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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 (24 matches)

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Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	Image	CM	RM	Self-dual	Twist minimal	Largest	Maximal	Minimal twist	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	Image	CM	RM	Self-dual	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
167.1.b.a	$167$	$1$	167.b	167.b	$2$	$5$	$5$	$0.083$	$\Q(\zeta_{22})^+$	$D_{11}$	$\Q(\sqrt{-167}) $	None	✓	✓	✓	✓	167.1.b.a	$2$	$0$	$-1$	$-1$	$0$	$-1$		$1$		$q+\beta _{4}q^{2}+(-1+\beta _{1}-\beta _{2}+\beta _{3}-\beta _{4})q^{3}+\cdots$
167.2.a.a	$167$	$2$	167.a	1.a	$1$	$2$	$2$	$1.334$	$\Q(\sqrt{5}) $	$_{}$	None	None	✓	✓	✓	✓	167.2.a.a	$1$	$1$	$-1$	$-1$	$-2$	$-5$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta q^{2}+(-1+\beta )q^{3}+(-1+\beta )q^{4}+\cdots$
167.2.a.b	$167$	$2$	167.a	1.a	$1$	$12$	$12$	$1.334$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	$_{}$	None	None	✓	✓	✓	✓	167.2.a.b	$1$	$0$	$2$	$3$	$4$	$11$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}-\beta _{8}q^{3}+(1+\beta _{4}+\beta _{6}+\beta _{7}+\cdots)q^{4}+\cdots$
167.2.c.a	$167$	$2$	167.c	167.c	$83$	$1066$	$13$	$1.334$		$_{}$	None	None		✓	✓	✓	167.2.c.a	$2$	$0$	$-81$	$-81$	$-79$	$-81$			$\mathrm{SU}(2)[C_{83}]$
167.3.b.a	$167$	$3$	167.b	167.b	$2$	$11$	$11$	$4.550$	$\mathbb{Q}[x]/(x^{11} - \cdots)$	$_{}$	$\Q(\sqrt{-167}) $	None	✓	✓			167.3.b.a	$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{U}(1)[D_{2}]$	$q+\beta _{2}q^{2}+(\beta _{3}-\beta _{8})q^{3}+(4+\beta _{4}+\beta _{7}+\cdots)q^{4}+\cdots$
167.3.b.b	$167$	$3$	167.b	167.b	$2$	$16$	$16$	$4.550$	$\mathbb{Q}[x]/(x^{16} + \cdots)$	$_{}$	None	None		✓	✓		167.3.b.b	$2$	$0$	$-2$	$-2$	$0$	$-2$		$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{9}q^{2}+\beta _{4}q^{3}+(1+\beta _{2})q^{4}-\beta _{1}q^{5}+\cdots$
167.3.d.a	$167$	$3$	167.d	167.d	$166$	$2214$	$27$	$4.550$		$_{}$	None	None		✓	✓	✓	167.3.d.a	$2$	$0$	$-81$	$-81$	$-83$	$-81$			$\mathrm{SU}(2)[C_{166}]$
167.4.a.a	$167$	$4$	167.a	1.a	$1$	$15$	$15$	$9.853$	$\mathbb{Q}[x]/(x^{15} - \cdots)$	$_{}$	None	None	✓	✓	✓	✓	167.4.a.a	$1$	$1$	$-7$	$-13$	$-26$	$-85$	$-$	$2^{3}$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+(-1-\beta _{5})q^{3}+(2+\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots$
167.4.a.b	$167$	$4$	167.a	1.a	$1$	$26$	$26$	$9.853$		$_{}$	None	None	✓	✓	✓	✓	167.4.a.b	$1$	$0$	$5$	$11$	$34$	$83$	$+$		$\mathrm{SU}(2)$
167.4.c.a	$167$	$4$	167.c	167.c	$83$	$3362$	$41$	$9.853$		$_{}$	None	None		✓	✓	✓	167.4.c.a	$2$	$0$	$-81$	$-81$	$-91$	$-81$			$\mathrm{SU}(2)[C_{83}]$
167.5.b.a	$167$	$5$	167.b	167.b	$2$	$11$	$11$	$17.263$	$\mathbb{Q}[x]/(x^{11} - \cdots)$	$_{}$	$\Q(\sqrt{-167}) $	None	✓	✓			167.5.b.a	$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{U}(1)[D_{2}]$	$q+(\beta _{4}+\beta _{7})q^{2}+(-3\beta _{5}+2\beta _{6})q^{3}+\cdots$
167.5.b.b	$167$	$5$	167.b	167.b	$2$	$44$	$44$	$17.263$		$_{}$	None	None		✓	✓		167.5.b.b	$2$	$0$	$-2$	$-2$	$0$	$-2$			$\mathrm{SU}(2)[C_{2}]$
167.6.a.a	$167$	$6$	167.a	1.a	$1$	$29$	$29$	$26.784$		$_{}$	None	None	✓	✓	✓	✓	167.6.a.a	$1$	$1$	$-13$	$-37$	$-176$	$-589$	$+$		$\mathrm{SU}(2)$
167.6.a.b	$167$	$6$	167.a	1.a	$1$	$40$	$40$	$26.784$		$_{}$	None	None	✓	✓	✓	✓	167.6.a.b	$1$	$0$	$11$	$35$	$124$	$587$	$-$		$\mathrm{SU}(2)$
167.7.b.a	$167$	$7$	167.b	167.b	$2$	$11$	$11$	$38.419$	$\mathbb{Q}[x]/(x^{11} - \cdots)$	$_{}$	$\Q(\sqrt{-167}) $	None	✓	✓			167.7.b.a	$2$	$0$	$0$	$0$	$0$	$0$		$5^{5}$	$\mathrm{U}(1)[D_{2}]$	$q+(\beta _{3}-\beta _{4})q^{2}+(-5\beta _{6}-2\beta _{8})q^{3}+\cdots$
167.7.b.b	$167$	$7$	167.b	167.b	$2$	$72$	$72$	$38.419$		$_{}$	None	None		✓	✓		167.7.b.b	$2$	$0$	$-2$	$-2$	$0$	$-2$			$\mathrm{SU}(2)[C_{2}]$
167.8.a.a	$167$	$8$	167.a	1.a	$1$	$43$	$43$	$52.168$		$_{}$	None	None	✓	✓	✓	✓	167.8.a.a	$1$	$1$	$-25$	$-109$	$-626$	$-4117$	$-$		$\mathrm{SU}(2)$
167.8.a.b	$167$	$8$	167.a	1.a	$1$	$54$	$54$	$52.168$		$_{}$	None	None	✓	✓	✓	✓	167.8.a.b	$1$	$0$	$23$	$107$	$874$	$4115$	$+$		$\mathrm{SU}(2)$
167.10.a.a	$167$	$10$	167.a	1.a	$1$	$57$	$57$	$86.011$		$_{}$	None	None	✓	✓	✓	✓	167.10.a.a	$1$	$1$	$-49$	$-325$	$-4376$	$-28813$	$+$		$\mathrm{SU}(2)$
167.10.a.b	$167$	$10$	167.a	1.a	$1$	$68$	$68$	$86.011$		$_{}$	None	None	✓	✓	✓	✓	167.10.a.b	$1$	$0$	$47$	$323$	$3124$	$28811$	$-$		$\mathrm{SU}(2)$
167.12.a.a	$167$	$12$	167.a	1.a	$1$	$70$	$70$	$128.313$		$_{}$	None	None	✓	✓	✓	✓	167.12.a.a	$1$	$1$	$-73$	$-1225$	$-20456$	$-184941$	$-$		$\mathrm{SU}(2)$
167.12.a.b	$167$	$12$	167.a	1.a	$1$	$81$	$81$	$128.313$		$_{}$	None	None	✓	✓	✓	✓	167.12.a.b	$1$	$0$	$119$	$719$	$17044$	$218427$	$+$		$\mathrm{SU}(2)$
167.14.a.a	$167$	$14$	167.a	1.a	$1$	$85$	$85$	$179.076$		$_{}$	None	None	✓	✓	✓	✓	167.14.a.a	$1$	$1$	$-193$	$-2917$	$-109376$	$-1411789$	$+$		$\mathrm{SU}(2)$
167.14.a.b	$167$	$14$	167.a	1.a	$1$	$96$	$96$	$179.076$		$_{}$	None	None	✓	✓	✓	✓	167.14.a.b	$1$	$0$	$191$	$2915$	$78124$	$1411787$	$-$		$\mathrm{SU}(2)$

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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.