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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 (1-50 of 147 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
592.1.b.a	$592$	$1$	592.b	148.b	$2$	$1$	$1$	$0.295$	$\Q$	$D_{2}$	$\Q(\sqrt{-1}) $, $\Q(\sqrt{-37}) $	$\Q(\sqrt{37}) $	✓	$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q+q^{9}+q^{25}-q^{37}-2q^{41}+q^{49}+\cdots$
592.1.b.b	$592$	$1$	592.b	148.b	$2$	$2$	$2$	$0.295$	$\Q(\sqrt{-3}) $	$D_{6}$	None	$\Q(\sqrt{37}) $		$4$	$0$	$0$	$0$	$0$	$0$		$2$		$q+(\zeta_{6}+\zeta_{6}^{2})q^{3}+(\zeta_{6}+\zeta_{6}^{2})q^{7}+(-1+\cdots)q^{9}+\cdots$
592.1.k.a	$592$	$1$	592.k	37.d	$4$	$2$	$1$	$0.295$	$\Q(\sqrt{-1}) $	$S_{4}$	None	None		$2$	$0$	$0$	$0$	$-2$	$2$		$1$		$q+iq^{3}+(-1-i)q^{5}+q^{7}+iq^{11}+\cdots$
592.1.k.b	$592$	$1$	592.k	37.d	$4$	$2$	$1$	$0.295$	$\Q(\sqrt{-1}) $	$S_{4}$	None	None		$2$	$0$	$0$	$0$	$0$	$2$		$1$		$q-iq^{3}+q^{7}+iq^{11}+(-1-i)q^{17}+\cdots$
592.1.z.a	$592$	$1$	592.z	148.i	$6$	$4$	$2$	$0.295$	$\Q(\sqrt{-2}, \sqrt{-3})$	$S_{4}$	None	None		$4$	$0$	$0$	$0$	$-2$	$0$		$1$		$q+(\beta _{1}-\beta _{3})q^{3}-\beta _{2}q^{5}+(1-\beta _{2})q^{9}+\cdots$
592.1.bb.a	$592$	$1$	592.bb	148.j	$6$	$2$	$1$	$0.295$	$\Q(\sqrt{-3}) $	$D_{6}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$0$	$0$	$3$	$0$		$1$		$q+(1+\zeta_{6})q^{5}-\zeta_{6}q^{9}+(-1+\zeta_{6}^{2}+\cdots)q^{17}+\cdots$
592.1.bt.a	$592$	$1$	592.bt	148.o	$18$	$6$	$1$	$0.295$	$\Q(\zeta_{18})$	$D_{18}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$0$	$0$	$-3$	$0$		$1$		$q+(-\zeta_{18}^{2}-\zeta_{18}^{3})q^{5}+\zeta_{18}^{8}q^{9}+\cdots$
592.2.a.a	$592$	$2$	592.a	1.a	$1$	$1$	$1$	$4.727$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$0$	$-1$	$0$	$1$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+q^{7}-2q^{9}-3q^{11}-4q^{13}+\cdots$
592.2.a.b	$592$	$2$	592.a	1.a	$1$	$1$	$1$	$4.727$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$0$	$1$	$-4$	$3$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-4q^{5}+3q^{7}-2q^{9}-5q^{11}+\cdots$
592.2.a.c	$592$	$2$	592.a	1.a	$1$	$1$	$1$	$4.727$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$0$	$1$	$-2$	$-1$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-2q^{5}-q^{7}-2q^{9}-q^{11}-6q^{13}+\cdots$
592.2.a.d	$592$	$2$	592.a	1.a	$1$	$1$	$1$	$4.727$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$0$	$1$	$0$	$3$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+3q^{7}-2q^{9}+3q^{11}+2q^{17}+\cdots$
592.2.a.e	$592$	$2$	592.a	1.a	$1$	$1$	$1$	$4.727$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$0$	$3$	$-2$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q+3q^{3}-2q^{5}+q^{7}+6q^{9}+5q^{11}+\cdots$
592.2.a.f	$592$	$2$	592.a	1.a	$1$	$2$	$2$	$4.727$	$\Q(\sqrt{13}) $	$_{}$	None	None	✓	$1$	$1$	$0$	$-3$	$-1$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1-\beta )q^{3}-\beta q^{5}+(-2+2\beta )q^{7}+\cdots$
592.2.a.g	$592$	$2$	592.a	1.a	$1$	$2$	$2$	$4.727$	$\Q(\sqrt{5}) $	$_{}$	None	None	✓	$1$	$0$	$0$	$1$	$1$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{3}+(-1+3\beta )q^{5}+2\beta q^{7}+(-2+\cdots)q^{9}+\cdots$
592.2.a.h	$592$	$2$	592.a	1.a	$1$	$2$	$2$	$4.727$	$\Q(\sqrt{17}) $	$_{}$	None	None	✓	$1$	$0$	$0$	$1$	$4$	$-1$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{3}+2q^{5}-\beta q^{7}+(1+\beta )q^{9}-\beta q^{11}+\cdots$
592.2.a.i	$592$	$2$	592.a	1.a	$1$	$3$	$3$	$4.727$	3.3.229.1	$_{}$	None	None	✓	$1$	$1$	$0$	$-2$	$-1$	$-7$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1-\beta _{2})q^{3}+\beta _{2}q^{5}+(-2-\beta _{1}+\cdots)q^{7}+\cdots$
592.2.a.j	$592$	$2$	592.a	1.a	$1$	$4$	$4$	$4.727$	4.4.48389.1	$_{}$	None	None	✓	$1$	$0$	$0$	$-2$	$5$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta _{1})q^{3}+(1-\beta _{3})q^{5}+(\beta _{2}-\beta _{3})q^{7}+\cdots$
592.2.g.a	$592$	$2$	592.g	37.b	$2$	$2$	$2$	$4.727$	$\Q(\sqrt{-3}) $	$_{}$	None	None		$2$	$1$	$0$	$-2$	$0$	$-2$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q-q^{3}-\zeta_{6}q^{5}-q^{7}-2q^{9}-3q^{11}+\cdots$
592.2.g.b	$592$	$2$	592.g	37.b	$2$	$2$	$2$	$4.727$	$\Q(\sqrt{-1}) $	$_{}$	None	None		$2$	$0$	$0$	$2$	$0$	$-6$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q+q^{3}+iq^{5}-3q^{7}-2q^{9}+3q^{11}+\cdots$
592.2.g.c	$592$	$2$	592.g	37.b	$2$	$4$	$4$	$4.727$	$\Q(i, \sqrt{21})$	$_{}$	None	None		$2$	$0$	$0$	$2$	$0$	$8$		$3$	$\mathrm{SU}(2)[C_{2}]$	$q+(1-\beta _{3})q^{3}-\beta _{1}q^{5}+2q^{7}+(3-\beta _{3})q^{9}+\cdots$
592.2.g.d	$592$	$2$	592.g	37.b	$2$	$10$	$10$	$4.727$	$\mathbb{Q}[x]/(x^{10} - \cdots)$	$_{}$	None	None		$2$	$0$	$0$	$-2$	$0$	$4$		$2^{8}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{2}q^{3}-\beta _{7}q^{5}+\beta _{3}q^{7}+(1+\beta _{1}+\cdots)q^{9}+\cdots$
592.2.i.a	$592$	$2$	592.i	37.c	$3$	$2$	$1$	$4.727$	$\Q(\sqrt{-3}) $	$_{}$	None	None		$2$	$0$	$0$	$-2$	$-3$	$-4$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q-2\zeta_{6}q^{3}-3\zeta_{6}q^{5}-4\zeta_{6}q^{7}+(-1+\cdots)q^{9}+\cdots$
592.2.i.b	$592$	$2$	592.i	37.c	$3$	$2$	$1$	$4.727$	$\Q(\sqrt{-3}) $	$_{}$	None	None		$2$	$0$	$0$	$-1$	$-3$	$3$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q-\zeta_{6}q^{3}-3\zeta_{6}q^{5}+3\zeta_{6}q^{7}+(2-2\zeta_{6})q^{9}+\cdots$
592.2.i.c	$592$	$2$	592.i	37.c	$3$	$2$	$1$	$4.727$	$\Q(\sqrt{-3}) $	$_{}$	None	None		$2$	$0$	$0$	$0$	$-1$	$2$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q-\zeta_{6}q^{5}+2\zeta_{6}q^{7}+(3-3\zeta_{6})q^{9}+2q^{11}+\cdots$
592.2.i.d	$592$	$2$	592.i	37.c	$3$	$2$	$1$	$4.727$	$\Q(\sqrt{-3}) $	$_{}$	None	None		$2$	$0$	$0$	$2$	$1$	$0$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+2\zeta_{6}q^{3}+\zeta_{6}q^{5}+(-1+\zeta_{6})q^{9}+\cdots$
592.2.i.e	$592$	$2$	592.i	37.c	$3$	$6$	$3$	$4.727$	6.0.4406832.1	$_{}$	None	None		$2$	$0$	$0$	$0$	$-1$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{3}]$	$q+\beta _{4}q^{3}+(-\beta _{1}-\beta _{5})q^{5}-\beta _{4}q^{7}+\cdots$
592.2.i.f	$592$	$2$	592.i	37.c	$3$	$6$	$3$	$4.727$	6.0.27870912.1	$_{}$	None	None		$2$	$0$	$0$	$1$	$3$	$1$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-\beta _{1}-\beta _{2})q^{3}+(1-\beta _{4})q^{5}+(-\beta _{1}+\cdots)q^{7}+\cdots$
592.2.i.g	$592$	$2$	592.i	37.c	$3$	$6$	$3$	$4.727$	6.0.591408.1	$_{}$	None	None		$2$	$0$	$0$	$2$	$1$	$-2$		$2^{2}$	$\mathrm{SU}(2)[C_{3}]$	$q+(-\beta _{1}+\beta _{3}-\beta _{5})q^{3}+(\beta _{1}+\beta _{5})q^{5}+\cdots$
592.2.i.h	$592$	$2$	592.i	37.c	$3$	$10$	$5$	$4.727$	$\mathbb{Q}[x]/(x^{10} - \cdots)$	$_{}$	None	None		$2$	$0$	$0$	$1$	$3$	$-3$		$2^{4}$	$\mathrm{SU}(2)[C_{3}]$	$q+\beta _{9}q^{3}+(\beta _{2}+\beta _{6}+\beta _{9})q^{5}+(-1+\cdots)q^{7}+\cdots$
592.2.m.a	$592$	$2$	592.m	592.m	$4$	$148$	$74$	$4.727$		$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$-8$			$\mathrm{SU}(2)[C_{4}]$
592.2.n.a	$592$	$2$	592.n	592.n	$4$	$148$	$74$	$4.727$		$_{}$	None	None		$4$	$0$	$0$	$-4$	$0$	$0$			$\mathrm{SU}(2)[C_{4}]$
592.2.o.a	$592$	$2$	592.o	16.e	$4$	$144$	$72$	$4.727$		$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{4}]$
592.2.s.a	$592$	$2$	592.s	592.s	$4$	$148$	$74$	$4.727$		$_{}$	None	None		$2$	$0$	$-4$	$0$	$-4$	$-8$			$\mathrm{SU}(2)[C_{4}]$
592.2.t.a	$592$	$2$	592.t	148.g	$4$	$2$	$1$	$4.727$	$\Q(\sqrt{-1}) $	$_{}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$0$	$0$	$-2$	$0$		$1$	$\mathrm{U}(1)[D_{4}]$	$q+(-1+i)q^{5}-3q^{9}+(-1+i)q^{13}+\cdots$
592.2.t.b	$592$	$2$	592.t	148.g	$4$	$4$	$2$	$4.727$	$\Q(i, \sqrt{7})$	$_{}$	None	None		$4$	$0$	$0$	$0$	$-4$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{4}]$	$q+\beta _{2}q^{3}+(-1+\beta _{1})q^{5}+\beta _{3}q^{7}+4q^{9}+\cdots$
592.2.t.c	$592$	$2$	592.t	148.g	$4$	$4$	$2$	$4.727$	$\Q(\zeta_{12})$	$_{}$	None	None		$4$	$0$	$0$	$0$	$8$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{4}]$	$q+\zeta_{12}^{3}q^{3}+(2-2\zeta_{12})q^{5}-\zeta_{12}^{2}q^{7}+\cdots$
592.2.t.d	$592$	$2$	592.t	148.g	$4$	$28$	$14$	$4.727$		$_{}$	None	None		$4$	$0$	$0$	$0$	$-8$	$0$			$\mathrm{SU}(2)[C_{4}]$
592.2.w.a	$592$	$2$	592.w	37.e	$6$	$2$	$1$	$4.727$	$\Q(\sqrt{-3}) $	$_{}$	None	None		$2$	$1$	$0$	$-2$	$-3$	$-2$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q-2\zeta_{6}q^{3}+(-2+\zeta_{6})q^{5}-2\zeta_{6}q^{7}+\cdots$
592.2.w.b	$592$	$2$	592.w	37.e	$6$	$2$	$1$	$4.727$	$\Q(\sqrt{-3}) $	$_{}$	None	None		$2$	$0$	$0$	$1$	$3$	$1$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q+\zeta_{6}q^{3}+(2-\zeta_{6})q^{5}+\zeta_{6}q^{7}+(2-2\zeta_{6})q^{9}+\cdots$
592.2.w.c	$592$	$2$	592.w	37.e	$6$	$4$	$2$	$4.727$	$\Q(\zeta_{12})$	$_{}$	None	None		$2$	$0$	$0$	$-2$	$-6$	$0$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q+(\zeta_{12}-\zeta_{12}^{2}+\zeta_{12}^{3})q^{3}+(-2-2\zeta_{12}+\cdots)q^{5}+\cdots$
592.2.w.d	$592$	$2$	592.w	37.e	$6$	$4$	$2$	$4.727$	$\Q(\zeta_{12})$	$_{}$	None	None		$2$	$0$	$0$	$2$	$-6$	$8$		$3$	$\mathrm{SU}(2)[C_{6}]$	$q+(\zeta_{12}-\zeta_{12}^{2})q^{3}+(-2+\zeta_{12})q^{5}+\cdots$
592.2.w.e	$592$	$2$	592.w	37.e	$6$	$4$	$2$	$4.727$	$\Q(\zeta_{12})$	$_{}$	None	None		$2$	$0$	$0$	$2$	$6$	$-4$		$3$	$\mathrm{SU}(2)[C_{6}]$	$q+(\zeta_{12}-\zeta_{12}^{2})q^{3}+(2-\zeta_{12})q^{5}-2\zeta_{12}q^{7}+\cdots$
592.2.w.f	$592$	$2$	592.w	37.e	$6$	$20$	$10$	$4.727$	$\mathbb{Q}[x]/(x^{20} + \cdots)$	$_{}$	None	None		$2$	$0$	$0$	$2$	$6$	$2$		$2^{18}$	$\mathrm{SU}(2)[C_{6}]$	$q+(\beta _{5}+\beta _{14})q^{3}+\beta _{4}q^{5}+(-\beta _{2}-\beta _{10}+\cdots)q^{7}+\cdots$
592.2.bc.a	$592$	$2$	592.bc	37.f	$9$	$6$	$1$	$4.727$	$\Q(\zeta_{18})$	$_{}$	None	None		$2$	$0$	$0$	$-3$	$-6$	$-3$		$1$	$\mathrm{SU}(2)[C_{9}]$	$q+(-\zeta_{18}+\zeta_{18}^{2}-\zeta_{18}^{3})q^{3}+(-2\zeta_{18}^{3}+\cdots)q^{5}+\cdots$
592.2.bc.b	$592$	$2$	592.bc	37.f	$9$	$6$	$1$	$4.727$	$\Q(\zeta_{18})$	$_{}$	None	None		$2$	$0$	$0$	$3$	$3$	$-6$		$1$	$\mathrm{SU}(2)[C_{9}]$	$q+(\zeta_{18}+\zeta_{18}^{3})q^{3}+(1+\zeta_{18}+2\zeta_{18}^{2}+\cdots)q^{5}+\cdots$
592.2.bc.c	$592$	$2$	592.bc	37.f	$9$	$6$	$1$	$4.727$	$\Q(\zeta_{18})$	$_{}$	None	None		$2$	$0$	$0$	$6$	$6$	$12$		$1$	$\mathrm{SU}(2)[C_{9}]$	$q+(1+\zeta_{18}^{4})q^{3}+(1+\zeta_{18}-\zeta_{18}^{2}+\cdots)q^{5}+\cdots$
592.2.bc.d	$592$	$2$	592.bc	37.f	$9$	$12$	$2$	$4.727$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	$_{}$	None	None		$2$	$0$	$0$	$3$	$-6$	$-6$		$1$	$\mathrm{SU}(2)[C_{9}]$	$q+(\beta _{1}+\beta _{9})q^{3}+(-1+\beta _{1}+\beta _{5})q^{5}+\cdots$
592.2.bc.e	$592$	$2$	592.bc	37.f	$9$	$24$	$4$	$4.727$		$_{}$	None	None		$2$	$0$	$0$	$-3$	$-3$	$9$			$\mathrm{SU}(2)[C_{9}]$
592.2.bc.f	$592$	$2$	592.bc	37.f	$9$	$24$	$4$	$4.727$		$_{}$	None	None		$2$	$0$	$0$	$0$	$3$	$3$			$\mathrm{SU}(2)[C_{9}]$
592.2.bc.g	$592$	$2$	592.bc	37.f	$9$	$30$	$5$	$4.727$		$_{}$	None	None		$2$	$0$	$0$	$0$	$-6$	$3$			$\mathrm{SU}(2)[C_{9}]$

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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.