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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 (47 matches)

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Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	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	CM	Self-dual	Inner twists	Rank*	$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
241.2.a.a	$241$	$2$	241.a	1.a	$1$	$7$	$7$	$1.924$	7.7.31056073.1	None	✓	$1$	$1$	$-4$	$-3$	$-8$	$-7$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta _{1})q^{2}+\beta _{6}q^{3}+(1-\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots$
241.2.a.b	$241$	$2$	241.a	1.a	$1$	$12$	$12$	$1.924$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	None	✓	$1$	$0$	$3$	$1$	$6$	$3$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+\beta _{8}q^{3}+(1+\beta _{2})q^{4}+(1-\beta _{9}+\cdots)q^{5}+\cdots$
241.2.b.a	$241$	$2$	241.b	241.b	$2$	$18$	$18$	$1.924$	$\mathbb{Q}[x]/(x^{18} + \cdots)$	None		$2$	$0$	$0$	$2$	$4$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{3}q^{2}+\beta _{7}q^{3}-\beta _{2}q^{4}-\beta _{13}q^{5}+\cdots$
241.2.c.a	$241$	$2$	241.c	241.c	$3$	$38$	$19$	$1.924$		None		$2$	$0$	$1$	$2$	$-4$	$-5$			$\mathrm{SU}(2)[C_{3}]$
241.2.d.a	$241$	$2$	241.d	241.d	$4$	$36$	$18$	$1.924$		None		$2$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{4}]$
241.2.e.a	$241$	$2$	241.e	241.e	$5$	$72$	$18$	$1.924$		None		$2$	$0$	$-16$	$1$	$3$	$7$			$\mathrm{SU}(2)[C_{5}]$
241.2.f.a	$241$	$2$	241.f	241.f	$6$	$38$	$19$	$1.924$		None		$2$	$0$	$-3$	$-4$	$-4$	$-9$			$\mathrm{SU}(2)[C_{6}]$
241.2.g.a	$241$	$2$	241.g	241.g	$8$	$76$	$19$	$1.924$		None		$2$	$0$	$-4$	$-4$	$-4$	$4$			$\mathrm{SU}(2)[C_{8}]$
241.2.h.a	$241$	$2$	241.h	241.h	$10$	$72$	$18$	$1.924$		None		$2$	$0$	$0$	$-7$	$-9$	$-5$			$\mathrm{SU}(2)[C_{10}]$
241.2.i.a	$241$	$2$	241.i	241.i	$12$	$76$	$19$	$1.924$		None		$2$	$0$	$-6$	$-6$	$0$	$-10$			$\mathrm{SU}(2)[C_{12}]$
241.2.j.a	$241$	$2$	241.j	241.j	$15$	$152$	$19$	$1.924$		None		$2$	$0$	$4$	$-12$	$-6$	$-5$			$\mathrm{SU}(2)[C_{15}]$
241.2.l.a	$241$	$2$	241.l	241.l	$20$	$144$	$18$	$1.924$		None		$2$	$0$	$0$	$-10$	$-10$	$-10$			$\mathrm{SU}(2)[C_{20}]$
241.2.m.a	$241$	$2$	241.m	241.m	$24$	$160$	$20$	$1.924$		None		$2$	$0$	$-8$	$-8$	$-8$	$8$			$\mathrm{SU}(2)[C_{24}]$
241.2.n.a	$241$	$2$	241.n	241.n	$30$	$152$	$19$	$1.924$		None		$2$	$0$	$-12$	$-6$	$-6$	$-1$			$\mathrm{SU}(2)[C_{30}]$
241.2.o.a	$241$	$2$	241.o	241.o	$40$	$304$	$19$	$1.924$		None		$2$	$0$	$-16$	$-16$	$-16$	$-24$			$\mathrm{SU}(2)[C_{40}]$
241.2.q.a	$241$	$2$	241.q	241.q	$60$	$304$	$19$	$1.924$		None		$2$	$0$	$-24$	$-14$	$-20$	$-10$			$\mathrm{SU}(2)[C_{60}]$
241.2.s.a	$241$	$2$	241.s	241.s	$120$	$640$	$20$	$1.924$		None		$2$	$0$	$-32$	$-32$	$-32$	$-48$			$\mathrm{SU}(2)[C_{120}]$
241.3.k.a	$241$	$3$	241.k	241.k	$16$	$320$	$40$	$6.567$		None		$2$	$0$	$-8$	$-8$	$-8$	$-8$			$\mathrm{SU}(2)[C_{16}]$
241.3.p.a	$241$	$3$	241.p	241.p	$48$	$624$	$39$	$6.567$		None		$2$	$0$	$-16$	$-16$	$-16$	$-16$			$\mathrm{SU}(2)[C_{48}]$
241.3.r.a	$241$	$3$	241.r	241.r	$80$	$1280$	$40$	$6.567$		None		$2$	$0$	$-32$	$-32$	$-32$	$-32$			$\mathrm{SU}(2)[C_{80}]$
241.3.t.a	$241$	$3$	241.t	241.t	$240$	$2496$	$39$	$6.567$		None		$2$	$0$	$-64$	$-64$	$-64$	$-64$			$\mathrm{SU}(2)[C_{240}]$
241.4.a.a	$241$	$4$	241.a	1.a	$1$	$27$	$27$	$14.219$		None	✓	$1$	$1$	$-11$	$-14$	$-50$	$-68$	$-$		$\mathrm{SU}(2)$
241.4.a.b	$241$	$4$	241.a	1.a	$1$	$33$	$33$	$14.219$		None	✓	$1$	$0$	$9$	$10$	$50$	$58$	$+$		$\mathrm{SU}(2)$
241.4.b.a	$241$	$4$	241.b	241.b	$2$	$60$	$60$	$14.219$		None		$2$	$0$	$-2$	$0$	$-4$	$0$			$\mathrm{SU}(2)[C_{2}]$
241.4.c.a	$241$	$4$	241.c	241.c	$3$	$120$	$60$	$14.219$		None		$2$	$0$	$-1$	$-5$	$24$	$13$			$\mathrm{SU}(2)[C_{3}]$
241.4.d.a	$241$	$4$	241.d	241.d	$4$	$120$	$60$	$14.219$		None		$2$	$0$	$0$	$0$	$0$	$30$			$\mathrm{SU}(2)[C_{4}]$
241.4.e.a	$241$	$4$	241.e	241.e	$5$	$240$	$60$	$14.219$		None		$2$	$0$	$-8$	$-1$	$-5$	$5$			$\mathrm{SU}(2)[C_{5}]$
241.4.f.a	$241$	$4$	241.f	241.f	$6$	$120$	$60$	$14.219$		None		$2$	$0$	$-1$	$3$	$-32$	$75$			$\mathrm{SU}(2)[C_{6}]$
241.4.g.a	$241$	$4$	241.g	241.g	$8$	$236$	$59$	$14.219$		None		$2$	$0$	$-4$	$-4$	$-4$	$-28$			$\mathrm{SU}(2)[C_{8}]$
241.4.h.a	$241$	$4$	241.h	241.h	$10$	$240$	$60$	$14.219$		None		$2$	$0$	$-8$	$-5$	$-1$	$-5$			$\mathrm{SU}(2)[C_{10}]$
241.4.i.a	$241$	$4$	241.i	241.i	$12$	$240$	$60$	$14.219$		None		$2$	$0$	$-6$	$-6$	$0$	$-48$			$\mathrm{SU}(2)[C_{12}]$
241.4.j.a	$241$	$4$	241.j	241.j	$15$	$480$	$60$	$14.219$		None		$2$	$0$	$-4$	$-5$	$-34$	$-23$			$\mathrm{SU}(2)[C_{15}]$
241.4.l.a	$241$	$4$	241.l	241.l	$20$	$480$	$60$	$14.219$		None		$2$	$0$	$0$	$-10$	$-10$	$-40$			$\mathrm{SU}(2)[C_{20}]$
241.4.m.a	$241$	$4$	241.m	241.m	$24$	$472$	$59$	$14.219$		None		$2$	$0$	$-8$	$-8$	$-8$	$-56$			$\mathrm{SU}(2)[C_{24}]$
241.4.n.a	$241$	$4$	241.n	241.n	$30$	$480$	$60$	$14.219$		None		$2$	$0$	$-4$	$-13$	$22$	$-85$			$\mathrm{SU}(2)[C_{30}]$
241.4.o.a	$241$	$4$	241.o	241.o	$40$	$944$	$59$	$14.219$		None		$2$	$0$	$-16$	$-16$	$-16$	$8$			$\mathrm{SU}(2)[C_{40}]$
241.4.q.a	$241$	$4$	241.q	241.q	$60$	$960$	$60$	$14.219$		None		$2$	$0$	$-24$	$-14$	$-20$	$28$			$\mathrm{SU}(2)[C_{60}]$
241.4.s.a	$241$	$4$	241.s	241.s	$120$	$1888$	$59$	$14.219$		None		$2$	$0$	$-32$	$-32$	$-32$	$16$			$\mathrm{SU}(2)[C_{120}]$
241.6.a.a	$241$	$6$	241.a	1.a	$1$	$47$	$47$	$38.653$		None	✓	$1$	$1$	$-21$	$-35$	$-268$	$-451$	$+$		$\mathrm{SU}(2)$
241.6.a.b	$241$	$6$	241.a	1.a	$1$	$53$	$53$	$38.653$		None	✓	$1$	$0$	$19$	$37$	$232$	$431$	$-$		$\mathrm{SU}(2)$
241.6.b.a	$241$	$6$	241.b	241.b	$2$	$100$	$100$	$38.653$		None		$2$	$0$	$-2$	$-6$	$32$	$0$			$\mathrm{SU}(2)[C_{2}]$
241.8.a.a	$241$	$8$	241.a	1.a	$1$	$67$	$67$	$75.285$		None	✓	$1$	$1$	$-33$	$-95$	$-1320$	$-3233$	$-$		$\mathrm{SU}(2)$
241.8.a.b	$241$	$8$	241.a	1.a	$1$	$73$	$73$	$75.285$		None	✓	$1$	$0$	$47$	$121$	$1180$	$2941$	$+$		$\mathrm{SU}(2)$
241.10.a.a	$241$	$10$	241.a	1.a	$1$	$87$	$87$	$124.124$		None	✓	$1$	$1$	$-97$	$-398$	$-5738$	$-17302$	$+$		$\mathrm{SU}(2)$
241.10.a.b	$241$	$10$	241.a	1.a	$1$	$93$	$93$	$124.124$		None	✓	$1$	$0$	$63$	$250$	$6762$	$25916$	$-$		$\mathrm{SU}(2)$
241.12.a.a	$241$	$12$	241.a	1.a	$1$	$107$	$107$	$185.171$		None	✓	$1$	$1$	$-137$	$-719$	$-27740$	$-187253$	$-$		$\mathrm{SU}(2)$
241.12.a.b	$241$	$12$	241.a	1.a	$1$	$113$	$113$	$185.171$		None	✓	$1$	$0$	$183$	$1225$	$34760$	$115273$	$+$		$\mathrm{SU}(2)$

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Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
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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.