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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	Image	CM	RM	Self-dual	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	Image	CM	RM	Self-dual	Inner twists	Rank*	$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$	Coefficient ring index	Sato-Tate	$q$-expansion
23.1.b.a	$23$	$1$	23.b	23.b	$2$	$1$	$1$	$0.011$	$\Q$	$D_{3}$	$\Q(\sqrt{-23}) $	None	✓	$2$	$0$	$-1$	$-1$	$0$	$0$	$1$		$q-q^{2}-q^{3}+q^{6}+q^{8}-q^{13}-q^{16}+\cdots$
31.1.b.a	$31$	$1$	31.b	31.b	$2$	$1$	$1$	$0.015$	$\Q$	$D_{3}$	$\Q(\sqrt{-31}) $	None	✓	$2$	$0$	$-1$	$0$	$-1$	$-1$	$1$		$q-q^{2}-q^{5}-q^{7}+q^{8}+q^{9}+q^{10}+\cdots$
44.1.d.a	$44$	$1$	44.d	11.b	$2$	$1$	$1$	$0.022$	$\Q$	$D_{3}$	$\Q(\sqrt{-11}) $	None	✓	$2$	$0$	$0$	$-1$	$-1$	$0$	$1$		$q-q^{3}-q^{5}+q^{11}+q^{15}-q^{23}+q^{27}+\cdots$
47.1.b.a	$47$	$1$	47.b	47.b	$2$	$2$	$2$	$0.023$	$\Q(\sqrt{5}) $	$D_{5}$	$\Q(\sqrt{-47}) $	None	✓	$2$	$0$	$-1$	$-1$	$0$	$-1$	$1$		$q+(-1+\beta )q^{2}-\beta q^{3}+(1-\beta )q^{4}-q^{6}+\cdots$
59.1.b.a	$59$	$1$	59.b	59.b	$2$	$1$	$1$	$0.029$	$\Q$	$D_{3}$	$\Q(\sqrt{-59}) $	None	✓	$2$	$0$	$0$	$-1$	$-1$	$-1$	$1$		$q-q^{3}+q^{4}-q^{5}-q^{7}-q^{12}+q^{15}+\cdots$
71.1.b.a	$71$	$1$	71.b	71.b	$2$	$3$	$3$	$0.035$	$\Q(\zeta_{14})^+$	$D_{7}$	$\Q(\sqrt{-71}) $	None	✓	$2$	$0$	$-1$	$-1$	$-1$	$0$	$1$		$q-\beta _{1}q^{2}+(-1+\beta _{1}-\beta _{2})q^{3}+(1+\beta _{2})q^{4}+\cdots$
76.1.c.a	$76$	$1$	76.c	19.b	$2$	$1$	$1$	$0.038$	$\Q$	$D_{3}$	$\Q(\sqrt{-19}) $	None	✓	$2$	$0$	$0$	$0$	$-1$	$-1$	$1$		$q-q^{5}-q^{7}+q^{9}-q^{11}-q^{17}+q^{19}+\cdots$
79.1.b.a	$79$	$1$	79.b	79.b	$2$	$2$	$2$	$0.039$	$\Q(\sqrt{5}) $	$D_{5}$	$\Q(\sqrt{-79}) $	None	✓	$2$	$0$	$-1$	$0$	$-1$	$0$	$1$		$q+(-1+\beta )q^{2}+(1-\beta )q^{4}-\beta q^{5}-q^{8}+\cdots$
83.1.b.a	$83$	$1$	83.b	83.b	$2$	$1$	$1$	$0.041$	$\Q$	$D_{3}$	$\Q(\sqrt{-83}) $	None	✓	$2$	$0$	$0$	$-1$	$0$	$-1$	$1$		$q-q^{3}+q^{4}-q^{7}-q^{11}-q^{12}+q^{16}+\cdots$
87.1.d.a	$87$	$1$	87.d	87.d	$2$	$1$	$1$	$0.043$	$\Q$	$D_{3}$	$\Q(\sqrt{-87}) $	None	✓	$2$	$0$	$-1$	$1$	$0$	$-1$	$1$		$q-q^{2}+q^{3}-q^{6}-q^{7}+q^{8}+q^{9}+\cdots$
87.1.d.b	$87$	$1$	87.d	87.d	$2$	$1$	$1$	$0.043$	$\Q$	$D_{3}$	$\Q(\sqrt{-87}) $	None	✓	$2$	$0$	$1$	$-1$	$0$	$-1$	$1$		$q+q^{2}-q^{3}-q^{6}-q^{7}-q^{8}+q^{9}+\cdots$
103.1.b.a	$103$	$1$	103.b	103.b	$2$	$2$	$2$	$0.051$	$\Q(\sqrt{5}) $	$D_{5}$	$\Q(\sqrt{-103}) $	None	✓	$2$	$0$	$-1$	$0$	$0$	$-1$	$1$		$q+(-1+\beta )q^{2}+(1-\beta )q^{4}-\beta q^{7}-q^{8}+\cdots$
104.1.h.a	$104$	$1$	104.h	104.h	$2$	$1$	$1$	$0.052$	$\Q$	$D_{3}$	$\Q(\sqrt{-26}) $	None	✓	$2$	$0$	$-1$	$-1$	$1$	$1$	$1$		$q-q^{2}-q^{3}+q^{4}+q^{5}+q^{6}+q^{7}+\cdots$
104.1.h.b	$104$	$1$	104.h	104.h	$2$	$1$	$1$	$0.052$	$\Q$	$D_{3}$	$\Q(\sqrt{-26}) $	None	✓	$2$	$0$	$1$	$-1$	$-1$	$-1$	$1$		$q+q^{2}-q^{3}+q^{4}-q^{5}-q^{6}-q^{7}+\cdots$
107.1.b.a	$107$	$1$	107.b	107.b	$2$	$1$	$1$	$0.053$	$\Q$	$D_{3}$	$\Q(\sqrt{-107}) $	None	✓	$2$	$0$	$0$	$-1$	$0$	$0$	$1$		$q-q^{3}+q^{4}-q^{11}-q^{12}-q^{13}+q^{16}+\cdots$
108.1.c.a	$108$	$1$	108.c	3.b	$2$	$1$	$1$	$0.054$	$\Q$	$D_{3}$	$\Q(\sqrt{-3}) $	None	✓	$2$	$0$	$0$	$0$	$0$	$-1$	$1$		$q-q^{7}-q^{13}-q^{19}+q^{25}+2q^{31}+\cdots$
116.1.d.a	$116$	$1$	116.d	116.d	$2$	$1$	$1$	$0.058$	$\Q$	$D_{3}$	$\Q(\sqrt{-29}) $	None	✓	$2$	$0$	$-1$	$1$	$-1$	$0$	$1$		$q-q^{2}+q^{3}+q^{4}-q^{5}-q^{6}-q^{8}+\cdots$
116.1.d.b	$116$	$1$	116.d	116.d	$2$	$1$	$1$	$0.058$	$\Q$	$D_{3}$	$\Q(\sqrt{-29}) $	None	✓	$2$	$0$	$1$	$-1$	$-1$	$0$	$1$		$q+q^{2}-q^{3}+q^{4}-q^{5}-q^{6}+q^{8}+\cdots$
119.1.d.a	$119$	$1$	119.d	119.d	$2$	$2$	$2$	$0.059$	$\Q(\sqrt{5}) $	$D_{5}$	$\Q(\sqrt{-119}) $	None	✓	$2$	$0$	$-1$	$-1$	$-1$	$2$	$1$		$q+(-1+\beta )q^{2}+(-1+\beta )q^{3}+(1-\beta )q^{4}+\cdots$
119.1.d.b	$119$	$1$	119.d	119.d	$2$	$2$	$2$	$0.059$	$\Q(\sqrt{5}) $	$D_{5}$	$\Q(\sqrt{-119}) $	None	✓	$2$	$0$	$-1$	$1$	$1$	$-2$	$1$		$q+(-1+\beta )q^{2}+(1-\beta )q^{3}+(1-\beta )q^{4}+\cdots$
127.1.b.a	$127$	$1$	127.b	127.b	$2$	$2$	$2$	$0.063$	$\Q(\sqrt{5}) $	$D_{5}$	$\Q(\sqrt{-127}) $	None	✓	$2$	$0$	$-1$	$0$	$0$	$0$	$1$		$q+(-1+\beta )q^{2}+(1-\beta )q^{4}-q^{8}+q^{9}+\cdots$
131.1.b.a	$131$	$1$	131.b	131.b	$2$	$2$	$2$	$0.065$	$\Q(\sqrt{5}) $	$D_{5}$	$\Q(\sqrt{-131}) $	None	✓	$2$	$0$	$0$	$-1$	$-1$	$-1$	$1$		$q+(-1+\beta )q^{3}+q^{4}-\beta q^{5}-\beta q^{7}+\cdots$
135.1.d.a	$135$	$1$	135.d	15.d	$2$	$1$	$1$	$0.067$	$\Q$	$D_{3}$	$\Q(\sqrt{-15}) $	None	✓	$2$	$0$	$-1$	$0$	$1$	$0$	$1$		$q-q^{2}+q^{5}+q^{8}-q^{10}-q^{16}-q^{17}+\cdots$
135.1.d.b	$135$	$1$	135.d	15.d	$2$	$1$	$1$	$0.067$	$\Q$	$D_{3}$	$\Q(\sqrt{-15}) $	None	✓	$2$	$0$	$1$	$0$	$-1$	$0$	$1$		$q+q^{2}-q^{5}-q^{8}-q^{10}-q^{16}+q^{17}+\cdots$
139.1.b.a	$139$	$1$	139.b	139.b	$2$	$1$	$1$	$0.069$	$\Q$	$D_{3}$	$\Q(\sqrt{-139}) $	None	✓	$2$	$0$	$0$	$0$	$-1$	$-1$	$1$		$q+q^{4}-q^{5}-q^{7}+q^{9}-q^{11}-q^{13}+\cdots$
140.1.h.a	$140$	$1$	140.h	35.c	$2$	$1$	$1$	$0.070$	$\Q$	$D_{3}$	$\Q(\sqrt{-35}) $	None	✓	$2$	$0$	$0$	$-1$	$1$	$1$	$1$		$q-q^{3}+q^{5}+q^{7}-q^{11}-q^{13}-q^{15}+\cdots$
140.1.h.b	$140$	$1$	140.h	35.c	$2$	$1$	$1$	$0.070$	$\Q$	$D_{3}$	$\Q(\sqrt{-35}) $	None	✓	$2$	$0$	$0$	$1$	$-1$	$-1$	$1$		$q+q^{3}-q^{5}-q^{7}-q^{11}+q^{13}-q^{15}+\cdots$
143.1.d.a	$143$	$1$	143.d	143.d	$2$	$2$	$2$	$0.071$	$\Q(\sqrt{5}) $	$D_{5}$	$\Q(\sqrt{-143}) $	None	✓	$2$	$0$	$-1$	$-1$	$0$	$-1$	$1$		$q+(-1+\beta )q^{2}+(-1+\beta )q^{3}+(1-\beta )q^{4}+\cdots$
143.1.d.b	$143$	$1$	143.d	143.d	$2$	$2$	$2$	$0.071$	$\Q(\sqrt{5}) $	$D_{5}$	$\Q(\sqrt{-143}) $	None	✓	$2$	$0$	$1$	$-1$	$0$	$1$	$1$		$q+(1-\beta )q^{2}+(-1+\beta )q^{3}+(1-\beta )q^{4}+\cdots$
148.1.f.a	$148$	$1$	148.f	37.d	$4$	$2$	$1$	$0.074$	$\Q(\sqrt{-1}) $	$S_{4}$	None	None		$2$	$0$	$0$	$0$	$0$	$-2$	$1$		$q+iq^{3}-q^{7}-iq^{11}+(-1-i)q^{17}+\cdots$
151.1.b.a	$151$	$1$	151.b	151.b	$2$	$3$	$3$	$0.075$	$\Q(\zeta_{14})^+$	$D_{7}$	$\Q(\sqrt{-151}) $	None	✓	$2$	$0$	$-1$	$0$	$-1$	$0$	$1$		$q-\beta _{1}q^{2}+(1+\beta _{2})q^{4}+(-1+\beta _{1}-\beta _{2})q^{5}+\cdots$
152.1.g.a	$152$	$1$	152.g	152.g	$2$	$1$	$1$	$0.076$	$\Q$	$D_{3}$	$\Q(\sqrt{-38}) $	None	✓	$2$	$0$	$-1$	$1$	$0$	$-1$	$1$		$q-q^{2}+q^{3}+q^{4}-q^{6}-q^{7}-q^{8}+\cdots$
152.1.g.b	$152$	$1$	152.g	152.g	$2$	$1$	$1$	$0.076$	$\Q$	$D_{3}$	$\Q(\sqrt{-38}) $	None	✓	$2$	$0$	$1$	$-1$	$0$	$-1$	$1$		$q+q^{2}-q^{3}+q^{4}-q^{6}-q^{7}+q^{8}+\cdots$
159.1.d.a	$159$	$1$	159.d	159.d	$2$	$2$	$2$	$0.079$	$\Q(\sqrt{5}) $	$D_{5}$	$\Q(\sqrt{-159}) $	None	✓	$2$	$0$	$-1$	$2$	$-1$	$-1$	$1$		$q+(-1+\beta )q^{2}+q^{3}+(1-\beta )q^{4}-\beta q^{5}+\cdots$
159.1.d.b	$159$	$1$	159.d	159.d	$2$	$2$	$2$	$0.079$	$\Q(\sqrt{5}) $	$D_{5}$	$\Q(\sqrt{-159}) $	None	✓	$2$	$0$	$1$	$-2$	$1$	$-1$	$1$		$q+(1-\beta )q^{2}-q^{3}+(1-\beta )q^{4}+\beta q^{5}+\cdots$
167.1.b.a	$167$	$1$	167.b	167.b	$2$	$5$	$5$	$0.083$	$\Q(\zeta_{22})^+$	$D_{11}$	$\Q(\sqrt{-167}) $	None	✓	$2$	$0$	$-1$	$-1$	$0$	$-1$	$1$		$q+\beta _{4}q^{2}+(-1+\beta _{1}-\beta _{2}+\beta _{3}-\beta _{4})q^{3}+\cdots$
172.1.b.a	$172$	$1$	172.b	43.b	$2$	$1$	$1$	$0.086$	$\Q$	$D_{3}$	$\Q(\sqrt{-43}) $	None	✓	$2$	$0$	$0$	$0$	$0$	$0$	$1$		$q+q^{9}-q^{11}-q^{13}-q^{17}-q^{23}+\cdots$
175.1.d.a	$175$	$1$	175.d	7.b	$2$	$1$	$1$	$0.087$	$\Q$	$D_{3}$	$\Q(\sqrt{-7}) $	None	✓	$2$	$0$	$-1$	$0$	$0$	$1$	$1$		$q-q^{2}+q^{7}+q^{8}+q^{9}-q^{11}-q^{14}+\cdots$
175.1.d.b	$175$	$1$	175.d	7.b	$2$	$1$	$1$	$0.087$	$\Q$	$D_{3}$	$\Q(\sqrt{-7}) $	None	✓	$2$	$0$	$1$	$0$	$0$	$-1$	$1$		$q+q^{2}-q^{7}-q^{8}+q^{9}-q^{11}-q^{14}+\cdots$
176.1.h.a	$176$	$1$	176.h	11.b	$2$	$1$	$1$	$0.088$	$\Q$	$D_{3}$	$\Q(\sqrt{-11}) $	None	✓	$2$	$0$	$0$	$1$	$-1$	$0$	$1$		$q+q^{3}-q^{5}-q^{11}-q^{15}+q^{23}-q^{27}+\cdots$
179.1.b.a	$179$	$1$	179.b	179.b	$2$	$2$	$2$	$0.089$	$\Q(\sqrt{5}) $	$D_{5}$	$\Q(\sqrt{-179}) $	None	✓	$2$	$0$	$0$	$-1$	$-1$	$0$	$1$		$q+(-1+\beta )q^{3}+q^{4}-\beta q^{5}+(1-\beta )q^{9}+\cdots$
191.1.b.a	$191$	$1$	191.b	191.b	$2$	$6$	$6$	$0.095$	$\Q(\zeta_{26})^+$	$D_{13}$	$\Q(\sqrt{-191}) $	None	✓	$2$	$0$	$-1$	$-1$	$-1$	$0$	$1$		$q-\beta _{3}q^{2}-\beta _{1}q^{3}+(\beta _{1}-\beta _{2}+\beta _{3}-\beta _{4}+\cdots)q^{4}+\cdots$
199.1.b.a	$199$	$1$	199.b	199.b	$2$	$1$	$1$	$0.099$	$\Q$	$D_{3}$	$\Q(\sqrt{-199}) $	None	✓	$2$	$0$	$-1$	$0$	$-1$	$2$	$1$		$q-q^{2}-q^{5}+2q^{7}+q^{8}+q^{9}+q^{10}+\cdots$
199.1.b.b	$199$	$1$	199.b	199.b	$2$	$3$	$3$	$0.099$	$\Q(\zeta_{18})^+$	$D_{9}$	$\Q(\sqrt{-199}) $	None	✓	$2$	$0$	$0$	$0$	$0$	$-3$	$1$		$q-\beta _{1}q^{2}+(1+\beta _{2})q^{4}+(\beta _{1}-\beta _{2})q^{5}+\cdots$
200.1.g.a	$200$	$1$	200.g	8.d	$2$	$1$	$1$	$0.100$	$\Q$	$D_{3}$	$\Q(\sqrt{-2}) $	None	✓	$2$	$0$	$-1$	$1$	$0$	$0$	$1$		$q-q^{2}+q^{3}+q^{4}-q^{6}-q^{8}-q^{11}+\cdots$
200.1.g.b	$200$	$1$	200.g	8.d	$2$	$1$	$1$	$0.100$	$\Q$	$D_{3}$	$\Q(\sqrt{-2}) $	None	✓	$2$	$0$	$1$	$-1$	$0$	$0$	$1$		$q+q^{2}-q^{3}+q^{4}-q^{6}+q^{8}-q^{11}+\cdots$
204.1.g.a	$204$	$1$	204.g	51.c	$2$	$1$	$1$	$0.102$	$\Q$	$D_{3}$	$\Q(\sqrt{-51}) $	None	✓	$2$	$0$	$0$	$-1$	$1$	$0$	$1$		$q-q^{3}+q^{5}+q^{9}+q^{11}-q^{13}-q^{15}+\cdots$
204.1.g.b	$204$	$1$	204.g	51.c	$2$	$1$	$1$	$0.102$	$\Q$	$D_{3}$	$\Q(\sqrt{-51}) $	None	✓	$2$	$0$	$0$	$1$	$-1$	$0$	$1$		$q+q^{3}-q^{5}+q^{9}-q^{11}-q^{13}-q^{15}+\cdots$
207.1.d.a	$207$	$1$	207.d	23.b	$2$	$1$	$1$	$0.103$	$\Q$	$D_{3}$	$\Q(\sqrt{-23}) $	None	✓	$2$	$0$	$1$	$0$	$0$	$0$	$1$		$q+q^{2}-q^{8}-q^{13}-q^{16}-q^{23}+q^{25}+\cdots$
13.2.e.a	$13$	$2$	13.e	13.e	$6$	$2$	$1$	$0.104$	$\Q(\sqrt{-3}) $	$_{}$	None	None		$2$	$0$	$-3$	$-2$	$0$	$0$	$1$	$\mathrm{SU}(2)[C_{6}]$	$q+(-1-\zeta_{6})q^{2}+(-2+2\zeta_{6})q^{3}+\zeta_{6}q^{4}+\cdots$

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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.