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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 116 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
532.1.n.a	$532$	$1$	532.n	532.n	$6$	$4$	$2$	$0.266$	$\Q(\zeta_{12})$	$A_{4}$	None	None		$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q+\zeta_{12}^{5}q^{2}-\zeta_{12}^{3}q^{3}-\zeta_{12}^{4}q^{4}+\cdots$
532.1.bc.a	$532$	$1$	532.bc	133.r	$6$	$2$	$1$	$0.266$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-19}) $	None		$4$	$0$	$0$	$0$	$-2$	$-1$		$1$		$q+\zeta_{6}^{2}q^{5}-\zeta_{6}q^{7}+\zeta_{6}^{2}q^{9}+\zeta_{6}q^{11}+\cdots$
532.1.bc.b	$532$	$1$	532.bc	133.r	$6$	$2$	$1$	$0.266$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-19}) $	None		$4$	$0$	$0$	$0$	$1$	$2$		$1$		$q-\zeta_{6}^{2}q^{5}+q^{7}+\zeta_{6}^{2}q^{9}-\zeta_{6}q^{11}+\cdots$
532.1.bk.a	$532$	$1$	532.bk	532.ak	$6$	$4$	$2$	$0.266$	$\Q(\zeta_{12})$	$A_{4}$	None	None		$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{12}^{3}q^{2}+\zeta_{12}^{5}q^{3}-q^{4}+\zeta_{12}^{2}q^{6}+\cdots$
532.2.a.a	$532$	$2$	532.a	1.a	$1$	$1$	$1$	$4.248$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$0$	$0$	$-2$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{5}+q^{7}-3q^{9}+4q^{11}+4q^{13}+\cdots$
532.2.a.b	$532$	$2$	532.a	1.a	$1$	$2$	$2$	$4.248$	$\Q(\sqrt{5}) $	$_{}$	None	None	✓	$1$	$1$	$0$	$-3$	$-2$	$2$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1-\beta )q^{3}-q^{5}+q^{7}+(-1+3\beta )q^{9}+\cdots$
532.2.a.c	$532$	$2$	532.a	1.a	$1$	$2$	$2$	$4.248$	$\Q(\sqrt{21}) $	$_{}$	None	None	✓	$1$	$0$	$0$	$-1$	$6$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta q^{3}+3q^{5}+q^{7}+(2+\beta )q^{9}+(-1+\cdots)q^{11}+\cdots$
532.2.a.d	$532$	$2$	532.a	1.a	$1$	$2$	$2$	$4.248$	$\Q(\sqrt{5}) $	$_{}$	None	None	✓	$1$	$1$	$0$	$1$	$-4$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{3}+(-1-2\beta )q^{5}-q^{7}+(-2+\cdots)q^{9}+\cdots$
532.2.a.e	$532$	$2$	532.a	1.a	$1$	$3$	$3$	$4.248$	3.3.733.1	$_{}$	None	None	✓	$1$	$0$	$0$	$-1$	$2$	$-3$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{3}+(1-\beta _{1}-\beta _{2})q^{5}-q^{7}+(2+\cdots)q^{9}+\cdots$
532.2.f.a	$532$	$2$	532.f	28.d	$2$	$4$	$4$	$4.248$	$\Q(i, \sqrt{5})$	$_{}$	None	None		$2$	$1$	$-4$	$-6$	$0$	$-6$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+(-1+\beta _{3})q^{2}+(-1+\beta _{2})q^{3}-2\beta _{3}q^{4}+\cdots$
532.2.f.b	$532$	$2$	532.f	28.d	$2$	$4$	$4$	$4.248$	$\Q(i, \sqrt{5})$	$_{}$	None	None		$2$	$0$	$-4$	$6$	$0$	$6$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+(-1-\beta _{3})q^{2}+(1-\beta _{2})q^{3}+2\beta _{3}q^{4}+\cdots$
532.2.f.c	$532$	$2$	532.f	28.d	$2$	$32$	$32$	$4.248$		$_{}$	None	None		$2$	$0$	$3$	$-6$	$0$	$-6$			$\mathrm{SU}(2)[C_{2}]$
532.2.f.d	$532$	$2$	532.f	28.d	$2$	$32$	$32$	$4.248$		$_{}$	None	None		$2$	$0$	$3$	$6$	$0$	$6$			$\mathrm{SU}(2)[C_{2}]$
532.2.g.a	$532$	$2$	532.g	133.c	$2$	$4$	$4$	$4.248$	$\Q(\sqrt{-3}, \sqrt{-19})$	$_{}$	$\Q(\sqrt{-19}) $	None		$4$	$0$	$0$	$0$	$0$	$3$		$2$	$\mathrm{U}(1)[D_{2}]$	$q+(\beta _{1}-\beta _{3})q^{5}+(1-\beta _{1}-\beta _{2})q^{7}-3q^{9}+\cdots$
532.2.g.b	$532$	$2$	532.g	133.c	$2$	$8$	$8$	$4.248$	8.0.$\cdots$.5	$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$-4$		$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{6}q^{3}-\beta _{3}q^{5}+(-1-\beta _{2}-\beta _{4}+\cdots)q^{7}+\cdots$
532.2.h.a	$532$	$2$	532.h	76.d	$2$	$4$	$4$	$4.248$	$\Q(i, \sqrt{29})$	$_{}$	None	None		$2$	$0$	$-4$	$2$	$4$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+(-1-\beta _{2})q^{2}+\beta _{3}q^{3}+2\beta _{2}q^{4}+\cdots$
532.2.h.b	$532$	$2$	532.h	76.d	$2$	$4$	$4$	$4.248$	$\Q(i, \sqrt{29})$	$_{}$	None	None		$2$	$0$	$4$	$-2$	$4$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+(1-\beta _{2})q^{2}+(-1+\beta _{3})q^{3}-2\beta _{2}q^{4}+\cdots$
532.2.h.c	$532$	$2$	532.h	76.d	$2$	$52$	$52$	$4.248$		$_{}$	None	None		$4$	$0$	$0$	$0$	$-8$	$0$			$\mathrm{SU}(2)[C_{2}]$
532.2.i.a	$532$	$2$	532.i	7.c	$3$	$4$	$2$	$4.248$	$\Q(\zeta_{12})$	$_{}$	None	None		$2$	$0$	$0$	$-2$	$0$	$-2$		$3$	$\mathrm{SU}(2)[C_{3}]$	$q+(-\zeta_{12}+\zeta_{12}^{2})q^{3}+(-2+3\zeta_{12}+\cdots)q^{7}+\cdots$
532.2.i.b	$532$	$2$	532.i	7.c	$3$	$6$	$3$	$4.248$	6.0.4406832.1	$_{}$	None	None		$2$	$0$	$0$	$2$	$3$	$1$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(\beta _{1}-\beta _{2}+\beta _{4})q^{3}+(1+\beta _{1}+\beta _{3}+\cdots)q^{5}+\cdots$
532.2.i.c	$532$	$2$	532.i	7.c	$3$	$14$	$7$	$4.248$	$\mathbb{Q}[x]/(x^{14} + \cdots)$	$_{}$	None	None		$2$	$0$	$0$	$0$	$2$	$4$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-\beta _{1}-\beta _{2})q^{3}+\beta _{13}q^{5}+(-\beta _{7}+\cdots)q^{7}+\cdots$
532.2.j.a	$532$	$2$	532.j	19.c	$3$	$2$	$1$	$4.248$	$\Q(\sqrt{-3}) $	$_{}$	None	None		$2$	$0$	$0$	$-1$	$3$	$2$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-1+\zeta_{6})q^{3}+(3-3\zeta_{6})q^{5}+q^{7}+\cdots$
532.2.j.b	$532$	$2$	532.j	19.c	$3$	$8$	$4$	$4.248$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	$_{}$	None	None		$2$	$0$	$0$	$2$	$-2$	$8$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-\beta _{1}+\beta _{4})q^{3}+(-\beta _{1}-\beta _{6})q^{5}+\cdots$
532.2.j.c	$532$	$2$	532.j	19.c	$3$	$10$	$5$	$4.248$	$\mathbb{Q}[x]/(x^{10} - \cdots)$	$_{}$	None	None		$2$	$0$	$0$	$-3$	$-1$	$-10$		$2^{2}$	$\mathrm{SU}(2)[C_{3}]$	$q+(\beta _{6}+\beta _{8})q^{3}+(-\beta _{4}-\beta _{9})q^{5}-q^{7}+\cdots$
532.2.k.a	$532$	$2$	532.k	133.h	$3$	$4$	$2$	$4.248$	$\Q(\sqrt{-3}, \sqrt{13})$	$_{}$	None	None		$2$	$0$	$0$	$-1$	$-10$	$10$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q-\beta _{1}q^{3}+(-3+\beta _{3})q^{5}+(3+\beta _{2})q^{7}+\cdots$
532.2.k.b	$532$	$2$	532.k	133.h	$3$	$24$	$12$	$4.248$		$_{}$	None	None		$2$	$0$	$0$	$-1$	$12$	$-6$			$\mathrm{SU}(2)[C_{3}]$
532.2.l.a	$532$	$2$	532.l	133.g	$3$	$4$	$2$	$4.248$	$\Q(\sqrt{-3}, \sqrt{13})$	$_{}$	None	None		$2$	$0$	$0$	$2$	$5$	$10$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(1-\beta _{3})q^{3}+(1-\beta _{1}-2\beta _{2}-\beta _{3})q^{5}+\cdots$
532.2.l.b	$532$	$2$	532.l	133.g	$3$	$24$	$12$	$4.248$		$_{}$	None	None		$2$	$0$	$0$	$2$	$-6$	$-6$			$\mathrm{SU}(2)[C_{3}]$
532.2.q.a	$532$	$2$	532.q	133.i	$6$	$28$	$14$	$4.248$		$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$2$			$\mathrm{SU}(2)[C_{6}]$
532.2.r.a	$532$	$2$	532.r	532.r	$6$	$4$	$2$	$4.248$	$\Q(\zeta_{12})$	$_{}$	None	None		$4$	$0$	$4$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q+(1+\zeta_{12}^{3})q^{2}+2\zeta_{12}^{3}q^{4}+(-1+\cdots)q^{5}+\cdots$
532.2.r.b	$532$	$2$	532.r	532.r	$6$	$148$	$74$	$4.248$		$_{}$	None	None		$4$	$0$	$-6$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{6}]$
532.2.s.a	$532$	$2$	532.s	76.f	$6$	$120$	$60$	$4.248$		$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{6}]$
532.2.t.a	$532$	$2$	532.t	532.t	$6$	$152$	$76$	$4.248$		$_{}$	None	None		$8$	$0$	$0$	$0$	$-4$	$0$			$\mathrm{SU}(2)[C_{6}]$
532.2.u.a	$532$	$2$	532.u	532.u	$6$	$16$	$8$	$4.248$	16.0.$\cdots$.16	$_{}$	None	None		$8$	$0$	$-4$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q+(\beta _{5}+\beta _{7})q^{2}+(\beta _{1}-\beta _{13})q^{3}+(-\beta _{5}+\cdots)q^{4}+\cdots$
532.2.u.b	$532$	$2$	532.u	532.u	$6$	$136$	$68$	$4.248$		$_{}$	None	None		$8$	$0$	$2$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{6}]$
532.2.v.a	$532$	$2$	532.v	133.o	$6$	$2$	$1$	$4.248$	$\Q(\sqrt{-3}) $	$_{}$	None	None		$2$	$0$	$0$	$-2$	$0$	$5$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q+(-2+2\zeta_{6})q^{3}+(3-\zeta_{6})q^{7}-\zeta_{6}q^{9}+\cdots$
532.2.v.b	$532$	$2$	532.v	133.o	$6$	$2$	$1$	$4.248$	$\Q(\sqrt{-3}) $	$_{}$	None	None		$2$	$0$	$0$	$2$	$0$	$5$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q+(2-2\zeta_{6})q^{3}+(3-\zeta_{6})q^{7}-\zeta_{6}q^{9}+\cdots$
532.2.v.c	$532$	$2$	532.v	133.o	$6$	$4$	$2$	$4.248$	$\Q(\sqrt{-3}, \sqrt{-19})$	$_{}$	$\Q(\sqrt{-19}) $	None		$4$	$0$	$0$	$0$	$0$	$3$		$1$	$\mathrm{U}(1)[D_{6}]$	$q+(-1+2\beta _{1}+\beta _{2})q^{5}+(2\beta _{2}+\beta _{3})q^{7}+\cdots$
532.2.v.d	$532$	$2$	532.v	133.o	$6$	$4$	$2$	$4.248$	$\Q(\sqrt{-3}, \sqrt{-19})$	$_{}$	$\Q(\sqrt{-19}) $	None		$4$	$0$	$0$	$0$	$3$	$-6$		$1$	$\mathrm{U}(1)[D_{6}]$	$q+(1-\beta _{2}-\beta _{3})q^{5}+(-1-\beta _{1}+\beta _{3})q^{7}+\cdots$
532.2.v.e	$532$	$2$	532.v	133.o	$6$	$16$	$8$	$4.248$	$\mathbb{Q}[x]/(x^{16} + \cdots)$	$_{}$	None	None		$4$	$0$	$0$	$0$	$-6$	$-14$		$2^{4}$	$\mathrm{SU}(2)[C_{6}]$	$q+\beta _{6}q^{3}+(-\beta _{3}+\beta _{4}-\beta _{8}-\beta _{9})q^{5}+\cdots$
532.2.w.a	$532$	$2$	532.w	28.f	$6$	$72$	$36$	$4.248$		$_{}$	None	None		$2$	$0$	$1$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{6}]$
532.2.w.b	$532$	$2$	532.w	28.f	$6$	$72$	$36$	$4.248$		$_{}$	None	None		$2$	$0$	$1$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{6}]$
532.2.x.a	$532$	$2$	532.x	133.p	$6$	$24$	$12$	$4.248$		$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$4$			$\mathrm{SU}(2)[C_{6}]$
532.2.y.a	$532$	$2$	532.y	532.y	$6$	$152$	$76$	$4.248$		$_{}$	None	None		$4$	$0$	$0$	$0$	$-4$	$0$			$\mathrm{SU}(2)[C_{6}]$
532.2.bl.a	$532$	$2$	532.bl	532.al	$6$	$152$	$76$	$4.248$		$_{}$	None	None		$4$	$0$	$-3$	$0$	$2$	$0$			$\mathrm{SU}(2)[C_{6}]$
532.2.bm.a	$532$	$2$	532.bm	133.s	$6$	$28$	$14$	$4.248$		$_{}$	None	None		$2$	$0$	$0$	$0$	$3$	$2$			$\mathrm{SU}(2)[C_{6}]$
532.2.bn.a	$532$	$2$	532.bn	532.an	$6$	$4$	$2$	$4.248$	$\Q(\zeta_{12})$	$_{}$	None	None		$4$	$0$	$-2$	$0$	$6$	$0$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q+(-\zeta_{12}-\zeta_{12}^{2}+\zeta_{12}^{3})q^{2}+2\zeta_{12}q^{4}+\cdots$
532.2.bn.b	$532$	$2$	532.bn	532.an	$6$	$148$	$74$	$4.248$		$_{}$	None	None		$4$	$0$	$3$	$0$	$-12$	$0$			$\mathrm{SU}(2)[C_{6}]$
532.2.bo.a	$532$	$2$	532.bo	19.e	$9$	$30$	$5$	$4.248$		$_{}$	None	None		$2$	$0$	$0$	$3$	$-3$	$-15$			$\mathrm{SU}(2)[C_{9}]$
532.2.bo.b	$532$	$2$	532.bo	19.e	$9$	$30$	$5$	$4.248$		$_{}$	None	None		$2$	$0$	$0$	$3$	$3$	$15$			$\mathrm{SU}(2)[C_{9}]$

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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.