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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 (33 matches)

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Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	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	Inner twists	Rank*	$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
163.2.a.a	$163$	$2$	163.a	1.a	$1$	$1$	$1$	$1.302$	$\Q$	None	✓	$1$	$1$	$0$	$0$	$-4$	$2$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{4}-4q^{5}+2q^{7}-3q^{9}-6q^{11}+\cdots$
163.2.a.b	$163$	$2$	163.a	1.a	$1$	$5$	$5$	$1.302$	5.5.65657.1	None	✓	$1$	$1$	$-5$	$-5$	$-9$	$-6$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta _{2}+\beta _{3})q^{2}+(-1+\beta _{1}-\beta _{2}+\cdots)q^{3}+\cdots$
163.2.a.c	$163$	$2$	163.a	1.a	$1$	$7$	$7$	$1.302$	$\mathbb{Q}[x]/(x^{7} - \cdots)$	None	✓	$1$	$0$	$3$	$1$	$11$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+\beta _{4}q^{3}+(1+\beta _{2})q^{4}+(2-\beta _{6})q^{5}+\cdots$
163.2.c.a	$163$	$2$	163.c	163.c	$3$	$24$	$12$	$1.302$		None		$2$	$0$	$-1$	$-1$	$-10$	$-3$			$\mathrm{SU}(2)[C_{3}]$
163.2.e.a	$163$	$2$	163.e	163.e	$9$	$72$	$12$	$1.302$		None		$2$	$0$	$-3$	$0$	$0$	$6$			$\mathrm{SU}(2)[C_{9}]$
163.2.g.a	$163$	$2$	163.g	163.g	$27$	$216$	$12$	$1.302$		None		$2$	$0$	$-18$	$-18$	$-9$	$-18$			$\mathrm{SU}(2)[C_{27}]$
163.2.i.a	$163$	$2$	163.i	163.i	$81$	$702$	$13$	$1.302$		None		$2$	$0$	$-54$	$-54$	$-54$	$-54$			$\mathrm{SU}(2)[C_{81}]$
163.3.b.a	$163$	$3$	163.b	163.b	$2$	$1$	$1$	$4.441$	$\Q$	$\Q(\sqrt{-163}) $	✓	$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{U}(1)[D_{2}]$	$q+4q^{4}+9q^{9}+2^{4}q^{16}+5^{2}q^{25}+\cdots$
163.3.b.b	$163$	$3$	163.b	163.b	$2$	$26$	$26$	$4.441$		None		$2$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
163.3.d.a	$163$	$3$	163.d	163.d	$6$	$54$	$27$	$4.441$		None		$2$	$0$	$0$	$-12$	$0$	$3$			$\mathrm{SU}(2)[C_{6}]$
163.3.f.a	$163$	$3$	163.f	163.f	$18$	$162$	$27$	$4.441$		None		$2$	$0$	$-9$	$3$	$18$	$-12$			$\mathrm{SU}(2)[C_{18}]$
163.3.h.a	$163$	$3$	163.h	163.h	$54$	$486$	$27$	$4.441$		None		$2$	$0$	$-18$	$-18$	$-45$	$-18$			$\mathrm{SU}(2)[C_{54}]$
163.3.j.a	$163$	$3$	163.j	163.j	$162$	$1404$	$26$	$4.441$		None		$2$	$0$	$-54$	$-54$	$-54$	$-54$			$\mathrm{SU}(2)[C_{162}]$
163.4.a.a	$163$	$4$	163.a	1.a	$1$	$19$	$19$	$9.617$	$\mathbb{Q}[x]/(x^{19} - \cdots)$	None	✓	$1$	$1$	$-10$	$-15$	$-71$	$-48$	$-$	$2$	$\mathrm{SU}(2)$	$q+(-1+\beta _{1})q^{2}+(-1+\beta _{4})q^{3}+(4+\cdots)q^{4}+\cdots$
163.4.a.b	$163$	$4$	163.a	1.a	$1$	$21$	$21$	$9.617$		None	✓	$1$	$0$	$12$	$15$	$79$	$36$	$+$		$\mathrm{SU}(2)$
163.4.c.a	$163$	$4$	163.c	163.c	$3$	$80$	$40$	$9.617$		None		$2$	$0$	$-2$	$0$	$-8$	$-27$			$\mathrm{SU}(2)[C_{3}]$
163.4.e.a	$163$	$4$	163.e	163.e	$9$	$240$	$40$	$9.617$		None		$2$	$0$	$-9$	$-9$	$-45$	$30$			$\mathrm{SU}(2)[C_{9}]$
163.4.g.a	$163$	$4$	163.g	163.g	$27$	$720$	$40$	$9.617$		None		$2$	$0$	$-18$	$-18$	$18$	$-18$			$\mathrm{SU}(2)[C_{27}]$
163.4.i.a	$163$	$4$	163.i	163.i	$81$	$2160$	$40$	$9.617$		None		$2$	$0$	$-54$	$-54$	$-54$	$-54$			$\mathrm{SU}(2)[C_{81}]$
163.5.b.a	$163$	$5$	163.b	163.b	$2$	$1$	$1$	$16.849$	$\Q$	$\Q(\sqrt{-163}) $	✓	$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{U}(1)[D_{2}]$	$q+2^{4}q^{4}+3^{4}q^{9}+2^{8}q^{16}+5^{4}q^{25}+\cdots$
163.5.b.b	$163$	$5$	163.b	163.b	$2$	$52$	$52$	$16.849$		None		$2$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
163.6.a.a	$163$	$6$	163.a	1.a	$1$	$33$	$33$	$26.143$		None	✓	$1$	$1$	$-24$	$-45$	$-383$	$-332$	$+$		$\mathrm{SU}(2)$
163.6.a.b	$163$	$6$	163.a	1.a	$1$	$35$	$35$	$26.143$		None	✓	$1$	$0$	$20$	$45$	$367$	$256$	$-$		$\mathrm{SU}(2)$
163.7.b.a	$163$	$7$	163.b	163.b	$2$	$1$	$1$	$37.499$	$\Q$	$\Q(\sqrt{-163}) $	✓	$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{U}(1)[D_{2}]$	$q+2^{6}q^{4}+3^{6}q^{9}+2^{12}q^{16}+5^{6}q^{25}+\cdots$
163.7.b.b	$163$	$7$	163.b	163.b	$2$	$80$	$80$	$37.499$		None		$2$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
163.8.a.a	$163$	$8$	163.a	1.a	$1$	$46$	$46$	$50.919$		None	✓	$1$	$1$	$-48$	$-135$	$-1681$	$-1384$	$-$		$\mathrm{SU}(2)$
163.8.a.b	$163$	$8$	163.a	1.a	$1$	$48$	$48$	$50.919$		None	✓	$1$	$0$	$40$	$135$	$2069$	$2732$	$+$		$\mathrm{SU}(2)$
163.10.a.a	$163$	$10$	163.a	1.a	$1$	$60$	$60$	$83.951$		None	✓	$1$	$1$	$-80$	$-405$	$-10513$	$-19284$	$+$		$\mathrm{SU}(2)$
163.10.a.b	$163$	$10$	163.a	1.a	$1$	$62$	$62$	$83.951$		None	✓	$1$	$0$	$96$	$405$	$8237$	$9528$	$-$		$\mathrm{SU}(2)$
163.12.a.a	$163$	$12$	163.a	1.a	$1$	$73$	$73$	$125.240$		None	✓	$1$	$1$	$-160$	$-1215$	$-52091$	$-85088$	$-$		$\mathrm{SU}(2)$
163.12.a.b	$163$	$12$	163.a	1.a	$1$	$75$	$75$	$125.240$		None	✓	$1$	$0$	$192$	$1215$	$41659$	$116596$	$+$		$\mathrm{SU}(2)$
163.14.a.a	$163$	$14$	163.a	1.a	$1$	$87$	$87$	$174.786$		None	✓	$1$	$1$	$-384$	$-3645$	$-213443$	$-624412$	$+$		$\mathrm{SU}(2)$
163.14.a.b	$163$	$14$	163.a	1.a	$1$	$89$	$89$	$174.786$		None	✓	$1$	$0$	$320$	$3645$	$255307$	$787376$	$-$		$\mathrm{SU}(2)$

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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.