$	$2$	4901.a	1.a	$1$	$1$	$1$	$39.135$	$\Q$	None	✓	$1$	$0$	$-1$	$0$	$2$	$0$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{4}+2q^{5}+3q^{8}-3q^{9}-2q^{10}+\cdots$
4901.2.a.c	$4901$	$2$	4901.a	1.a	$1$	$1$	$1$	$39.135$	$\Q$	None	✓	$1$	$1$	$2$	$2$	$-3$	$0$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+2q^{2}+2q^{3}+2q^{4}-3q^{5}+4q^{6}+\cdots$
4901.2.a.d	$4901$	$2$	4901.a	1.a	$1$	$2$	$2$	$39.135$	$\Q(\sqrt{3}) $	None	✓	$2$	$0$	$0$	$-2$	$0$	$0$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{2}-q^{3}+q^{4}+\beta q^{5}-\beta q^{6}-\beta q^{8}+\cdots$
4901.2.a.e	$4901$	$2$	4901.a	1.a	$1$	$2$	$2$	$39.135$	$\Q(\sqrt{3}) $	None	✓	$1$	$0$	$0$	$2$	$0$	$-6$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{2}+(1-\beta )q^{3}+q^{4}-2\beta q^{5}+(-3+\cdots)q^{6}+\cdots$
4901.2.a.f	$4901$	$2$	4901.a	1.a	$1$	$2$	$2$	$39.135$	$\Q(\sqrt{3}) $	None	✓	$2$	$1$	$0$	$4$	$0$	$0$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{2}+2q^{3}+q^{4}+2\beta q^{6}-\beta q^{8}+\cdots$
4901.2.a.g	$4901$	$2$	4901.a	1.a	$1$	$2$	$2$	$39.135$	$\Q(\sqrt{2}) $	None	✓	$1$	$0$	$2$	$2$	$2$	$0$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1+\beta )q^{2}+(1+\beta )q^{3}+(1+2\beta )q^{4}+\cdots$
4901.2.a.h	$4901$	$2$	4901.a	1.a	$1$	$4$	$4$	$39.135$	$\Q(\zeta_{24})^+$	None	✓	$2$	$0$	$0$	$0$	$0$	$0$	$-$	$+$	$-$	$2$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+\beta _{3}q^{3}+q^{4}+2\beta _{2}q^{5}+3\beta _{2}q^{6}+\cdots$
4901.2.a.i	$4901$	$2$	4901.a	1.a	$1$	$5$	$5$	$39.135$	5.5.36497.1	None	✓	$1$	$1$	$1$	$-4$	$2$	$11$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta _{3}q^{2}+(-1-\beta _{4})q^{3}+(\beta _{1}+\beta _{4})q^{4}+\cdots$
4901.2.a.j	$4901$	$2$	4901.a	1.a	$1$	$5$	$5$	$39.135$	5.5.202817.1	None	✓	$1$	$0$	$3$	$-4$	$-2$	$15$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1-\beta _{4})q^{2}+(-1-\beta _{3})q^{3}+(2-\beta _{1}+\cdots)q^{4}+\cdots$
4901.2.a.k	$4901$	$2$	4901.a	1.a	$1$	$7$	$7$	$39.135$	$\mathbb{Q}[x]/(x^{7} - \cdots)$	None	✓	$1$	$0$	$-3$	$2$	$2$	$-7$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{6}q^{2}+\beta _{2}q^{3}+(2-\beta _{1}-\beta _{2}+\beta _{3}+\cdots)q^{4}+\cdots$
4901.2.a.l	$4901$	$2$	4901.a	1.a	$1$	$9$	$9$	$39.135$	$\mathbb{Q}[x]/(x^{9} - \cdots)$	None	✓	$1$	$1$	$-1$	$0$	$-2$	$-17$	$+$	$+$	$+$	$2$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}-\beta _{8}q^{3}+(1+\beta _{2})q^{4}+\beta _{4}q^{5}+\cdots$
4901.2.a.m	$4901$	$2$	4901.a	1.a	$1$	$12$	$12$	$39.135$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	None	✓	$1$	$1$	$-2$	$-7$	$3$	$1$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+(-1+\beta _{5})q^{3}+(\beta _{1}+\beta _{4}+\cdots)q^{4}+\cdots$
4901.2.a.n	$4901$	$2$	4901.a	1.a	$1$	$12$	$12$	$39.135$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	None	✓	$2$	$1$	$0$	$-12$	$0$	$0$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+(-1+\beta _{5})q^{3}+(1+\beta _{2})q^{4}+\cdots$
4901.2.a.o	$4901$	$2$	4901.a	1.a	$1$	$12$	$12$	$39.135$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	None	✓	$1$	$1$	$2$	$-7$	$-3$	$-1$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+(-1+\beta _{5})q^{3}+(\beta _{1}+\beta _{4}+\cdots)q^{4}+\cdots$
4901.2.a.p	$4901$	$2$	4901.a	1.a	$1$	$14$	$14$	$39.135$	$\mathbb{Q}[x]/(x^{14} - \cdots)$	None	✓	$2$	$0$	$0$	$6$	$0$	$0$	$-$	$+$	$-$	$2$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+\beta _{4}q^{3}+(2+\beta _{2})q^{4}+\beta _{9}q^{5}+\cdots$
4901.2.a.q	$4901$	$2$	4901.a	1.a	$1$	$19$	$19$	$39.135$	$\mathbb{Q}[x]/(x^{19} - \cdots)$	None	✓	$1$	$0$	$0$	$7$	$0$	$-1$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+\beta _{8}q^{3}+(1+\beta _{2})q^{4}-\beta _{7}q^{5}+\cdots$
4901.2.a.r	$4901$	$2$	4901.a	1.a	$1$	$19$	$19$	$39.135$	$\mathbb{Q}[x]/(x^{19} - \cdots)$	None	✓	$1$	$0$	$0$	$7$	$0$	$1$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+\beta _{8}q^{3}+(1+\beta _{2})q^{4}+\beta _{7}q^{5}+\cdots$
4901.2.a.s	$4901$	$2$	4901.a	1.a	$1$	$26$	$26$	$39.135$		None	✓	$2$	$1$	$0$	$-14$	$0$	$0$	$-$	$-$	$+$		$\mathrm{SU}(2)$
4901.2.a.t	$4901$	$2$	4901.a	1.a	$1$	$38$	$38$	$39.135$		None	✓	$2$	$0$	$0$	$10$	$0$	$0$	$-$	$+$	$-$		$\mathrm{SU}(2)$
4901.2.a.u	$4901$	$2$	4901.a	1.a	$1$	$42$	$42$	$39.135$		None	✓	$1$	$1$	$-6$	$2$	$-10$	$-23$	$-$	$-$	$+$		$\mathrm{SU}(2)$
4901.2.a.v	$4901$	$2$	4901.a	1.a	$1$	$42$	$42$	$39.135$		None	✓	$1$	$1$	$0$	$2$	$-14$	$-25$	$+$	$+$	$+$		$\mathrm{SU}(2)$
4901.2.a.w	$4901$	$2$	4901.a	1.a	$1$	$42$	$42$	$39.135$		None	✓	$1$	$0$	$0$	$2$	$14$	$25$	$-$	$+$	$-$		$\mathrm{SU}(2)$
4901.2.a.x	$4901$	$2$	4901.a	1.a	$1$	$42$	$42$	$39.135$		None	✓	$1$	$0$	$6$	$2$	$10$	$23$	$+$	$-$	$-$		$\mathrm{SU}(2)$

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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.