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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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Results (40 matches)

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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				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	Inner twists	Rank*	$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
3844.1.b.a	$3844$	$1$	3844.b	4.b	$2$	$1$	$1$	$1.918$	$\Q$	$D_{2}$	$\Q(\sqrt{-1}) $, $\Q(\sqrt{-31}) $	$\Q(\sqrt{31}) $	✓	$4$	$0$	$1$	$0$	$-2$	$0$		$1$		$q+q^{2}+q^{4}-2q^{5}+q^{8}+q^{9}-2q^{10}+\cdots$
3844.1.b.b	$3844$	$1$	3844.b	4.b	$2$	$2$	$2$	$1.918$	$\Q(\sqrt{-3}) $	$D_{6}$	$\Q(\sqrt{-31}) $	None		$4$	$0$	$-1$	$0$	$2$	$0$		$1$		$q+\zeta_{6}^{2}q^{2}-\zeta_{6}q^{4}+q^{5}+(\zeta_{6}+\zeta_{6}^{2}+\cdots)q^{7}+\cdots$
3844.1.b.c	$3844$	$1$	3844.b	4.b	$2$	$2$	$2$	$1.918$	$\Q(\sqrt{-1}) $	$A_{4}$	None	None		$2$	$0$	$0$	$0$	$2$	$0$		$1$		$q-iq^{2}-iq^{3}-q^{4}+q^{5}-q^{6}-iq^{7}+\cdots$
3844.1.b.d	$3844$	$1$	3844.b	4.b	$2$	$2$	$2$	$1.918$	$\Q(\sqrt{-1}) $	$A_{4}$	None	None		$2$	$0$	$0$	$0$	$2$	$0$		$1$		$q+iq^{2}-iq^{3}-q^{4}+q^{5}+q^{6}+iq^{7}+\cdots$
3844.1.b.e	$3844$	$1$	3844.b	4.b	$2$	$2$	$2$	$1.918$	$\Q(\sqrt{2}) $	$D_{4}$	$\Q(\sqrt{-1}) $	None	✓	$4$	$0$	$2$	$0$	$0$	$0$		$1$		$q+q^{2}+q^{4}+q^{8}+q^{9}-\beta q^{13}+q^{16}+\cdots$
3844.1.b.f	$3844$	$1$	3844.b	4.b	$2$	$4$	$4$	$1.918$	$\Q(\zeta_{16})^+$	$D_{8}$	$\Q(\sqrt{-1}) $	None	✓	$4$	$0$	$-4$	$0$	$0$	$0$		$1$		$q-q^{2}+q^{4}-\beta _{2}q^{5}-q^{8}+q^{9}+\beta _{2}q^{10}+\cdots$
3844.1.i.a	$3844$	$1$	3844.i	124.i	$6$	$2$	$1$	$1.918$	$\Q(\sqrt{-3}) $	$D_{6}$	$\Q(\sqrt{-31}) $	None		$4$	$0$	$-1$	$0$	$-1$	$-3$		$1$		$q-\zeta_{6}q^{2}+\zeta_{6}^{2}q^{4}+\zeta_{6}^{2}q^{5}+(-1+\cdots)q^{7}+\cdots$
3844.1.i.b	$3844$	$1$	3844.i	124.i	$6$	$2$	$1$	$1.918$	$\Q(\sqrt{-3}) $	$D_{6}$	$\Q(\sqrt{-31}) $	None		$4$	$0$	$-1$	$0$	$-1$	$3$		$1$		$q+\zeta_{6}^{2}q^{2}-\zeta_{6}q^{4}+\zeta_{6}^{2}q^{5}+(1-\zeta_{6}^{2}+\cdots)q^{7}+\cdots$
3844.1.i.c	$3844$	$1$	3844.i	124.i	$6$	$2$	$1$	$1.918$	$\Q(\sqrt{-3}) $	$D_{2}$	$\Q(\sqrt{-1}) $, $\Q(\sqrt{-31}) $	$\Q(\sqrt{31}) $		$8$	$0$	$2$	$0$	$2$	$0$		$1$		$q+q^{2}+q^{4}-\zeta_{6}^{2}q^{5}+q^{8}+\zeta_{6}^{2}q^{9}+\cdots$
3844.1.i.d	$3844$	$1$	3844.i	124.i	$6$	$4$	$2$	$1.918$	$\Q(\zeta_{12})$	$A_{4}$	None	None		$4$	$0$	$0$	$0$	$-2$	$0$		$1$		$q+\zeta_{12}^{3}q^{2}-\zeta_{12}q^{3}-q^{4}-\zeta_{12}^{2}q^{5}+\cdots$
3844.1.i.e	$3844$	$1$	3844.i	124.i	$6$	$4$	$2$	$1.918$	$\Q(\sqrt{2}, \sqrt{-3})$	$D_{4}$	$\Q(\sqrt{-1}) $	None		$8$	$0$	$4$	$0$	$0$	$0$		$1$		$q+q^{2}+q^{4}+q^{8}+(-1-\beta _{2})q^{9}-\beta _{1}q^{13}+\cdots$
3844.1.i.f	$3844$	$1$	3844.i	124.i	$6$	$8$	$4$	$1.918$	8.0.339738624.2	$D_{8}$	$\Q(\sqrt{-1}) $	None		$8$	$0$	$-8$	$0$	$0$	$0$		$1$		$q-q^{2}+q^{4}+(-\beta _{2}-\beta _{6})q^{5}-q^{8}+\cdots$
3844.1.l.a	$3844$	$1$	3844.l	124.l	$10$	$4$	$1$	$1.918$	$\Q(\zeta_{10})$	$D_{2}$	$\Q(\sqrt{-1}) $, $\Q(\sqrt{-31}) $	$\Q(\sqrt{31}) $		$16$	$0$	$-1$	$0$	$-8$	$0$		$1$		$q-\zeta_{10}q^{2}+\zeta_{10}^{2}q^{4}-q^{5}-\zeta_{10}^{3}q^{8}+\cdots$
3844.1.l.b	$3844$	$1$	3844.l	124.l	$10$	$8$	$2$	$1.918$	8.0.64000000.2	$D_{4}$	$\Q(\sqrt{-1}) $	None		$16$	$0$	$-2$	$0$	$0$	$0$		$1$		$q+\beta _{4}q^{2}+(-1-\beta _{2}-\beta _{4}-\beta _{6})q^{4}+\cdots$
3844.1.l.c	$3844$	$1$	3844.l	124.l	$10$	$8$	$2$	$1.918$	$\Q(\zeta_{20})$	$A_{4}$	None	None		$8$	$0$	$0$	$0$	$8$	$0$		$1$		$q-\zeta_{20}^{7}q^{2}-\zeta_{20}^{3}q^{3}-\zeta_{20}^{4}q^{4}+\cdots$
3844.1.l.d	$3844$	$1$	3844.l	124.l	$10$	$8$	$2$	$1.918$	$\Q(\zeta_{20})$	$A_{4}$	None	None		$8$	$0$	$0$	$0$	$8$	$0$		$1$		$q-\zeta_{20}^{7}q^{2}+\zeta_{20}^{3}q^{3}-\zeta_{20}^{4}q^{4}+\cdots$
3844.1.l.e	$3844$	$1$	3844.l	124.l	$10$	$8$	$2$	$1.918$	$\Q(\zeta_{15})$	$D_{6}$	$\Q(\sqrt{-31}) $	None		$16$	$0$	$1$	$0$	$8$	$0$		$1$		$q+\zeta_{30}^{8}q^{2}-\zeta_{30}q^{4}+q^{5}+(\zeta_{30}-\zeta_{30}^{11}+\cdots)q^{7}+\cdots$
3844.1.l.f	$3844$	$1$	3844.l	124.l	$10$	$16$	$4$	$1.918$	16.0.$\cdots$.1	$D_{8}$	$\Q(\sqrt{-1}) $	None		$16$	$0$	$4$	$0$	$0$	$0$		$1$		$q+(1-\beta _{3}+\beta _{8}-\beta _{12})q^{2}-\beta _{3}q^{4}+\cdots$
3844.1.n.a	$3844$	$1$	3844.n	124.n	$30$	$8$	$1$	$1.918$	$\Q(\zeta_{15})$	$D_{2}$	$\Q(\sqrt{-1}) $, $\Q(\sqrt{-31}) $	$\Q(\sqrt{31}) $		$32$	$0$	$-2$	$0$	$8$	$0$		$1$		$q-\zeta_{30}^{9}q^{2}-\zeta_{30}^{3}q^{4}+\zeta_{30}^{5}q^{5}+\cdots$
3844.1.n.b	$3844$	$1$	3844.n	124.n	$30$	$8$	$1$	$1.918$	$\Q(\zeta_{15})$	$D_{6}$	$\Q(\sqrt{-31}) $	None		$16$	$0$	$1$	$0$	$-4$	$-3$		$1$		$q+\zeta_{30}^{14}q^{2}-\zeta_{30}^{13}q^{4}-\zeta_{30}^{5}q^{5}+\cdots$
3844.1.n.c	$3844$	$1$	3844.n	124.n	$30$	$8$	$1$	$1.918$	$\Q(\zeta_{15})$	$D_{6}$	$\Q(\sqrt{-31}) $	None		$16$	$0$	$1$	$0$	$-4$	$3$		$1$		$q+\zeta_{30}^{4}q^{2}+\zeta_{30}^{8}q^{4}-\zeta_{30}^{5}q^{5}+\cdots$
3844.1.n.d	$3844$	$1$	3844.n	124.n	$30$	$16$	$2$	$1.918$	16.0.$\cdots$.2	$D_{4}$	$\Q(\sqrt{-1}) $	None		$32$	$0$	$-4$	$0$	$0$	$0$		$1$		$q+(-1-\beta _{10}+\beta _{14}+\beta _{15})q^{2}+\beta _{10}q^{4}+\cdots$
3844.1.n.e	$3844$	$1$	3844.n	124.n	$30$	$16$	$2$	$1.918$	$\Q(\zeta_{60})$	$A_{4}$	None	None		$16$	$0$	$0$	$0$	$-8$	$0$		$1$		$q-\zeta_{60}^{9}q^{2}-\zeta_{60}^{11}q^{3}+\zeta_{60}^{18}q^{4}+\cdots$
3844.1.n.f	$3844$	$1$	3844.n	124.n	$30$	$16$	$2$	$1.918$	$\Q(\zeta_{60})$	$A_{4}$	None	None		$16$	$0$	$0$	$0$	$-8$	$0$		$1$		$q+\zeta_{60}^{9}q^{2}-\zeta_{60}^{11}q^{3}+\zeta_{60}^{18}q^{4}+\cdots$
3844.1.n.g	$3844$	$1$	3844.n	124.n	$30$	$32$	$4$	$1.918$	32.0.$\cdots$.1	$D_{8}$	$\Q(\sqrt{-1}) $	None		$32$	$0$	$8$	$0$	$0$	$0$		$1$		$q-\beta _{12}q^{2}-\beta _{23}q^{4}+(-\beta _{2}-\beta _{18}+\cdots)q^{5}+\cdots$
3844.2.a.a	$3844$	$2$	3844.a	1.a	$1$	$1$	$1$	$30.694$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$0$	$-2$	$1$	$-1$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{3}+q^{5}-q^{7}+q^{9}+4q^{11}-2q^{13}+\cdots$
3844.2.a.b	$3844$	$2$	3844.a	1.a	$1$	$1$	$1$	$30.694$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$0$	$0$	$1$	$3$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{5}+3q^{7}-3q^{9}-6q^{11}+4q^{13}+\cdots$
3844.2.a.c	$3844$	$2$	3844.a	1.a	$1$	$1$	$1$	$30.694$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$0$	$2$	$-3$	$-1$	$+$	$1$	$\mathrm{SU}(2)$	$q+2q^{3}-3q^{5}-q^{7}+q^{9}+6q^{11}+\cdots$
3844.2.a.d	$3844$	$2$	3844.a	1.a	$1$	$1$	$1$	$30.694$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$0$	$2$	$1$	$-1$	$+$	$1$	$\mathrm{SU}(2)$	$q+2q^{3}+q^{5}-q^{7}+q^{9}-4q^{11}+2q^{13}+\cdots$
3844.2.a.e	$3844$	$2$	3844.a	1.a	$1$	$2$	$2$	$30.694$	$\Q(\sqrt{5}) $	$_{}$	None	None	✓	$1$	$1$	$0$	$-1$	$4$	$3$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta q^{3}+2q^{5}+(1+\beta )q^{7}+(-2+\beta )q^{9}+\cdots$
3844.2.a.f	$3844$	$2$	3844.a	1.a	$1$	$2$	$2$	$30.694$	$\Q(\sqrt{5}) $	$_{}$	None	None	✓	$1$	$1$	$0$	$0$	$-3$	$-4$	$+$	$1$	$\mathrm{SU}(2)$	$q+(1-2\beta )q^{3}+(-1-\beta )q^{5}+(-1-2\beta )q^{7}+\cdots$
3844.2.a.g	$3844$	$2$	3844.a	1.a	$1$	$2$	$2$	$30.694$	$\Q(\sqrt{5}) $	$_{}$	None	None	✓	$1$	$0$	$0$	$0$	$-3$	$-4$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1-2\beta )q^{3}+(-2+\beta )q^{5}+(-3+2\beta )q^{7}+\cdots$
3844.2.a.h	$3844$	$2$	3844.a	1.a	$1$	$2$	$2$	$30.694$	$\Q(\sqrt{5}) $	$_{}$	None	None	✓	$1$	$0$	$0$	$1$	$4$	$3$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{3}+2q^{5}+(1+\beta )q^{7}+(-2+\beta )q^{9}+\cdots$
3844.2.a.i	$3844$	$2$	3844.a	1.a	$1$	$3$	$3$	$30.694$	3.3.564.1	$_{}$	None	None	✓	$1$	$0$	$0$	$-1$	$1$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{3}-\beta _{2}q^{5}+(1-\beta _{1}+\beta _{2})q^{7}+\cdots$
3844.2.a.j	$3844$	$2$	3844.a	1.a	$1$	$3$	$3$	$30.694$	3.3.564.1	$_{}$	None	None	✓	$1$	$1$	$0$	$1$	$1$	$1$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{3}-\beta _{2}q^{5}+(1-\beta _{1}+\beta _{2})q^{7}+\cdots$
3844.2.a.k	$3844$	$2$	3844.a	1.a	$1$	$4$	$4$	$30.694$	$\Q(\sqrt{2}, \sqrt{5})$	$_{}$	None	None	✓	$2$	$1$	$0$	$0$	$-8$	$0$	$+$	$2$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{3}+(-2+\beta _{3})q^{5}-\beta _{3}q^{7}+\beta _{3}q^{9}+\cdots$
3844.2.a.l	$3844$	$2$	3844.a	1.a	$1$	$8$	$8$	$30.694$	8.8.2621440000.1	$_{}$	None	None	✓	$2$	$1$	$0$	$0$	$-8$	$0$	$+$	$2$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{3}+(-1-\beta _{3})q^{5}+(\beta _{3}+\beta _{5}+\cdots)q^{7}+\cdots$
3844.2.a.m	$3844$	$2$	3844.a	1.a	$1$	$12$	$12$	$30.694$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	$_{}$	None	None	✓	$1$	$1$	$0$	$-6$	$-1$	$-1$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta _{1})q^{3}-\beta _{10}q^{5}+(\beta _{3}-\beta _{4}+\cdots)q^{7}+\cdots$
3844.2.a.n	$3844$	$2$	3844.a	1.a	$1$	$12$	$12$	$30.694$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	$_{}$	None	None	✓	$1$	$0$	$0$	$6$	$-1$	$-1$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1-\beta _{1})q^{3}-\beta _{10}q^{5}+(\beta _{3}-\beta _{4}-\beta _{9}+\cdots)q^{7}+\cdots$
3844.2.a.o	$3844$	$2$	3844.a	1.a	$1$	$24$	$24$	$30.694$		$_{}$	None	None	✓	$2$	$0$	$0$	$0$	$16$	$0$	$-$		$\mathrm{SU}(2)$

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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.