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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 (45 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
633.1.m.a	$633$	$1$	633.m	633.m	$10$	$4$	$1$	$0.316$	$\Q(\zeta_{10})$	$D_{5}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$-1$	$0$	$3$		$1$		$q-\zeta_{10}^{3}q^{3}+\zeta_{10}^{2}q^{4}+(1-\zeta_{10}^{3}+\cdots)q^{7}+\cdots$
633.1.m.b	$633$	$1$	633.m	633.m	$10$	$8$	$2$	$0.316$	$\Q(\zeta_{20})$	$A_{5}$	None	None		$4$	$0$	$0$	$2$	$0$	$-2$		$1$		$q+(\zeta_{20}^{5}+\zeta_{20}^{9})q^{2}+\zeta_{20}^{6}q^{3}+(-1+\cdots)q^{4}+\cdots$
633.1.p.a	$633$	$1$	633.p	633.p	$14$	$6$	$1$	$0.316$	$\Q(\zeta_{14})$	$D_{7}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$-1$	$0$	$-2$		$1$		$q+\zeta_{14}^{2}q^{3}+\zeta_{14}^{4}q^{4}-\zeta_{14}^{5}q^{7}+\cdots$
633.1.z.a	$633$	$1$	633.z	633.z	$70$	$24$	$1$	$0.316$	$\Q(\zeta_{35})$	$D_{35}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$1$	$0$	$-3$		$1$		$q-\zeta_{70}^{9}q^{3}-\zeta_{70}^{11}q^{4}+(-\zeta_{70}^{5}+\cdots)q^{7}+\cdots$
633.2.a.a	$633$	$2$	633.a	1.a	$1$	$1$	$1$	$5.055$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$-1$	$-1$	$-3$	$2$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}-q^{4}-3q^{5}+q^{6}+2q^{7}+\cdots$
633.2.a.b	$633$	$2$	633.a	1.a	$1$	$4$	$4$	$5.055$	4.4.725.1	$_{}$	None	None	✓	$1$	$1$	$-2$	$4$	$-3$	$-11$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{2}q^{2}+q^{3}+(\beta _{2}-\beta _{3})q^{4}+(-1+\cdots)q^{5}+\cdots$
633.2.a.c	$633$	$2$	633.a	1.a	$1$	$8$	$8$	$5.055$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	$_{}$	None	None	✓	$1$	$1$	$-3$	$-8$	$-2$	$-11$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}-q^{3}+(1+\beta _{1}+\beta _{2})q^{4}+(-\beta _{2}+\cdots)q^{5}+\cdots$
633.2.a.d	$633$	$2$	633.a	1.a	$1$	$8$	$8$	$5.055$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	$_{}$	None	None	✓	$1$	$0$	$4$	$-8$	$3$	$7$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1-\beta _{1})q^{2}-q^{3}+(2-\beta _{1}+\beta _{2})q^{4}+\cdots$
633.2.a.e	$633$	$2$	633.a	1.a	$1$	$14$	$14$	$5.055$	$\mathbb{Q}[x]/(x^{14} - \cdots)$	$_{}$	None	None	✓	$1$	$0$	$3$	$14$	$-1$	$13$	$-$	$2$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+q^{3}+(2+\beta _{2})q^{4}-\beta _{6}q^{5}+\cdots$
633.2.d.a	$633$	$2$	633.d	633.d	$2$	$68$	$68$	$5.055$		$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
633.2.e.a	$633$	$2$	633.e	211.c	$3$	$34$	$17$	$5.055$		$_{}$	None	None		$2$	$0$	$-3$	$17$	$-4$	$-4$			$\mathrm{SU}(2)[C_{3}]$
633.2.e.b	$633$	$2$	633.e	211.c	$3$	$36$	$18$	$5.055$		$_{}$	None	None		$2$	$0$	$-1$	$-18$	$4$	$1$			$\mathrm{SU}(2)[C_{3}]$
633.2.f.a	$633$	$2$	633.f	211.d	$5$	$68$	$17$	$5.055$		$_{}$	None	None		$2$	$0$	$0$	$17$	$2$	$-8$			$\mathrm{SU}(2)[C_{5}]$
633.2.f.b	$633$	$2$	633.f	211.d	$5$	$76$	$19$	$5.055$		$_{}$	None	None		$2$	$0$	$-4$	$-19$	$-2$	$10$			$\mathrm{SU}(2)[C_{5}]$
633.2.g.a	$633$	$2$	633.g	633.g	$6$	$2$	$1$	$5.055$	$\Q(\sqrt{-3}) $	$_{}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$-3$	$0$	$9$		$1$	$\mathrm{U}(1)[D_{6}]$	$q+(-1-\zeta_{6})q^{3}+2\zeta_{6}q^{4}+(3+3\zeta_{6})q^{7}+\cdots$
633.2.g.b	$633$	$2$	633.g	633.g	$6$	$136$	$68$	$5.055$		$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$-12$			$\mathrm{SU}(2)[C_{6}]$
633.2.j.a	$633$	$2$	633.j	211.f	$7$	$102$	$17$	$5.055$		$_{}$	None	None		$2$	$0$	$7$	$17$	$2$	$2$			$\mathrm{SU}(2)[C_{7}]$
633.2.j.b	$633$	$2$	633.j	211.f	$7$	$114$	$19$	$5.055$		$_{}$	None	None		$2$	$0$	$3$	$-19$	$-2$	$-10$			$\mathrm{SU}(2)[C_{7}]$
633.2.k.a	$633$	$2$	633.k	633.k	$10$	$272$	$68$	$5.055$		$_{}$	None	None		$4$	$0$	$0$	$-10$	$0$	$-30$			$\mathrm{SU}(2)[C_{10}]$
633.2.n.a	$633$	$2$	633.n	633.n	$14$	$408$	$68$	$5.055$		$_{}$	None	None		$4$	$0$	$0$	$-7$	$0$	$-14$			$\mathrm{SU}(2)[C_{14}]$
633.2.q.a	$633$	$2$	633.q	211.i	$15$	$136$	$17$	$5.055$		$_{}$	None	None		$2$	$0$	$3$	$-17$	$4$	$-1$			$\mathrm{SU}(2)[C_{15}]$
633.2.q.b	$633$	$2$	633.q	211.i	$15$	$144$	$18$	$5.055$		$_{}$	None	None		$2$	$0$	$1$	$18$	$-4$	$-1$			$\mathrm{SU}(2)[C_{15}]$
633.2.r.a	$633$	$2$	633.r	211.j	$21$	$204$	$17$	$5.055$		$_{}$	None	None		$2$	$0$	$-4$	$-17$	$4$	$4$			$\mathrm{SU}(2)[C_{21}]$
633.2.r.b	$633$	$2$	633.r	211.j	$21$	$216$	$18$	$5.055$		$_{}$	None	None		$2$	$0$	$-6$	$18$	$-4$	$-1$			$\mathrm{SU}(2)[C_{21}]$
633.2.u.a	$633$	$2$	633.u	633.u	$30$	$8$	$1$	$5.055$	$\Q(\zeta_{15})$	$_{}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$3$	$0$	$16$		$1$	$\mathrm{U}(1)[D_{30}]$	$q+(\zeta_{15}-\zeta_{15}^{6})q^{3}-2\zeta_{15}^{4}q^{4}+(3+\cdots)q^{7}+\cdots$
633.2.u.b	$633$	$2$	633.u	633.u	$30$	$544$	$68$	$5.055$		$_{}$	None	None		$4$	$0$	$0$	$-5$	$0$	$-18$			$\mathrm{SU}(2)[C_{30}]$
633.2.v.a	$633$	$2$	633.v	211.l	$35$	$408$	$17$	$5.055$		$_{}$	None	None		$2$	$0$	$-7$	$-17$	$-2$	$8$			$\mathrm{SU}(2)[C_{35}]$
633.2.v.b	$633$	$2$	633.v	211.l	$35$	$456$	$19$	$5.055$		$_{}$	None	None		$2$	$0$	$-3$	$19$	$2$	$-10$			$\mathrm{SU}(2)[C_{35}]$
633.2.y.a	$633$	$2$	633.y	633.y	$42$	$12$	$1$	$5.055$	$\Q(\zeta_{21})$	$_{}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$3$	$0$	$-9$		$1$	$\mathrm{U}(1)[D_{42}]$	$q+(2\zeta_{21}+\zeta_{21}^{8})q^{3}+(2\zeta_{21}^{2}+2\zeta_{21}^{9}+\cdots)q^{4}+\cdots$
633.2.y.b	$633$	$2$	633.y	633.y	$42$	$816$	$68$	$5.055$		$_{}$	None	None		$4$	$0$	$0$	$-14$	$0$	$-16$			$\mathrm{SU}(2)[C_{42}]$
633.2.bb.a	$633$	$2$	633.bb	633.ab	$70$	$1632$	$68$	$5.055$		$_{}$	None	None		$4$	$0$	$0$	$-18$	$0$	$-26$			$\mathrm{SU}(2)[C_{70}]$
633.2.bc.a	$633$	$2$	633.bc	211.o	$105$	$816$	$17$	$5.055$		$_{}$	None	None		$2$	$0$	$4$	$17$	$-4$	$1$			$\mathrm{SU}(2)[C_{105}]$
633.2.bc.b	$633$	$2$	633.bc	211.o	$105$	$864$	$18$	$5.055$		$_{}$	None	None		$2$	$0$	$6$	$-18$	$4$	$1$			$\mathrm{SU}(2)[C_{105}]$
633.2.bd.a	$633$	$2$	633.bd	633.ad	$210$	$48$	$1$	$5.055$		$_{}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$-3$	$0$	$-16$			$\mathrm{U}(1)[D_{210}]$
633.2.bd.b	$633$	$2$	633.bd	633.ad	$210$	$3264$	$68$	$5.055$		$_{}$	None	None		$4$	$0$	$0$	$-51$	$0$	$-94$			$\mathrm{SU}(2)[C_{210}]$
633.3.c.a	$633$	$3$	633.c	211.b	$2$	$70$	$70$	$17.248$		$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
633.4.a.a	$633$	$4$	633.a	1.a	$1$	$1$	$1$	$37.348$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$-4$	$-3$	$3$	$30$	$-$	$1$	$\mathrm{SU}(2)$	$q-4q^{2}-3q^{3}+8q^{4}+3q^{5}+12q^{6}+\cdots$
633.4.a.b	$633$	$4$	633.a	1.a	$1$	$21$	$21$	$37.348$		$_{}$	None	None	✓	$1$	$1$	$-8$	$63$	$-25$	$-104$	$-$		$\mathrm{SU}(2)$
633.4.a.c	$633$	$4$	633.a	1.a	$1$	$26$	$26$	$37.348$		$_{}$	None	None	✓	$1$	$1$	$-6$	$-78$	$-18$	$-92$	$-$		$\mathrm{SU}(2)$
633.4.a.d	$633$	$4$	633.a	1.a	$1$	$26$	$26$	$37.348$		$_{}$	None	None	✓	$1$	$0$	$6$	$-78$	$25$	$50$	$+$		$\mathrm{SU}(2)$
633.4.a.e	$633$	$4$	633.a	1.a	$1$	$32$	$32$	$37.348$		$_{}$	None	None	✓	$1$	$0$	$8$	$96$	$15$	$120$	$+$		$\mathrm{SU}(2)$
633.6.a.a	$633$	$6$	633.a	1.a	$1$	$38$	$38$	$101.523$		$_{}$	None	None	✓	$1$	$1$	$-16$	$342$	$-81$	$-755$	$+$		$\mathrm{SU}(2)$
633.6.a.b	$633$	$6$	633.a	1.a	$1$	$43$	$43$	$101.523$		$_{}$	None	None	✓	$1$	$0$	$20$	$-387$	$75$	$519$	$-$		$\mathrm{SU}(2)$
633.6.a.c	$633$	$6$	633.a	1.a	$1$	$44$	$44$	$101.523$		$_{}$	None	None	✓	$1$	$1$	$-12$	$-396$	$-125$	$-265$	$+$		$\mathrm{SU}(2)$
633.6.a.d	$633$	$6$	633.a	1.a	$1$	$49$	$49$	$101.523$		$_{}$	None	None	✓	$1$	$0$	$16$	$441$	$119$	$813$	$-$		$\mathrm{SU}(2)$

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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.