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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*	$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$	3	19	47	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
8037.2.a.a	$8037$	$2$	8037.a	1.a	$1$	$1$	$1$	$64.176$	$\Q$	None	✓	$1$	$1$	$-2$	$0$	$3$	$1$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{2}+2q^{4}+3q^{5}+q^{7}-6q^{10}+\cdots$
8037.2.a.b	$8037$	$2$	8037.a	1.a	$1$	$1$	$1$	$64.176$	$\Q$	None	✓	$1$	$2$	$0$	$0$	$-1$	$-3$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{4}-q^{5}-3q^{7}-3q^{11}-2q^{13}+\cdots$
8037.2.a.c	$8037$	$2$	8037.a	1.a	$1$	$1$	$1$	$64.176$	$\Q$	None	✓	$1$	$1$	$2$	$0$	$1$	$1$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+2q^{2}+2q^{4}+q^{5}+q^{7}+2q^{10}+\cdots$
8037.2.a.d	$8037$	$2$	8037.a	1.a	$1$	$1$	$1$	$64.176$	$\Q$	None	✓	$1$	$0$	$2$	$0$	$3$	$1$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{2}+2q^{4}+3q^{5}+q^{7}+6q^{10}+\cdots$
8037.2.a.e	$8037$	$2$	8037.a	1.a	$1$	$3$	$3$	$64.176$	$\Q(\zeta_{18})^+$	None	✓	$1$	$0$	$0$	$0$	$3$	$-6$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+\beta _{2}q^{4}+(1-\beta _{2})q^{5}+(-2+\cdots)q^{7}+\cdots$
8037.2.a.f	$8037$	$2$	8037.a	1.a	$1$	$3$	$3$	$64.176$	$\Q(\zeta_{18})^+$	None	✓	$1$	$1$	$0$	$0$	$3$	$0$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+\beta _{2}q^{4}+(1+\beta _{1}-\beta _{2})q^{5}+\cdots$
8037.2.a.g	$8037$	$2$	8037.a	1.a	$1$	$4$	$4$	$64.176$	4.4.2777.1	None	✓	$1$	$0$	$0$	$0$	$-2$	$-5$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{2}q^{2}+(1-\beta _{3})q^{4}-\beta _{3}q^{5}+(-1+\cdots)q^{7}+\cdots$
8037.2.a.h	$8037$	$2$	8037.a	1.a	$1$	$4$	$4$	$64.176$	4.4.1957.1	None	✓	$1$	$1$	$0$	$0$	$-5$	$-5$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+(\beta _{1}+\beta _{2}+\beta _{3})q^{2}+(1+\beta _{1})q^{4}+(-1+\cdots)q^{5}+\cdots$
8037.2.a.i	$8037$	$2$	8037.a	1.a	$1$	$6$	$6$	$64.176$	6.6.5476681.1	None	✓	$1$	$1$	$-4$	$0$	$4$	$2$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1-\beta _{4})q^{2}+(1+\beta _{2}+2\beta _{4})q^{4}+\cdots$
8037.2.a.j	$8037$	$2$	8037.a	1.a	$1$	$7$	$7$	$64.176$	$\mathbb{Q}[x]/(x^{7} - \cdots)$	None	✓	$1$	$1$	$2$	$0$	$-6$	$-3$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}+(-1+\beta _{5})q^{5}+\cdots$
8037.2.a.k	$8037$	$2$	8037.a	1.a	$1$	$7$	$7$	$64.176$	$\mathbb{Q}[x]/(x^{7} - \cdots)$	None	✓	$1$	$0$	$2$	$0$	$6$	$7$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+(1+\beta _{1}+\beta _{4}+\beta _{5})q^{4}+(1+\cdots)q^{5}+\cdots$
8037.2.a.l	$8037$	$2$	8037.a	1.a	$1$	$7$	$7$	$64.176$	$\mathbb{Q}[x]/(x^{7} - \cdots)$	None	✓	$1$	$0$	$4$	$0$	$10$	$3$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1-\beta _{1})q^{2}+(1-\beta _{1}+\beta _{2})q^{4}+(1+\cdots)q^{5}+\cdots$
8037.2.a.m	$8037$	$2$	8037.a	1.a	$1$	$12$	$12$	$64.176$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	None	✓	$1$	$1$	$1$	$0$	$7$	$-13$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}+(1+\beta _{6})q^{5}+\cdots$
8037.2.a.n	$8037$	$2$	8037.a	1.a	$1$	$16$	$16$	$64.176$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	None	✓	$1$	$1$	$4$	$0$	$1$	$-9$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}-\beta _{9}q^{5}+(-2+\cdots)q^{7}+\cdots$
8037.2.a.o	$8037$	$2$	8037.a	1.a	$1$	$18$	$18$	$64.176$	$\mathbb{Q}[x]/(x^{18} - \cdots)$	None	✓	$1$	$0$	$-1$	$0$	$-5$	$3$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+(1+\beta _{2})q^{4}-\beta _{10}q^{5}+(\beta _{14}+\cdots)q^{7}+\cdots$
8037.2.a.p	$8037$	$2$	8037.a	1.a	$1$	$23$	$23$	$64.176$		None	✓	$1$	$1$	$-5$	$0$	$-12$	$-2$	$-$	$-$	$+$	$+$		$\mathrm{SU}(2)$
8037.2.a.q	$8037$	$2$	8037.a	1.a	$1$	$23$	$23$	$64.176$		None	✓	$1$	$0$	$-2$	$0$	$-9$	$5$	$-$	$+$	$+$	$-$		$\mathrm{SU}(2)$
8037.2.a.r	$8037$	$2$	8037.a	1.a	$1$	$23$	$23$	$64.176$		None	✓	$1$	$0$	$-1$	$0$	$-1$	$15$	$-$	$-$	$-$	$-$		$\mathrm{SU}(2)$
8037.2.a.s	$8037$	$2$	8037.a	1.a	$1$	$24$	$24$	$64.176$		None	✓	$1$	$1$	$-6$	$0$	$-10$	$6$	$-$	$+$	$-$	$+$		$\mathrm{SU}(2)$
8037.2.a.t	$8037$	$2$	8037.a	1.a	$1$	$24$	$24$	$64.176$		None	✓	$1$	$0$	$-2$	$0$	$2$	$6$	$-$	$-$	$-$	$-$		$\mathrm{SU}(2)$
8037.2.a.u	$8037$	$2$	8037.a	1.a	$1$	$34$	$34$	$64.176$		None	✓	$1$	$1$	$-5$	$0$	$-14$	$0$	$+$	$-$	$-$	$+$		$\mathrm{SU}(2)$
8037.2.a.v	$8037$	$2$	8037.a	1.a	$1$	$34$	$34$	$64.176$		None	✓	$1$	$1$	$-5$	$0$	$-6$	$0$	$+$	$+$	$+$	$+$		$\mathrm{SU}(2)$
8037.2.a.w	$8037$	$2$	8037.a	1.a	$1$	$34$	$34$	$64.176$		None	✓	$1$	$0$	$5$	$0$	$6$	$0$	$+$	$+$	$-$	$-$		$\mathrm{SU}(2)$
8037.2.a.x	$8037$	$2$	8037.a	1.a	$1$	$34$	$34$	$64.176$		None	✓	$1$	$0$	$5$	$0$	$14$	$0$	$+$	$-$	$+$	$-$		$\mathrm{SU}(2)$

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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.