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Level	Weight	Analytic conductor	Analytic rank	Dim.

Bad $p$	Char.	Primitive character	Character order	Is maximal/largest

Coefficient field	Self-twists	CM/RM discriminant	Inner twist count	Is self-dual

Coefficient ring index	Coefficient ring gens.	Is twist minimal	Projective image

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Results (1-50 of 111 matches)

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Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Twist minimal	Largest	Maximal	Minimal twist	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	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
366.2.a.a	$366$	$2$	366.a	1.a	$1$	$1$	$1$	$2.923$	$\Q$	None	✓	✓			366.2.a.a	$1$	$0$	$-1$	$-1$	$-2$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}-2q^{5}+q^{6}+4q^{7}+\cdots$
366.2.a.b	$366$	$2$	366.a	1.a	$1$	$1$	$1$	$2.923$	$\Q$	None	✓	✓	✓	✓	366.2.a.b	$1$	$1$	$-1$	$1$	$-3$	$-1$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}-3q^{5}-q^{6}-q^{7}+\cdots$
366.2.a.c	$366$	$2$	366.a	1.a	$1$	$1$	$1$	$2.923$	$\Q$	None	✓	✓	✓	✓	366.2.a.c	$1$	$0$	$-1$	$1$	$1$	$-2$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}+q^{5}-q^{6}-2q^{7}+\cdots$
366.2.a.d	$366$	$2$	366.a	1.a	$1$	$1$	$1$	$2.923$	$\Q$	None	✓	✓	✓	✓	366.2.a.d	$1$	$1$	$1$	$-1$	$-3$	$-3$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}-3q^{5}-q^{6}-3q^{7}+\cdots$
366.2.a.e	$366$	$2$	366.a	1.a	$1$	$1$	$1$	$2.923$	$\Q$	None	✓	✓	✓	✓	366.2.a.e	$1$	$0$	$1$	$-1$	$-1$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}-q^{5}-q^{6}+2q^{7}+\cdots$
366.2.a.f	$366$	$2$	366.a	1.a	$1$	$1$	$1$	$2.923$	$\Q$	None	✓	✓			366.2.a.f	$1$	$0$	$1$	$1$	$1$	$-2$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}+q^{5}+q^{6}-2q^{7}+\cdots$
366.2.a.g	$366$	$2$	366.a	1.a	$1$	$1$	$1$	$2.923$	$\Q$	None	✓	✓			366.2.a.g	$1$	$0$	$1$	$1$	$1$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}+q^{5}+q^{6}+q^{7}+\cdots$
366.2.a.h	$366$	$2$	366.a	1.a	$1$	$2$	$2$	$2.923$	$\Q(\sqrt{17}) $	None	✓	✓	✓		366.2.a.h	$1$	$0$	$-2$	$-2$	$0$	$-3$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}+(1-2\beta )q^{5}+q^{6}+\cdots$
366.2.d.a	$366$	$2$	366.d	61.b	$2$	$4$	$4$	$2.923$	$\Q(i, \sqrt{41})$	None		✓			366.2.d.a	$2$	$0$	$0$	$4$	$4$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{2}q^{2}+q^{3}-q^{4}+q^{5}-\beta _{2}q^{6}+\cdots$
366.2.d.b	$366$	$2$	366.d	61.b	$2$	$6$	$6$	$2.923$	6.0.59105344.1	None		✓	✓		366.2.d.b	$2$	$0$	$0$	$-6$	$4$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{2}q^{2}-q^{3}-q^{4}+(\beta _{4}-\beta _{5})q^{5}+\cdots$
366.2.e.a	$366$	$2$	366.e	61.c	$3$	$2$	$1$	$2.923$	$\Q(\sqrt{-3}) $	None		✓			366.2.e.a	$2$	$1$	$-1$	$-2$	$-3$	$0$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-1+\zeta_{6})q^{2}-q^{3}-\zeta_{6}q^{4}+(-3+\cdots)q^{5}+\cdots$
366.2.e.b	$366$	$2$	366.e	61.c	$3$	$2$	$1$	$2.923$	$\Q(\sqrt{-3}) $	None		✓			366.2.e.b	$2$	$0$	$-1$	$-2$	$1$	$-2$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-1+\zeta_{6})q^{2}-q^{3}-\zeta_{6}q^{4}+(1-\zeta_{6})q^{5}+\cdots$
366.2.e.c	$366$	$2$	366.e	61.c	$3$	$4$	$2$	$2.923$	$\Q(\sqrt{-3}, \sqrt{-5})$	None		✓			366.2.e.c	$2$	$0$	$-2$	$4$	$-2$	$-2$		$3$	$\mathrm{SU}(2)[C_{3}]$	$q-\beta _{1}q^{2}+q^{3}+(-1+\beta _{1})q^{4}-\beta _{1}q^{5}+\cdots$
366.2.e.d	$366$	$2$	366.e	61.c	$3$	$6$	$3$	$2.923$	6.0.65370672.1	None		✓			366.2.e.d	$2$	$0$	$3$	$-6$	$-1$	$2$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(1+\beta _{4})q^{2}-q^{3}+\beta _{4}q^{4}+(-1-\beta _{1}+\cdots)q^{5}+\cdots$
366.2.e.e	$366$	$2$	366.e	61.c	$3$	$6$	$3$	$2.923$	6.0.954288.1	None		✓			366.2.e.e	$2$	$0$	$3$	$6$	$-1$	$-2$		$3$	$\mathrm{SU}(2)[C_{3}]$	$q+\beta _{3}q^{2}+q^{3}+(-1+\beta _{3})q^{4}-\beta _{1}q^{5}+\cdots$
366.2.g.a	$366$	$2$	366.g	183.g	$4$	$4$	$2$	$2.923$	$\Q(\zeta_{8})$	None		✓			366.2.g.a	$4$	$0$	$0$	$0$	$0$	$12$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+\zeta_{8}q^{2}+(-\zeta_{8}+\zeta_{8}^{2}+\zeta_{8}^{3})q^{3}+\cdots$
366.2.g.b	$366$	$2$	366.g	183.g	$4$	$40$	$20$	$2.923$		None		✓	✓		366.2.g.b	$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{4}]$
366.2.h.a	$366$	$2$	366.h	61.e	$5$	$4$	$1$	$2.923$	$\Q(\zeta_{10})$	None		✓			366.2.h.a	$2$	$0$	$-1$	$-1$	$-1$	$-1$		$1$	$\mathrm{SU}(2)[C_{5}]$	$q+(-1+\zeta_{10}-\zeta_{10}^{2}+\zeta_{10}^{3})q^{2}+\cdots$
366.2.h.b	$366$	$2$	366.h	61.e	$5$	$8$	$2$	$2.923$	8.0.9048765625.1	None		✓			366.2.h.b	$2$	$0$	$-2$	$2$	$-1$	$6$		$1$	$\mathrm{SU}(2)[C_{5}]$	$q+(-1-\beta _{2}-\beta _{3}-\beta _{5})q^{2}+(1+\beta _{2}+\cdots)q^{3}+\cdots$
366.2.h.c	$366$	$2$	366.h	61.e	$5$	$8$	$2$	$2.923$	8.0.2512515625.1	None		✓			366.2.h.c	$2$	$0$	$2$	$-2$	$2$	$-7$		$1$	$\mathrm{SU}(2)[C_{5}]$	$q+(1-\beta _{2}+\beta _{3}+\beta _{5})q^{2}+(-1+\beta _{2}+\cdots)q^{3}+\cdots$
366.2.h.d	$366$	$2$	366.h	61.e	$5$	$12$	$3$	$2.923$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	None		✓	✓		366.2.h.d	$2$	$0$	$3$	$3$	$2$	$4$		$1$	$\mathrm{SU}(2)[C_{5}]$	$q+(1+\beta _{7}-\beta _{8}+\beta _{9})q^{2}+(1+\beta _{7}-\beta _{8}+\cdots)q^{3}+\cdots$
366.2.i.a	$366$	$2$	366.i	61.f	$6$	$12$	$6$	$2.923$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	None		✓			366.2.i.a	$2$	$0$	$0$	$-12$	$2$	$-12$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q-\beta _{6}q^{2}-q^{3}+\beta _{7}q^{4}-\beta _{8}q^{5}+\beta _{6}q^{6}+\cdots$
366.2.i.b	$366$	$2$	366.i	61.f	$6$	$12$	$6$	$2.923$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	None		✓			366.2.i.b	$2$	$0$	$0$	$12$	$2$	$0$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q-\beta _{3}q^{2}+q^{3}+\beta _{8}q^{4}+(\beta _{1}-\beta _{2}-\beta _{7}+\cdots)q^{5}+\cdots$
366.2.l.a	$366$	$2$	366.l	61.g	$10$	$8$	$2$	$2.923$	$\Q(\zeta_{20})$	None		✓			366.2.l.a	$2$	$0$	$0$	$-2$	$-2$	$10$		$1$	$\mathrm{SU}(2)[C_{10}]$	$q+\zeta_{20}q^{2}-\zeta_{20}^{6}q^{3}+\zeta_{20}^{2}q^{4}+(-1+\cdots)q^{5}+\cdots$
366.2.l.b	$366$	$2$	366.l	61.g	$10$	$8$	$2$	$2.923$	$\Q(\zeta_{20})$	None		✓			366.2.l.b	$2$	$0$	$0$	$-2$	$-2$	$10$		$1$	$\mathrm{SU}(2)[C_{10}]$	$q+\zeta_{20}q^{2}-\zeta_{20}^{6}q^{3}+\zeta_{20}^{2}q^{4}+(-\zeta_{20}+\cdots)q^{5}+\cdots$
366.2.l.c	$366$	$2$	366.l	61.g	$10$	$24$	$6$	$2.923$		None		✓	✓		366.2.l.c	$2$	$0$	$0$	$6$	$-4$	$-10$			$\mathrm{SU}(2)[C_{10}]$
366.2.o.a	$366$	$2$	366.o	183.o	$12$	$80$	$20$	$2.923$		None		✓	✓	✓	366.2.o.a	$4$	$0$	$0$	$0$	$0$	$16$			$\mathrm{SU}(2)[C_{12}]$
366.2.q.a	$366$	$2$	366.q	61.i	$15$	$16$	$2$	$2.923$	$\mathbb{Q}[x]/(x^{16} + \cdots)$	None		✓			366.2.q.a	$2$	$0$	$2$	$-4$	$7$	$-8$		$1$	$\mathrm{SU}(2)[C_{15}]$	$q-\beta _{11}q^{2}+(-\beta _{10}+\beta _{11})q^{3}-\beta _{4}q^{4}+\cdots$
366.2.q.b	$366$	$2$	366.q	61.i	$15$	$16$	$2$	$2.923$	$\mathbb{Q}[x]/(x^{16} + \cdots)$	None		✓			366.2.q.b	$2$	$0$	$2$	$4$	$7$	$12$		$1$	$\mathrm{SU}(2)[C_{15}]$	$q+(1+\beta _{6}-\beta _{8}-\beta _{10}+\beta _{11}-\beta _{13}+\cdots)q^{2}+\cdots$
366.2.q.c	$366$	$2$	366.q	61.i	$15$	$24$	$3$	$2.923$		None		✓			366.2.q.c	$2$	$0$	$-3$	$-6$	$1$	$-8$			$\mathrm{SU}(2)[C_{15}]$
366.2.q.d	$366$	$2$	366.q	61.i	$15$	$24$	$3$	$2.923$		None		✓			366.2.q.d	$2$	$0$	$-3$	$6$	$1$	$8$			$\mathrm{SU}(2)[C_{15}]$
366.2.r.a	$366$	$2$	366.r	183.r	$20$	$176$	$22$	$2.923$		None		✓	✓	✓	366.2.r.a	$4$	$0$	$0$	$0$	$0$	$-12$			$\mathrm{SU}(2)[C_{20}]$
366.2.v.a	$366$	$2$	366.v	61.k	$30$	$48$	$6$	$2.923$		None		✓			366.2.v.a	$2$	$0$	$0$	$-12$	$-2$	$20$			$\mathrm{SU}(2)[C_{30}]$
366.2.v.b	$366$	$2$	366.v	61.k	$30$	$48$	$6$	$2.923$		None		✓			366.2.v.b	$2$	$0$	$0$	$12$	$-2$	$-8$			$\mathrm{SU}(2)[C_{30}]$
366.2.x.a	$366$	$2$	366.x	183.x	$60$	$320$	$20$	$2.923$		None		✓	✓	✓	366.2.x.a	$4$	$0$	$0$	$0$	$0$	$-16$			$\mathrm{SU}(2)[C_{60}]$
366.3.b.a	$366$	$3$	366.b	183.d	$2$	$40$	$40$	$9.973$		None		✓	✓	✓	366.3.b.a	$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
366.3.c.a	$366$	$3$	366.c	3.b	$2$	$40$	$40$	$9.973$		None		✓	✓	✓	366.3.c.a	$2$	$0$	$0$	$0$	$0$	$-8$			$\mathrm{SU}(2)[C_{2}]$
366.3.f.a	$366$	$3$	366.f	61.d	$4$	$20$	$10$	$9.973$	$\mathbb{Q}[x]/(x^{20} + \cdots)$	None		✓			366.3.f.a	$2$	$0$	$20$	$0$	$0$	$-20$		$2^{12}$	$\mathrm{SU}(2)[C_{4}]$	$q+(1+\beta _{11})q^{2}+\beta _{7}q^{3}+2\beta _{11}q^{4}+\cdots$
366.3.f.b	$366$	$3$	366.f	61.d	$4$	$24$	$12$	$9.973$		None		✓	✓		366.3.f.b	$2$	$0$	$-24$	$0$	$0$	$-4$			$\mathrm{SU}(2)[C_{4}]$
366.3.j.a	$366$	$3$	366.j	183.k	$6$	$84$	$42$	$9.973$		None		✓	✓	✓	366.3.j.a	$4$	$0$	$0$	$0$	$0$	$4$			$\mathrm{SU}(2)[C_{6}]$
366.3.k.a	$366$	$3$	366.k	183.i	$6$	$84$	$42$	$9.973$		None		✓	✓	✓	366.3.k.a	$4$	$0$	$0$	$0$	$0$	$-24$			$\mathrm{SU}(2)[C_{6}]$
366.3.m.a	$366$	$3$	366.m	183.n	$10$	$160$	$40$	$9.973$		None		✓	✓	✓	366.3.m.a	$4$	$0$	$0$	$0$	$0$	$-12$			$\mathrm{SU}(2)[C_{10}]$
366.3.n.a	$366$	$3$	366.n	183.l	$10$	$160$	$40$	$9.973$		None		✓	✓	✓	366.3.n.a	$4$	$0$	$0$	$0$	$0$	$20$			$\mathrm{SU}(2)[C_{10}]$
366.3.p.a	$366$	$3$	366.p	61.h	$12$	$16$	$4$	$9.973$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	None		✓			366.3.p.a	$2$	$0$	$-8$	$0$	$12$	$-18$		$2^{6}$	$\mathrm{SU}(2)[C_{12}]$	$q+(-1+\beta _{2}-\beta _{3})q^{2}+(1-2\beta _{2})q^{3}+\cdots$
366.3.p.b	$366$	$3$	366.p	61.h	$12$	$20$	$5$	$9.973$	$\mathbb{Q}[x]/(x^{20} - \cdots)$	None		✓			366.3.p.b	$2$	$0$	$-10$	$0$	$12$	$-8$		$2^{6}$	$\mathrm{SU}(2)[C_{12}]$	$q+(-1+\beta _{1}-\beta _{8})q^{2}+(-1-2\beta _{8}+\cdots)q^{3}+\cdots$
366.3.p.c	$366$	$3$	366.p	61.h	$12$	$20$	$5$	$9.973$	$\mathbb{Q}[x]/(x^{20} + \cdots)$	None		✓			366.3.p.c	$2$	$0$	$10$	$0$	$0$	$-14$		$2^{6}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{12}]$	$q+(-\beta _{4}+\beta _{12})q^{2}+(-1+2\beta _{12})q^{3}+\cdots$
366.3.p.d	$366$	$3$	366.p	61.h	$12$	$24$	$6$	$9.973$		None		✓	✓		366.3.p.d	$2$	$0$	$12$	$0$	$0$	$-4$			$\mathrm{SU}(2)[C_{12}]$
366.3.s.a	$366$	$3$	366.s	61.j	$20$	$80$	$10$	$9.973$		None		✓			366.3.s.a	$2$	$0$	$-20$	$0$	$-40$	$20$			$\mathrm{SU}(2)[C_{20}]$
366.3.s.b	$366$	$3$	366.s	61.j	$20$	$96$	$12$	$9.973$		None		✓	✓		366.3.s.b	$2$	$0$	$24$	$0$	$0$	$4$			$\mathrm{SU}(2)[C_{20}]$
366.3.t.a	$366$	$3$	366.t	183.v	$30$	$336$	$42$	$9.973$		None		✓	✓	✓	366.3.t.a	$4$	$0$	$0$	$0$	$0$	$-46$			$\mathrm{SU}(2)[C_{30}]$

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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.