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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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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
177.2.a.a	$177$	$2$	177.a	1.a	$1$	$2$	$2$	$1.413$	$\Q(\sqrt{5}) $	None	✓	$1$	$1$	$-3$	$2$	$-6$	$-7$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1-\beta )q^{2}+q^{3}+3\beta q^{4}-3q^{5}+\cdots$
177.2.a.b	$177$	$2$	177.a	1.a	$1$	$2$	$2$	$1.413$	$\Q(\sqrt{5}) $	None	✓	$1$	$1$	$-1$	$-2$	$0$	$-7$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta q^{2}-q^{3}+(-1+\beta )q^{4}+(-1+2\beta )q^{5}+\cdots$
177.2.a.c	$177$	$2$	177.a	1.a	$1$	$2$	$2$	$1.413$	$\Q(\sqrt{5}) $	None	✓	$1$	$0$	$1$	$2$	$2$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{2}+q^{3}+(-1+\beta )q^{4}+q^{5}+\beta q^{6}+\cdots$
177.2.a.d	$177$	$2$	177.a	1.a	$1$	$3$	$3$	$1.413$	3.3.229.1	None	✓	$1$	$0$	$0$	$-3$	$-2$	$9$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}+(-1+\beta _{1}+\cdots)q^{5}+\cdots$
177.2.d.a	$177$	$2$	177.d	177.d	$2$	$6$	$6$	$1.413$	6.0.19298288.1	None		$2$	$0$	$-4$	$-1$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+(-1+\beta _{1}+\beta _{2}+\beta _{5})q^{2}-\beta _{1}q^{3}+\cdots$
177.2.d.b	$177$	$2$	177.d	177.d	$2$	$6$	$6$	$1.413$	6.0.149721291.1	$\Q(\sqrt{-59}) $		$4$	$0$	$0$	$0$	$0$	$0$		$3$	$\mathrm{U}(1)[D_{2}]$	$q+\beta _{1}q^{3}-2q^{4}+(\beta _{2}+\beta _{3})q^{5}+(-\beta _{1}+\cdots)q^{7}+\cdots$
177.2.d.c	$177$	$2$	177.d	177.d	$2$	$6$	$6$	$1.413$	6.0.19298288.1	None		$2$	$0$	$4$	$-1$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+(1-\beta _{1}-\beta _{2}-\beta _{5})q^{2}-\beta _{1}q^{3}+(2+\cdots)q^{4}+\cdots$
177.2.e.a	$177$	$2$	177.e	59.c	$29$	$140$	$5$	$1.413$		None		$2$	$0$	$-1$	$-5$	$-2$	$-2$			$\mathrm{SU}(2)[C_{29}]$
177.2.e.b	$177$	$2$	177.e	59.c	$29$	$140$	$5$	$1.413$		None		$2$	$0$	$1$	$5$	$2$	$-2$			$\mathrm{SU}(2)[C_{29}]$
177.2.f.a	$177$	$2$	177.f	177.f	$58$	$504$	$18$	$1.413$		None		$4$	$0$	$0$	$-27$	$0$	$-58$			$\mathrm{SU}(2)[C_{58}]$
177.3.b.a	$177$	$3$	177.b	3.b	$2$	$38$	$38$	$4.823$		None		$2$	$0$	$0$	$0$	$0$	$-12$			$\mathrm{SU}(2)[C_{2}]$
177.3.c.a	$177$	$3$	177.c	59.b	$2$	$20$	$20$	$4.823$	$\mathbb{Q}[x]/(x^{20} + \cdots)$	None		$2$	$0$	$0$	$0$	$0$	$-8$		$2^{7}\cdot 3$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{2}-\beta _{8}q^{3}+(-2+\beta _{2})q^{4}-\beta _{6}q^{5}+\cdots$
177.3.g.a	$177$	$3$	177.g	59.d	$58$	$560$	$20$	$4.823$		None		$2$	$0$	$0$	$0$	$0$	$8$			$\mathrm{SU}(2)[C_{58}]$
177.3.h.a	$177$	$3$	177.h	177.h	$58$	$1064$	$38$	$4.823$		None		$4$	$0$	$0$	$-29$	$0$	$-46$			$\mathrm{SU}(2)[C_{58}]$
177.4.a.a	$177$	$4$	177.a	1.a	$1$	$7$	$7$	$10.443$	$\mathbb{Q}[x]/(x^{7} - \cdots)$	None	✓	$1$	$1$	$-8$	$21$	$-28$	$-59$	$-$	$2^{2}$	$\mathrm{SU}(2)$	$q+(-1-\beta _{1})q^{2}+3q^{3}+(3+2\beta _{1}-\beta _{2}+\cdots)q^{4}+\cdots$
177.4.a.b	$177$	$4$	177.a	1.a	$1$	$7$	$7$	$10.443$	$\mathbb{Q}[x]/(x^{7} - \cdots)$	None	✓	$1$	$1$	$0$	$-21$	$-2$	$-59$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}-3q^{3}+(4+\beta _{2})q^{4}+(-1+\cdots)q^{5}+\cdots$
177.4.a.c	$177$	$4$	177.a	1.a	$1$	$8$	$8$	$10.443$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	None	✓	$1$	$0$	$2$	$-24$	$-12$	$53$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}-3q^{3}+(5+\beta _{2})q^{4}+(-2+\cdots)q^{5}+\cdots$
177.4.a.d	$177$	$4$	177.a	1.a	$1$	$8$	$8$	$10.443$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	None	✓	$1$	$0$	$6$	$24$	$42$	$53$	$+$	$2$	$\mathrm{SU}(2)$	$q+(1-\beta _{1})q^{2}+3q^{3}+(5-\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots$
177.4.d.a	$177$	$4$	177.d	177.d	$2$	$2$	$2$	$10.443$	$\Q(\sqrt{-59}) $	$\Q(\sqrt{-59}) $		$4$	$0$	$0$	$7$	$0$	$58$		$1$	$\mathrm{U}(1)[D_{2}]$	$q+(4-\beta )q^{3}-8q^{4}+(-1+2\beta )q^{5}+\cdots$
177.4.d.b	$177$	$4$	177.d	177.d	$2$	$4$	$4$	$10.443$	$\Q(\sqrt{-3}, \sqrt{-59})$	$\Q(\sqrt{-59}) $		$4$	$0$	$0$	$-7$	$0$	$-58$		$2\cdot 3$	$\mathrm{U}(1)[D_{2}]$	$q+(-2-\beta _{2}-\beta _{3})q^{3}-8q^{4}+(4\beta _{1}+\cdots)q^{5}+\cdots$
177.4.d.c	$177$	$4$	177.d	177.d	$2$	$52$	$52$	$10.443$		None		$4$	$0$	$0$	$-8$	$0$	$-16$			$\mathrm{SU}(2)[C_{2}]$
177.4.e.a	$177$	$4$	177.e	59.c	$29$	$420$	$15$	$10.443$		None		$2$	$0$	$-2$	$45$	$14$	$6$			$\mathrm{SU}(2)[C_{29}]$
177.4.e.b	$177$	$4$	177.e	59.c	$29$	$420$	$15$	$10.443$		None		$2$	$0$	$2$	$-45$	$-14$	$6$			$\mathrm{SU}(2)[C_{29}]$
177.4.f.a	$177$	$4$	177.f	177.f	$58$	$1624$	$58$	$10.443$		None		$4$	$0$	$0$	$-21$	$0$	$-42$			$\mathrm{SU}(2)[C_{58}]$
177.5.b.a	$177$	$5$	177.b	3.b	$2$	$78$	$78$	$18.296$		None		$2$	$0$	$0$	$0$	$0$	$76$			$\mathrm{SU}(2)[C_{2}]$
177.5.c.a	$177$	$5$	177.c	59.b	$2$	$40$	$40$	$18.296$		None		$2$	$0$	$0$	$0$	$0$	$80$			$\mathrm{SU}(2)[C_{2}]$
177.6.a.a	$177$	$6$	177.a	1.a	$1$	$11$	$11$	$28.388$	$\mathbb{Q}[x]/(x^{11} - \cdots)$	None	✓	$1$	$1$	$-6$	$99$	$-192$	$-371$	$+$	$2^{2}$	$\mathrm{SU}(2)$	$q+(-1+\beta _{1})q^{2}+9q^{3}+(14-\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots$
177.6.a.b	$177$	$6$	177.a	1.a	$1$	$12$	$12$	$28.388$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	None	✓	$1$	$1$	$-4$	$-108$	$36$	$-411$	$+$	$2^{3}$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}-9q^{3}+(17+\beta _{2})q^{4}+(3+\beta _{1}+\cdots)q^{5}+\cdots$
177.6.a.c	$177$	$6$	177.a	1.a	$1$	$12$	$12$	$28.388$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	None	✓	$1$	$0$	$22$	$108$	$158$	$413$	$-$	$2^{3}$	$\mathrm{SU}(2)$	$q+(2-\beta _{1})q^{2}+9q^{3}+(17-2\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots$
177.6.a.d	$177$	$6$	177.a	1.a	$1$	$13$	$13$	$28.388$	$\mathbb{Q}[x]/(x^{13} - \cdots)$	None	✓	$1$	$0$	$0$	$-117$	$-14$	$373$	$-$	$2^{4}$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}-9q^{3}+(19+\beta _{2})q^{4}+(-1+\cdots)q^{5}+\cdots$
177.6.d.a	$177$	$6$	177.d	177.d	$2$	$6$	$6$	$28.388$	6.0.149721291.1	$\Q(\sqrt{-59}) $		$4$	$0$	$0$	$0$	$0$	$0$		$3$	$\mathrm{U}(1)[D_{2}]$	$q+(4\beta _{2}+3\beta _{3}-3\beta _{4})q^{3}-2^{5}q^{4}+(21\beta _{1}+\cdots)q^{5}+\cdots$
177.6.d.b	$177$	$6$	177.d	177.d	$2$	$92$	$92$	$28.388$		None		$4$	$0$	$0$	$22$	$0$	$-80$			$\mathrm{SU}(2)[C_{2}]$
177.7.c.a	$177$	$7$	177.c	59.b	$2$	$60$	$60$	$40.720$		None		$2$	$0$	$0$	$0$	$0$	$-408$			$\mathrm{SU}(2)[C_{2}]$
177.8.a.a	$177$	$8$	177.a	1.a	$1$	$16$	$16$	$55.292$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	None	✓	$1$	$1$	$-6$	$-432$	$-68$	$-2343$	$-$	$2^{9}\cdot 3^{5}$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}-3^{3}q^{3}+(61+\beta _{2})q^{4}+(-5+\cdots)q^{5}+\cdots$
177.8.a.b	$177$	$8$	177.a	1.a	$1$	$17$	$17$	$55.292$	$\mathbb{Q}[x]/(x^{17} - \cdots)$	None	✓	$1$	$1$	$-32$	$459$	$-1072$	$-2407$	$-$	$2^{10}\cdot 3^{5}$	$\mathrm{SU}(2)$	$q+(-2+\beta _{1})q^{2}+3^{3}q^{3}+(69-3\beta _{1}+\cdots)q^{4}+\cdots$
177.8.a.c	$177$	$8$	177.a	1.a	$1$	$17$	$17$	$55.292$	$\mathbb{Q}[x]/(x^{17} - \cdots)$	None	✓	$1$	$0$	$2$	$-459$	$-318$	$3145$	$+$	$2^{10}\cdot 3^{5}$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}-3^{3}q^{3}+(68+\beta _{1}+\beta _{2})q^{4}+\cdots$
177.8.a.d	$177$	$8$	177.a	1.a	$1$	$18$	$18$	$55.292$	$\mathbb{Q}[x]/(x^{18} - \cdots)$	None	✓	$1$	$0$	$24$	$486$	$678$	$3081$	$+$	$2^{12}\cdot 3^{5}$	$\mathrm{SU}(2)$	$q+(1+\beta _{1})q^{2}+3^{3}q^{3}+(75+\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots$
177.9.c.a	$177$	$9$	177.c	59.b	$2$	$80$	$80$	$72.106$		None		$2$	$0$	$0$	$0$	$0$	$160$			$\mathrm{SU}(2)[C_{2}]$
177.10.a.a	$177$	$10$	177.a	1.a	$1$	$21$	$21$	$91.161$		None	✓	$1$	$1$	$-66$	$1701$	$-2964$	$-30775$	$+$		$\mathrm{SU}(2)$
177.10.a.b	$177$	$10$	177.a	1.a	$1$	$21$	$21$	$91.161$		None	✓	$1$	$1$	$20$	$-1701$	$2058$	$-17167$	$+$		$\mathrm{SU}(2)$
177.10.a.c	$177$	$10$	177.a	1.a	$1$	$22$	$22$	$91.161$		None	✓	$1$	$0$	$36$	$-1782$	$808$	$21249$	$-$		$\mathrm{SU}(2)$
177.10.a.d	$177$	$10$	177.a	1.a	$1$	$22$	$22$	$91.161$		None	✓	$1$	$0$	$46$	$1782$	$5786$	$7641$	$-$		$\mathrm{SU}(2)$
177.11.c.a	$177$	$11$	177.c	59.b	$2$	$100$	$100$	$112.458$		None		$2$	$0$	$0$	$0$	$0$	$18392$			$\mathrm{SU}(2)[C_{2}]$
177.12.a.a	$177$	$12$	177.a	1.a	$1$	$26$	$26$	$135.997$		None	✓	$1$	$1$	$-78$	$-6318$	$3808$	$-98819$	$-$		$\mathrm{SU}(2)$
177.12.a.b	$177$	$12$	177.a	1.a	$1$	$27$	$27$	$135.997$		None	✓	$1$	$1$	$-128$	$6561$	$-17188$	$-126579$	$-$		$\mathrm{SU}(2)$
177.12.a.c	$177$	$12$	177.a	1.a	$1$	$27$	$27$	$135.997$		None	✓	$1$	$0$	$-46$	$-6561$	$-2442$	$170093$	$+$		$\mathrm{SU}(2)$
177.12.a.d	$177$	$12$	177.a	1.a	$1$	$28$	$28$	$135.997$		None	✓	$1$	$0$	$96$	$6804$	$26562$	$142333$	$+$		$\mathrm{SU}(2)$
177.14.a.a	$177$	$14$	177.a	1.a	$1$	$30$	$30$	$189.799$		None	✓	$1$	$1$	$-138$	$21870$	$-137742$	$-879443$	$+$		$\mathrm{SU}(2)$
177.14.a.b	$177$	$14$	177.a	1.a	$1$	$31$	$31$	$189.799$		None	✓	$1$	$1$	$-52$	$-22599$	$33486$	$-1135539$	$+$		$\mathrm{SU}(2)$
177.14.a.c	$177$	$14$	177.a	1.a	$1$	$31$	$31$	$189.799$		None	✓	$1$	$0$	$310$	$22599$	$81008$	$1002941$	$-$		$\mathrm{SU}(2)$

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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.