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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
2001.4.a.a	$2001$	$4$	2001.a	1.a	$1$	$31$	$31$	$118.063$		None	✓	$1$	$1$	$-10$	$93$	$-25$	$-76$	$-$		$\mathrm{SU}(2)$
2001.4.a.b	$2001$	$4$	2001.a	1.a	$1$	$36$	$36$	$118.063$		None	✓	$1$	$1$	$2$	$108$	$-15$	$-48$	$-$		$\mathrm{SU}(2)$
2001.4.a.c	$2001$	$4$	2001.a	1.a	$1$	$37$	$37$	$118.063$		None	✓	$1$	$1$	$-8$	$-111$	$-15$	$-6$	$-$		$\mathrm{SU}(2)$
2001.4.a.d	$2001$	$4$	2001.a	1.a	$1$	$37$	$37$	$118.063$		None	✓	$1$	$0$	$4$	$-111$	$15$	$8$	$+$		$\mathrm{SU}(2)$
2001.4.a.e	$2001$	$4$	2001.a	1.a	$1$	$38$	$38$	$118.063$		None	✓	$1$	$1$	$0$	$-114$	$-25$	$-34$	$-$		$\mathrm{SU}(2)$
2001.4.a.f	$2001$	$4$	2001.a	1.a	$1$	$42$	$42$	$118.063$		None	✓	$1$	$0$	$4$	$-126$	$25$	$36$	$+$		$\mathrm{SU}(2)$
2001.4.a.g	$2001$	$4$	2001.a	1.a	$1$	$43$	$43$	$118.063$		None	✓	$1$	$0$	$2$	$129$	$25$	$106$	$+$		$\mathrm{SU}(2)$
2001.4.a.h	$2001$	$4$	2001.a	1.a	$1$	$44$	$44$	$118.063$		None	✓	$1$	$0$	$6$	$132$	$15$	$78$	$+$		$\mathrm{SU}(2)$
2002.4.a.a	$2002$	$4$	2002.a	1.a	$1$	$1$	$1$	$118.122$	$\Q$	None	✓	$1$	$1$	$2$	$-2$	$-3$	$7$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{2}-2q^{3}+4q^{4}-3q^{5}-4q^{6}+\cdots$
2002.4.a.b	$2002$	$4$	2002.a	1.a	$1$	$8$	$8$	$118.122$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	None	✓	$1$	$1$	$16$	$-5$	$-25$	$56$	$-$	$3^{3}$	$\mathrm{SU}(2)$	$q+2q^{2}+(-1+\beta _{1})q^{3}+4q^{4}+(-3+\cdots)q^{5}+\cdots$
2002.4.a.c	$2002$	$4$	2002.a	1.a	$1$	$9$	$9$	$118.122$	$\mathbb{Q}[x]/(x^{9} - \cdots)$	None	✓	$1$	$1$	$18$	$-6$	$-24$	$-63$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{2}+(-1+\beta _{1})q^{3}+4q^{4}+(-2+\cdots)q^{5}+\cdots$
2002.4.a.d	$2002$	$4$	2002.a	1.a	$1$	$10$	$10$	$118.122$	$\mathbb{Q}[x]/(x^{10} - \cdots)$	None	✓	$1$	$0$	$-20$	$0$	$12$	$70$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{2}-\beta _{1}q^{3}+4q^{4}+(1+\beta _{6})q^{5}+\cdots$
2002.4.a.e	$2002$	$4$	2002.a	1.a	$1$	$10$	$10$	$118.122$	$\mathbb{Q}[x]/(x^{10} - \cdots)$	None	✓	$1$	$0$	$-20$	$11$	$22$	$-70$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{2}+(1+\beta _{1})q^{3}+4q^{4}+(2+\beta _{6}+\cdots)q^{5}+\cdots$
2002.4.a.f	$2002$	$4$	2002.a	1.a	$1$	$10$	$10$	$118.122$	$\mathbb{Q}[x]/(x^{10} - \cdots)$	None	✓	$1$	$1$	$20$	$-18$	$-38$	$70$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{2}+(-2+\beta _{1})q^{3}+4q^{4}+(-4+\cdots)q^{5}+\cdots$
2002.4.a.g	$2002$	$4$	2002.a	1.a	$1$	$10$	$10$	$118.122$	$\mathbb{Q}[x]/(x^{10} - \cdots)$	None	✓	$1$	$1$	$20$	$5$	$2$	$-70$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{2}+(1-\beta _{1})q^{3}+4q^{4}-\beta _{3}q^{5}+\cdots$
2002.4.a.h	$2002$	$4$	2002.a	1.a	$1$	$11$	$11$	$118.122$	$\mathbb{Q}[x]/(x^{11} - \cdots)$	None	✓	$1$	$1$	$-22$	$-4$	$4$	$-77$	$-$	$2^{6}$	$\mathrm{SU}(2)$	$q-2q^{2}-\beta _{1}q^{3}+4q^{4}+\beta _{5}q^{5}+2\beta _{1}q^{6}+\cdots$
2002.4.a.i	$2002$	$4$	2002.a	1.a	$1$	$11$	$11$	$118.122$	$\mathbb{Q}[x]/(x^{11} - \cdots)$	None	✓	$1$	$0$	$-22$	$0$	$-14$	$-77$	$+$	$2$	$\mathrm{SU}(2)$	$q-2q^{2}+\beta _{1}q^{3}+4q^{4}+(-1+\beta _{5}+\cdots)q^{5}+\cdots$
2002.4.a.j	$2002$	$4$	2002.a	1.a	$1$	$11$	$11$	$118.122$	$\mathbb{Q}[x]/(x^{11} - \cdots)$	None	✓	$1$	$0$	$-22$	$11$	$12$	$77$	$+$	$2\cdot 3$	$\mathrm{SU}(2)$	$q-2q^{2}+(1-\beta _{1})q^{3}+4q^{4}+(1+\beta _{5}+\cdots)q^{5}+\cdots$
2002.4.a.k	$2002$	$4$	2002.a	1.a	$1$	$12$	$12$	$118.122$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	None	✓	$1$	$1$	$-24$	$-9$	$-36$	$84$	$-$	$2^{4}$	$\mathrm{SU}(2)$	$q-2q^{2}+(-1+\beta _{1})q^{3}+4q^{4}+(-3+\cdots)q^{5}+\cdots$
2002.4.a.l	$2002$	$4$	2002.a	1.a	$1$	$12$	$12$	$118.122$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	None	✓	$1$	$1$	$-24$	$2$	$-10$	$84$	$-$	$2^{5}$	$\mathrm{SU}(2)$	$q-2q^{2}+\beta _{1}q^{3}+4q^{4}+(-1-\beta _{4}+\cdots)q^{5}+\cdots$
2002.4.a.m	$2002$	$4$	2002.a	1.a	$1$	$12$	$12$	$118.122$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	None	✓	$1$	$0$	$24$	$14$	$40$	$84$	$+$	$2^{5}$	$\mathrm{SU}(2)$	$q+2q^{2}+(1+\beta _{1})q^{3}+4q^{4}+(3-\beta _{5}+\cdots)q^{5}+\cdots$
2002.4.a.n	$2002$	$4$	2002.a	1.a	$1$	$13$	$13$	$118.122$	$\mathbb{Q}[x]/(x^{13} - \cdots)$	None	✓	$1$	$1$	$-26$	$-3$	$-6$	$-91$	$-$	$2^{4}\cdot 5$	$\mathrm{SU}(2)$	$q-2q^{2}-\beta _{1}q^{3}+4q^{4}+\beta _{3}q^{5}+2\beta _{1}q^{6}+\cdots$
2002.4.a.o	$2002$	$4$	2002.a	1.a	$1$	$13$	$13$	$118.122$	$\mathbb{Q}[x]/(x^{13} - \cdots)$	None	✓	$1$	$0$	$26$	$-3$	$-6$	$-91$	$+$	$2^{4}\cdot 7$	$\mathrm{SU}(2)$	$q+2q^{2}-\beta _{1}q^{3}+4q^{4}+\beta _{3}q^{5}-2\beta _{1}q^{6}+\cdots$
2002.4.a.p	$2002$	$4$	2002.a	1.a	$1$	$13$	$13$	$118.122$	$\mathbb{Q}[x]/(x^{13} - \cdots)$	None	✓	$1$	$0$	$26$	$8$	$14$	$-91$	$+$	$2^{6}$	$\mathrm{SU}(2)$	$q+2q^{2}+(1-\beta _{1})q^{3}+4q^{4}+(1+\beta _{3}+\cdots)q^{5}+\cdots$
2002.4.a.q	$2002$	$4$	2002.a	1.a	$1$	$14$	$14$	$118.122$	$\mathbb{Q}[x]/(x^{14} - \cdots)$	None	✓	$1$	$0$	$28$	$15$	$24$	$98$	$+$	$2^{6}\cdot 3^{3}$	$\mathrm{SU}(2)$	$q+2q^{2}+(1+\beta _{1})q^{3}+4q^{4}+(2-\beta _{4}+\cdots)q^{5}+\cdots$
2003.4.a.a	$2003$	$4$	2003.a	1.a	$1$	$241$	$241$	$118.181$		None	✓	$1$	$1$	$-14$	$-57$	$-135$	$-282$	$-$		$\mathrm{SU}(2)$
2003.4.a.b	$2003$	$4$	2003.a	1.a	$1$	$259$	$259$	$118.181$		None	✓	$1$	$0$	$16$	$57$	$135$	$306$	$+$		$\mathrm{SU}(2)$
2004.4.a.a	$2004$	$4$	2004.a	1.a	$1$	$18$	$18$	$118.240$	$\mathbb{Q}[x]/(x^{18} - \cdots)$	None	✓	$1$	$1$	$0$	$54$	$-24$	$-22$	$-$	$2^{9}$	$\mathrm{SU}(2)$	$q+3q^{3}+(-1-\beta _{1})q^{5}+(-1+\beta _{5}+\cdots)q^{7}+\cdots$
2004.4.a.b	$2004$	$4$	2004.a	1.a	$1$	$19$	$19$	$118.240$	$\mathbb{Q}[x]/(x^{19} - \cdots)$	None	✓	$1$	$1$	$0$	$-57$	$-8$	$-14$	$-$	$2^{8}$	$\mathrm{SU}(2)$	$q-3q^{3}-\beta _{1}q^{5}+(-1-\beta _{10})q^{7}+9q^{9}+\cdots$
2004.4.a.c	$2004$	$4$	2004.a	1.a	$1$	$22$	$22$	$118.240$		None	✓	$1$	$0$	$0$	$66$	$56$	$6$	$+$		$\mathrm{SU}(2)$
2004.4.a.d	$2004$	$4$	2004.a	1.a	$1$	$23$	$23$	$118.240$		None	✓	$1$	$0$	$0$	$-69$	$12$	$14$	$+$		$\mathrm{SU}(2)$
2005.4.a.a	$2005$	$4$	2005.a	1.a	$1$	$96$	$96$	$118.299$		None	✓	$1$	$1$	$-27$	$-42$	$480$	$-274$	$-$		$\mathrm{SU}(2)$
2005.4.a.b	$2005$	$4$	2005.a	1.a	$1$	$96$	$96$	$118.299$		None	✓	$1$	$1$	$-9$	$-12$	$-480$	$86$	$-$		$\mathrm{SU}(2)$
2005.4.a.c	$2005$	$4$	2005.a	1.a	$1$	$104$	$104$	$118.299$		None	✓	$1$	$0$	$15$	$6$	$-520$	$-110$	$+$		$\mathrm{SU}(2)$
2005.4.a.d	$2005$	$4$	2005.a	1.a	$1$	$104$	$104$	$118.299$		None	✓	$1$	$0$	$21$	$48$	$520$	$258$	$+$		$\mathrm{SU}(2)$
2006.4.a.a	$2006$	$4$	2006.a	1.a	$1$	$25$	$25$	$118.358$		None	✓	$1$	$1$	$50$	$-28$	$-18$	$-79$	$-$		$\mathrm{SU}(2)$
2006.4.a.b	$2006$	$4$	2006.a	1.a	$1$	$26$	$26$	$118.358$		None	✓	$1$	$1$	$-52$	$-2$	$-18$	$-17$	$-$		$\mathrm{SU}(2)$
2006.4.a.c	$2006$	$4$	2006.a	1.a	$1$	$26$	$26$	$118.358$		None	✓	$1$	$1$	$52$	$-10$	$-12$	$-23$	$-$		$\mathrm{SU}(2)$
2006.4.a.d	$2006$	$4$	2006.a	1.a	$1$	$27$	$27$	$118.358$		None	✓	$1$	$1$	$-54$	$10$	$-12$	$-31$	$-$		$\mathrm{SU}(2)$
2006.4.a.e	$2006$	$4$	2006.a	1.a	$1$	$31$	$31$	$118.358$		None	✓	$1$	$0$	$-62$	$4$	$32$	$-3$	$+$		$\mathrm{SU}(2)$
2006.4.a.f	$2006$	$4$	2006.a	1.a	$1$	$32$	$32$	$118.358$		None	✓	$1$	$0$	$-64$	$-2$	$-12$	$11$	$+$		$\mathrm{SU}(2)$
2006.4.a.g	$2006$	$4$	2006.a	1.a	$1$	$32$	$32$	$118.358$		None	✓	$1$	$0$	$64$	$26$	$32$	$103$	$+$		$\mathrm{SU}(2)$
2006.4.a.h	$2006$	$4$	2006.a	1.a	$1$	$33$	$33$	$118.358$		None	✓	$1$	$0$	$66$	$14$	$-12$	$47$	$+$		$\mathrm{SU}(2)$
2007.4.a.a	$2007$	$4$	2007.a	1.a	$1$	$23$	$23$	$118.417$		None	✓	$1$	$1$	$6$	$0$	$20$	$-107$	$-$		$\mathrm{SU}(2)$
2007.4.a.b	$2007$	$4$	2007.a	1.a	$1$	$24$	$24$	$118.417$		None	✓	$1$	$0$	$17$	$0$	$50$	$-61$	$+$		$\mathrm{SU}(2)$
2007.4.a.c	$2007$	$4$	2007.a	1.a	$1$	$26$	$26$	$118.417$		None	✓	$1$	$1$	$-6$	$0$	$-20$	$5$	$-$		$\mathrm{SU}(2)$
2007.4.a.d	$2007$	$4$	2007.a	1.a	$1$	$30$	$30$	$118.417$		None	✓	$1$	$0$	$4$	$0$	$30$	$5$	$+$		$\mathrm{SU}(2)$
2007.4.a.e	$2007$	$4$	2007.a	1.a	$1$	$31$	$31$	$118.417$		None	✓	$1$	$1$	$-15$	$0$	$-50$	$51$	$-$		$\mathrm{SU}(2)$
2007.4.a.f	$2007$	$4$	2007.a	1.a	$1$	$33$	$33$	$118.417$		None	✓	$1$	$0$	$-4$	$0$	$-30$	$117$	$+$		$\mathrm{SU}(2)$
2007.4.a.g	$2007$	$4$	2007.a	1.a	$1$	$48$	$48$	$118.417$		None	✓	$2$	$1$	$0$	$0$	$0$	$-122$	$-$		$\mathrm{SU}(2)$

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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.