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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
841.2.a.a	$841$	$2$	841.a	1.a	$1$	$2$	$2$	$6.715$	$\Q(\sqrt{5}) $	None	✓	$1$	$1$	$-1$	$1$	$1$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta q^{2}+\beta q^{3}+(-1+\beta )q^{4}+(2-3\beta )q^{5}+\cdots$
841.2.a.b	$841$	$2$	841.a	1.a	$1$	$2$	$2$	$6.715$	$\Q(\sqrt{5}) $	None	✓	$2$	$0$	$0$	$0$	$6$	$4$	$-$	$2$	$\mathrm{SU}(2)$	$q-\beta q^{2}+\beta q^{3}+3q^{4}+3q^{5}-5q^{6}+\cdots$
841.2.a.c	$841$	$2$	841.a	1.a	$1$	$2$	$2$	$6.715$	$\Q(\sqrt{5}) $	None	✓	$1$	$0$	$1$	$-1$	$1$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{2}-\beta q^{3}+(-1+\beta )q^{4}+(2-3\beta )q^{5}+\cdots$
841.2.a.d	$841$	$2$	841.a	1.a	$1$	$2$	$2$	$6.715$	$\Q(\sqrt{2}) $	None	✓	$1$	$1$	$2$	$-2$	$-2$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+(1+\beta )q^{2}+(-1-\beta )q^{3}+(1+2\beta )q^{4}+\cdots$
841.2.a.e	$841$	$2$	841.a	1.a	$1$	$3$	$3$	$6.715$	$\Q(\zeta_{14})^+$	None	✓	$1$	$1$	$-1$	$1$	$-3$	$-3$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+(1-\beta _{1}+\beta _{2})q^{3}+\beta _{2}q^{4}+\cdots$
841.2.a.f	$841$	$2$	841.a	1.a	$1$	$3$	$3$	$6.715$	$\Q(\zeta_{14})^+$	None	✓	$1$	$1$	$1$	$-1$	$-3$	$-3$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+(-1+\beta _{1}-\beta _{2})q^{3}+\beta _{2}q^{4}+\cdots$
841.2.a.g	$841$	$2$	841.a	1.a	$1$	$6$	$6$	$6.715$	6.6.11973625.1	None	✓	$1$	$1$	$-2$	$-2$	$-2$	$-4$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+\beta _{5}q^{3}+(2-\beta _{3}+\beta _{4})q^{4}+\cdots$
841.2.a.h	$841$	$2$	841.a	1.a	$1$	$6$	$6$	$6.715$	6.6.11973625.1	None	✓	$1$	$0$	$2$	$2$	$-2$	$-4$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}-\beta _{5}q^{3}+(2-\beta _{3}+\beta _{4})q^{4}+\cdots$
841.2.a.i	$841$	$2$	841.a	1.a	$1$	$8$	$8$	$6.715$	8.8.2841328125.1	None	✓	$1$	$1$	$-4$	$-6$	$-1$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+(-1+\beta _{5})q^{3}+(\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots$
841.2.a.j	$841$	$2$	841.a	1.a	$1$	$8$	$8$	$6.715$	8.8.2841328125.1	None	✓	$1$	$0$	$4$	$6$	$-1$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+(1-\beta _{5})q^{3}+(\beta _{1}+\beta _{2})q^{4}+\cdots$
841.2.a.k	$841$	$2$	841.a	1.a	$1$	$12$	$12$	$6.715$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	None	✓	$2$	$0$	$0$	$0$	$8$	$10$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{11}q^{2}+(-\beta _{6}-\beta _{9})q^{3}+(1-\beta _{1}+\cdots)q^{4}+\cdots$
841.2.b.a	$841$	$2$	841.b	29.b	$2$	$4$	$4$	$6.715$	$\Q(\zeta_{8})$	None		$2$	$0$	$0$	$0$	$4$	$0$		$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	$q+\zeta_{8}q^{2}-\zeta_{8}q^{3}+(-1-\zeta_{8}^{3})q^{4}+\cdots$
841.2.b.b	$841$	$2$	841.b	29.b	$2$	$4$	$4$	$6.715$	$\Q(i, \sqrt{5})$	None		$2$	$0$	$0$	$0$	$-2$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{2}-\beta _{1}q^{3}+(1+\beta _{2})q^{4}+(-2+\cdots)q^{5}+\cdots$
841.2.b.c	$841$	$2$	841.b	29.b	$2$	$6$	$6$	$6.715$	6.0.153664.1	None		$2$	$0$	$0$	$0$	$6$	$-6$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{2}+\beta _{3}q^{3}+\beta _{2}q^{4}+(2-\beta _{2}+\cdots)q^{5}+\cdots$
841.2.b.d	$841$	$2$	841.b	29.b	$2$	$12$	$12$	$6.715$	$\mathbb{Q}[x]/(x^{12} + \cdots)$	None		$2$	$0$	$0$	$0$	$4$	$-8$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{2}+\beta _{8}q^{3}+(-2+\beta _{2}-\beta _{3}+\cdots)q^{4}+\cdots$
841.2.b.e	$841$	$2$	841.b	29.b	$2$	$12$	$12$	$6.715$	12.0.$\cdots$.1	None		$2$	$0$	$0$	$0$	$-8$	$10$		$2^{6}$	$\mathrm{SU}(2)[C_{2}]$	$q+(-\beta _{1}+\beta _{11})q^{2}+(-\beta _{5}+\beta _{11})q^{3}+\cdots$
841.2.b.f	$841$	$2$	841.b	29.b	$2$	$16$	$16$	$6.715$	$\mathbb{Q}[x]/(x^{16} + \cdots)$	None		$2$	$0$	$0$	$0$	$2$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{2}+(\beta _{6}-\beta _{9}-\beta _{15})q^{3}+(-1+\cdots)q^{4}+\cdots$
841.2.d.a	$841$	$2$	841.d	29.d	$7$	$6$	$1$	$6.715$	$\Q(\zeta_{14})$	None		$2$	$1$	$-5$	$-2$	$-6$	$-6$		$1$	$\mathrm{SU}(2)[C_{7}]$	$q+(-1+\zeta_{14})q^{2}+(-\zeta_{14}+\zeta_{14}^{4}+\cdots)q^{3}+\cdots$
841.2.d.b	$841$	$2$	841.d	29.d	$7$	$6$	$1$	$6.715$	$\Q(\zeta_{14})$	None		$2$	$0$	$-2$	$2$	$8$	$8$		$1$	$\mathrm{SU}(2)[C_{7}]$	$q+(-\zeta_{14}^{3}-\zeta_{14}^{5})q^{2}+(-\zeta_{14}^{2}+\zeta_{14}^{3}+\cdots)q^{3}+\cdots$
841.2.d.c	$841$	$2$	841.d	29.d	$7$	$6$	$1$	$6.715$	$\Q(\zeta_{14})$	None		$2$	$0$	$2$	$-2$	$8$	$8$		$1$	$\mathrm{SU}(2)[C_{7}]$	$q+(\zeta_{14}^{3}+\zeta_{14}^{5})q^{2}+(\zeta_{14}^{2}-\zeta_{14}^{3}+\cdots)q^{3}+\cdots$
841.2.d.d	$841$	$2$	841.d	29.d	$7$	$6$	$1$	$6.715$	$\Q(\zeta_{14})$	None		$2$	$0$	$2$	$5$	$1$	$1$		$1$	$\mathrm{SU}(2)[C_{7}]$	$q+(1-\zeta_{14}-\zeta_{14}^{3}+\zeta_{14}^{4}-\zeta_{14}^{5})q^{2}+\cdots$
841.2.d.e	$841$	$2$	841.d	29.d	$7$	$6$	$1$	$6.715$	$\Q(\zeta_{14})$	None		$2$	$0$	$5$	$2$	$-6$	$-6$		$1$	$\mathrm{SU}(2)[C_{7}]$	$q+(1-\zeta_{14})q^{2}+(\zeta_{14}-\zeta_{14}^{4})q^{3}+(1+\cdots)q^{4}+\cdots$
841.2.d.f	$841$	$2$	841.d	29.d	$7$	$12$	$2$	$6.715$	12.0.$\cdots$.2	None		$6$	$0$	$-2$	$2$	$2$	$0$		$1$	$\mathrm{SU}(2)[C_{7}]$	$q+(\beta _{1}+\beta _{8})q^{2}+(1+\beta _{2}+\beta _{4}-\beta _{5}+\cdots)q^{3}+\cdots$
841.2.d.g	$841$	$2$	841.d	29.d	$7$	$12$	$2$	$6.715$	12.0.$\cdots$.1	None		$6$	$0$	$-1$	$1$	$-1$	$0$		$1$	$\mathrm{SU}(2)[C_{7}]$	$q-\beta _{1}q^{2}-\beta _{10}q^{3}+(\beta _{4}-\beta _{5})q^{4}+(3\beta _{1}+\cdots)q^{5}+\cdots$
841.2.d.h	$841$	$2$	841.d	29.d	$7$	$12$	$2$	$6.715$	12.0.$\cdots$.1	None		$12$	$0$	$0$	$0$	$-6$	$-4$		$2^{6}$	$\mathrm{SU}(2)[C_{7}]$	$q+\beta _{6}q^{2}-\beta _{9}q^{3}+3\beta _{5}q^{4}+3\beta _{3}q^{5}+\cdots$
841.2.d.i	$841$	$2$	841.d	29.d	$7$	$12$	$2$	$6.715$	12.0.$\cdots$.1	None		$6$	$0$	$1$	$-1$	$-1$	$0$		$1$	$\mathrm{SU}(2)[C_{7}]$	$q+\beta _{1}q^{2}+\beta _{10}q^{3}+(\beta _{4}-\beta _{5})q^{4}+(3\beta _{1}+\cdots)q^{5}+\cdots$
841.2.d.j	$841$	$2$	841.d	29.d	$7$	$12$	$2$	$6.715$	12.0.$\cdots$.2	None		$6$	$0$	$2$	$-2$	$2$	$0$		$1$	$\mathrm{SU}(2)[C_{7}]$	$q+(-\beta _{2}+\beta _{9})q^{2}+(-\beta _{3}+\beta _{10})q^{3}+\cdots$
841.2.d.k	$841$	$2$	841.d	29.d	$7$	$24$	$4$	$6.715$		None		$4$	$0$	$0$	$0$	$2$	$20$			$\mathrm{SU}(2)[C_{7}]$
841.2.d.l	$841$	$2$	841.d	29.d	$7$	$24$	$4$	$6.715$		None		$4$	$0$	$0$	$0$	$-12$	$-8$			$\mathrm{SU}(2)[C_{7}]$
841.2.d.m	$841$	$2$	841.d	29.d	$7$	$24$	$4$	$6.715$		None		$4$	$0$	$0$	$0$	$2$	$-22$			$\mathrm{SU}(2)[C_{7}]$
841.2.d.n	$841$	$2$	841.d	29.d	$7$	$36$	$6$	$6.715$		None		$6$	$0$	$-2$	$-2$	$2$	$4$			$\mathrm{SU}(2)[C_{7}]$
841.2.d.o	$841$	$2$	841.d	29.d	$7$	$36$	$6$	$6.715$		None		$6$	$0$	$2$	$2$	$2$	$4$			$\mathrm{SU}(2)[C_{7}]$
841.2.d.p	$841$	$2$	841.d	29.d	$7$	$48$	$8$	$6.715$		None		$6$	$0$	$-4$	$-6$	$1$	$0$			$\mathrm{SU}(2)[C_{7}]$
841.2.d.q	$841$	$2$	841.d	29.d	$7$	$48$	$8$	$6.715$		None		$6$	$0$	$4$	$6$	$1$	$0$			$\mathrm{SU}(2)[C_{7}]$
841.2.e.a	$841$	$2$	841.e	29.e	$14$	$12$	$2$	$6.715$	12.0.$\cdots$.1	None		$2$	$0$	$-7$	$0$	$6$	$-4$		$1$	$\mathrm{SU}(2)[C_{14}]$	$q+(1+2\beta _{1}-\beta _{3}-\beta _{4}+\beta _{5}-\beta _{6}-\beta _{9}+\cdots)q^{2}+\cdots$
841.2.e.b	$841$	$2$	841.e	29.e	$14$	$12$	$2$	$6.715$	$\Q(\zeta_{28})$	None		$4$	$0$	$0$	$0$	$12$	$-12$		$1$	$\mathrm{SU}(2)[C_{14}]$	$q+(-\zeta_{28}^{7}+\zeta_{28}^{9})q^{2}+(-\zeta_{28}-\zeta_{28}^{9}+\cdots)q^{3}+\cdots$
841.2.e.c	$841$	$2$	841.e	29.e	$14$	$12$	$2$	$6.715$	$\Q(\zeta_{28})$	None		$4$	$0$	$0$	$0$	$-16$	$16$		$1$	$\mathrm{SU}(2)[C_{14}]$	$q+(-\zeta_{28}-\zeta_{28}^{5}+\zeta_{28}^{7}-\zeta_{28}^{9}+\cdots)q^{2}+\cdots$
841.2.e.d	$841$	$2$	841.e	29.e	$14$	$12$	$2$	$6.715$	$\Q(\zeta_{28})$	None		$4$	$0$	$0$	$0$	$-2$	$2$		$1$	$\mathrm{SU}(2)[C_{14}]$	$q+(-\zeta_{28}^{3}+\zeta_{28}^{9})q^{2}+(\zeta_{28}^{7}+\zeta_{28}^{11})q^{3}+\cdots$
841.2.e.e	$841$	$2$	841.e	29.e	$14$	$12$	$2$	$6.715$	12.0.$\cdots$.1	None		$2$	$0$	$0$	$0$	$-1$	$10$		$1$	$\mathrm{SU}(2)[C_{14}]$	$q+(\beta _{4}-\beta _{10}+\beta _{11})q^{2}+(1+2\beta _{1}+\beta _{2}+\cdots)q^{3}+\cdots$
841.2.e.f	$841$	$2$	841.e	29.e	$14$	$12$	$2$	$6.715$	12.0.$\cdots$.1	None		$2$	$0$	$0$	$0$	$-1$	$10$		$1$	$\mathrm{SU}(2)[C_{14}]$	$q+(-\beta _{4}-\beta _{8}-\beta _{11})q^{2}+(-\beta _{1}-\beta _{2}+\cdots)q^{3}+\cdots$
841.2.e.g	$841$	$2$	841.e	29.e	$14$	$12$	$2$	$6.715$	12.0.$\cdots$.3	None		$12$	$0$	$0$	$0$	$6$	$-4$		$1$	$\mathrm{SU}(2)[C_{14}]$	$q+\beta _{1}q^{2}-\beta _{5}q^{3}+3\beta _{2}q^{4}-3\beta _{8}q^{5}+\cdots$
841.2.e.h	$841$	$2$	841.e	29.e	$14$	$12$	$2$	$6.715$	12.0.$\cdots$.1	None		$2$	$0$	$7$	$0$	$6$	$-4$		$1$	$\mathrm{SU}(2)[C_{14}]$	$q+(-1-2\beta _{1}+\beta _{3}+\beta _{4}-\beta _{5}+\beta _{6}+\cdots)q^{2}+\cdots$
841.2.e.i	$841$	$2$	841.e	29.e	$14$	$12$	$2$	$6.715$	12.0.$\cdots$.1	None		$2$	$0$	$7$	$7$	$-1$	$-11$		$1$	$\mathrm{SU}(2)[C_{14}]$	$q+(1-\beta _{3}-\beta _{7}-\beta _{9}-\beta _{10})q^{2}+(-1+\cdots)q^{3}+\cdots$
841.2.e.j	$841$	$2$	841.e	29.e	$14$	$24$	$4$	$6.715$		None		$12$	$0$	$0$	$0$	$2$	$0$			$\mathrm{SU}(2)[C_{14}]$
841.2.e.k	$841$	$2$	841.e	29.e	$14$	$24$	$4$	$6.715$		None		$12$	$0$	$0$	$0$	$-4$	$0$			$\mathrm{SU}(2)[C_{14}]$
841.2.e.l	$841$	$2$	841.e	29.e	$14$	$72$	$12$	$6.715$		None		$12$	$0$	$0$	$0$	$-4$	$8$			$\mathrm{SU}(2)[C_{14}]$
841.2.e.m	$841$	$2$	841.e	29.e	$14$	$96$	$16$	$6.715$		None		$12$	$0$	$0$	$0$	$-2$	$0$			$\mathrm{SU}(2)[C_{14}]$
841.2.g.a	$841$	$2$	841.g	841.g	$29$	$1988$	$71$	$6.715$		None		$2$	$0$	$-24$	$-27$	$-21$	$-79$			$\mathrm{SU}(2)[C_{29}]$
841.2.h.a	$841$	$2$	841.h	841.h	$58$	$2016$	$72$	$6.715$		None		$2$	$0$	$-29$	$-29$	$-23$	$25$			$\mathrm{SU}(2)[C_{58}]$
841.2.j.a	$841$	$2$	841.j	841.j	$203$	$11928$	$71$	$6.715$		None		$2$	$0$	$-172$	$-169$	$-175$	$-117$			$\mathrm{SU}(2)[C_{203}]$

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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.