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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 (41 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
211.1.b.a	$211$	$1$	211.b	211.b	$2$	$1$	$1$	$0.105$	$\Q$	$D_{3}$	$\Q(\sqrt{-211}) $	None	✓	$2$	$0$	$0$	$0$	$-1$	$0$		$1$		$q+q^{4}-q^{5}+q^{9}-q^{11}-q^{13}+q^{16}+\cdots$
211.2.a.a	$211$	$2$	211.a	1.a	$1$	$2$	$2$	$1.685$	$\Q(\sqrt{5}) $	$_{}$	None	None	✓	$1$	$0$	$1$	$3$	$2$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{2}+(1+\beta )q^{3}+(-1+\beta )q^{4}+(2+\cdots)q^{5}+\cdots$
211.2.a.b	$211$	$2$	211.a	1.a	$1$	$3$	$3$	$1.685$	$\Q(\zeta_{14})^+$	$_{}$	None	None	✓	$1$	$1$	$-2$	$-1$	$-8$	$2$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1-\beta _{2})q^{2}-\beta _{1}q^{3}+(\beta _{1}+\beta _{2})q^{4}+\cdots$
211.2.a.c	$211$	$2$	211.a	1.a	$1$	$3$	$3$	$1.685$	3.3.229.1	$_{}$	None	None	✓	$1$	$1$	$0$	$-3$	$-5$	$-3$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+(-1+\beta _{1})q^{3}+(1+\beta _{2})q^{4}+\cdots$
211.2.a.d	$211$	$2$	211.a	1.a	$1$	$9$	$9$	$1.685$	$\mathbb{Q}[x]/(x^{9} - \cdots)$	$_{}$	None	None	✓	$1$	$0$	$-1$	$-1$	$15$	$-2$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+\beta _{7}q^{3}+(1+\beta _{2})q^{4}+(2+\beta _{3}+\cdots)q^{5}+\cdots$
211.2.c.a	$211$	$2$	211.c	211.c	$3$	$34$	$17$	$1.685$		$_{}$	None	None		$2$	$0$	$2$	$2$	$-4$	$2$			$\mathrm{SU}(2)[C_{3}]$
211.2.d.a	$211$	$2$	211.d	211.d	$5$	$4$	$1$	$1.685$	$\Q(\zeta_{10})$	$_{}$	None	None		$2$	$0$	$2$	$1$	$-1$	$2$		$1$	$\mathrm{SU}(2)[C_{5}]$	$q+(\zeta_{10}-\zeta_{10}^{2})q^{2}-\zeta_{10}^{2}q^{3}+(-1+\cdots)q^{4}+\cdots$
211.2.d.b	$211$	$2$	211.d	211.d	$5$	$60$	$15$	$1.685$		$_{}$	None	None		$2$	$0$	$-2$	$-5$	$-2$	$-12$			$\mathrm{SU}(2)[C_{5}]$
211.2.f.a	$211$	$2$	211.f	211.f	$7$	$96$	$16$	$1.685$		$_{}$	None	None		$2$	$0$	$-9$	$-1$	$-5$	$3$			$\mathrm{SU}(2)[C_{7}]$
211.2.i.a	$211$	$2$	211.i	211.i	$15$	$136$	$17$	$1.685$		$_{}$	None	None		$2$	$0$	$-12$	$-7$	$-6$	$-2$			$\mathrm{SU}(2)[C_{15}]$
211.2.j.a	$211$	$2$	211.j	211.j	$21$	$204$	$17$	$1.685$		$_{}$	None	None		$2$	$0$	$-9$	$-16$	$-10$	$-16$			$\mathrm{SU}(2)[C_{21}]$
211.2.l.a	$211$	$2$	211.l	211.l	$35$	$384$	$16$	$1.685$		$_{}$	None	None		$2$	$0$	$-21$	$-24$	$-25$	$-18$			$\mathrm{SU}(2)[C_{35}]$
211.2.o.a	$211$	$2$	211.o	211.o	$105$	$816$	$17$	$1.685$		$_{}$	None	None		$2$	$0$	$-51$	$-49$	$-50$	$-54$			$\mathrm{SU}(2)[C_{105}]$
211.3.b.a	$211$	$3$	211.b	211.b	$2$	$3$	$3$	$5.749$	3.3.5697.1	$_{}$	$\Q(\sqrt{-211}) $	None	✓	$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{U}(1)[D_{2}]$	$q+4q^{4}+(2\beta _{1}+\beta _{2})q^{5}+9q^{9}+(-5\beta _{1}+\cdots)q^{11}+\cdots$
211.3.b.b	$211$	$3$	211.b	211.b	$2$	$32$	$32$	$5.749$		$_{}$	None	None		$2$	$0$	$0$	$0$	$-2$	$0$			$\mathrm{SU}(2)[C_{2}]$
211.3.e.a	$211$	$3$	211.e	211.e	$6$	$68$	$34$	$5.749$		$_{}$	None	None		$2$	$0$	$-3$	$0$	$-4$	$-24$			$\mathrm{SU}(2)[C_{6}]$
211.3.g.a	$211$	$3$	211.g	211.g	$10$	$140$	$35$	$5.749$		$_{}$	None	None		$2$	$0$	$-5$	$5$	$-3$	$20$			$\mathrm{SU}(2)[C_{10}]$
211.3.h.a	$211$	$3$	211.h	211.h	$14$	$210$	$35$	$5.749$		$_{}$	None	None		$2$	$0$	$-14$	$-7$	$-5$	$-7$			$\mathrm{SU}(2)[C_{14}]$
211.3.k.a	$211$	$3$	211.k	211.k	$30$	$272$	$34$	$5.749$		$_{}$	None	None		$2$	$0$	$-7$	$-20$	$-6$	$-36$			$\mathrm{SU}(2)[C_{30}]$
211.3.m.a	$211$	$3$	211.m	211.m	$42$	$408$	$34$	$5.749$		$_{}$	None	None		$2$	$0$	$-4$	$-14$	$-10$	$10$			$\mathrm{SU}(2)[C_{42}]$
211.3.n.a	$211$	$3$	211.n	211.n	$70$	$840$	$35$	$5.749$		$_{}$	None	None		$2$	$0$	$-16$	$-33$	$-25$	$-48$			$\mathrm{SU}(2)[C_{70}]$
211.3.p.a	$211$	$3$	211.p	211.p	$210$	$1632$	$34$	$5.749$		$_{}$	None	None		$2$	$0$	$-56$	$-36$	$-50$	$-20$			$\mathrm{SU}(2)[C_{210}]$
211.4.a.a	$211$	$4$	211.a	1.a	$1$	$23$	$23$	$12.449$		$_{}$	None	None	✓	$1$	$1$	$-4$	$-17$	$-91$	$-32$	$-$		$\mathrm{SU}(2)$
211.4.a.b	$211$	$4$	211.a	1.a	$1$	$29$	$29$	$12.449$		$_{}$	None	None	✓	$1$	$0$	$6$	$13$	$89$	$24$	$+$		$\mathrm{SU}(2)$
211.4.c.a	$211$	$4$	211.c	211.c	$3$	$104$	$52$	$12.449$		$_{}$	None	None		$2$	$0$	$-5$	$-5$	$-4$	$-49$			$\mathrm{SU}(2)[C_{3}]$
211.4.d.a	$211$	$4$	211.d	211.d	$5$	$208$	$52$	$12.449$		$_{}$	None	None		$2$	$0$	$-7$	$-6$	$-3$	$-47$			$\mathrm{SU}(2)[C_{5}]$
211.4.f.a	$211$	$4$	211.f	211.f	$7$	$312$	$52$	$12.449$		$_{}$	None	None		$2$	$0$	$-2$	$-3$	$-5$	$1$			$\mathrm{SU}(2)[C_{7}]$
211.4.i.a	$211$	$4$	211.i	211.i	$15$	$416$	$52$	$12.449$		$_{}$	None	None		$2$	$0$	$-5$	$0$	$-6$	$-1$			$\mathrm{SU}(2)[C_{15}]$
211.4.j.a	$211$	$4$	211.j	211.j	$21$	$624$	$52$	$12.449$		$_{}$	None	None		$2$	$0$	$-16$	$-9$	$-10$	$35$			$\mathrm{SU}(2)[C_{21}]$
211.4.l.a	$211$	$4$	211.l	211.l	$35$	$1248$	$52$	$12.449$		$_{}$	None	None		$2$	$0$	$-28$	$-22$	$-25$	$19$			$\mathrm{SU}(2)[C_{35}]$
211.4.o.a	$211$	$4$	211.o	211.o	$105$	$2496$	$52$	$12.449$		$_{}$	None	None		$2$	$0$	$-44$	$-56$	$-50$	$-55$			$\mathrm{SU}(2)[C_{105}]$
211.5.b.a	$211$	$5$	211.b	211.b	$2$	$3$	$3$	$21.811$	3.3.5697.1	$_{}$	$\Q(\sqrt{-211}) $	None	✓	$2$	$0$	$0$	$0$	$0$	$0$		$3$	$\mathrm{U}(1)[D_{2}]$	$q+2^{4}q^{4}+(-\beta _{1}+4\beta _{2})q^{5}+3^{4}q^{9}+\cdots$
211.5.b.b	$211$	$5$	211.b	211.b	$2$	$66$	$66$	$21.811$		$_{}$	None	None		$2$	$0$	$0$	$0$	$-2$	$0$			$\mathrm{SU}(2)[C_{2}]$
211.6.a.a	$211$	$6$	211.a	1.a	$1$	$41$	$41$	$33.841$		$_{}$	None	None	✓	$1$	$1$	$-12$	$-44$	$-451$	$-293$	$+$		$\mathrm{SU}(2)$
211.6.a.b	$211$	$6$	211.a	1.a	$1$	$47$	$47$	$33.841$		$_{}$	None	None	✓	$1$	$0$	$8$	$46$	$449$	$99$	$-$		$\mathrm{SU}(2)$
211.8.a.a	$211$	$8$	211.a	1.a	$1$	$58$	$58$	$65.913$		$_{}$	None	None	✓	$1$	$1$	$-24$	$-122$	$-2251$	$-501$	$-$		$\mathrm{SU}(2)$
211.8.a.b	$211$	$8$	211.a	1.a	$1$	$64$	$64$	$65.913$		$_{}$	None	None	✓	$1$	$0$	$16$	$148$	$2249$	$2243$	$+$		$\mathrm{SU}(2)$
211.10.a.a	$211$	$10$	211.a	1.a	$1$	$76$	$76$	$108.673$		$_{}$	None	None	✓	$1$	$1$	$-32$	$-479$	$-11251$	$-12576$	$+$		$\mathrm{SU}(2)$
211.10.a.b	$211$	$10$	211.a	1.a	$1$	$82$	$82$	$108.673$		$_{}$	None	None	✓	$1$	$0$	$48$	$331$	$11249$	$6632$	$-$		$\mathrm{SU}(2)$
211.12.a.a	$211$	$12$	211.a	1.a	$1$	$93$	$93$	$162.120$		$_{}$	None	None	✓	$1$	$1$	$-64$	$-962$	$-61081$	$-70657$	$-$		$\mathrm{SU}(2)$
211.12.a.b	$211$	$12$	211.a	1.a	$1$	$99$	$99$	$162.120$		$_{}$	None	None	✓	$1$	$0$	$96$	$1468$	$51419$	$63799$	$+$		$\mathrm{SU}(2)$

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Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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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.