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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 91 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
185.2.a.a	$185$	$2$	185.a	1.a	$1$	$1$	$1$	$1.477$	$\Q$	None	✓	✓			185.2.a.a	$1$	$1$	$-2$	$1$	$-1$	$-5$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{2}+q^{3}+2q^{4}-q^{5}-2q^{6}-5q^{7}+\cdots$
185.2.a.b	$185$	$2$	185.a	1.a	$1$	$1$	$1$	$1.477$	$\Q$	None	✓	✓	✓	✓	185.2.a.b	$1$	$1$	$0$	$-1$	$1$	$-3$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-2q^{4}+q^{5}-3q^{7}-2q^{9}-5q^{11}+\cdots$
185.2.a.c	$185$	$2$	185.a	1.a	$1$	$1$	$1$	$1.477$	$\Q$	None	✓	✓			185.2.a.c	$1$	$1$	$1$	$-2$	$-1$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-2q^{3}-q^{4}-q^{5}-2q^{6}-2q^{7}+\cdots$
185.2.a.d	$185$	$2$	185.a	1.a	$1$	$5$	$5$	$1.477$	5.5.368464.1	None	✓	✓	✓	✓	185.2.a.d	$1$	$0$	$0$	$-1$	$5$	$7$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta _{2}q^{2}-\beta _{3}q^{3}+(2-\beta _{1}-\beta _{4})q^{4}+\cdots$
185.2.a.e	$185$	$2$	185.a	1.a	$1$	$5$	$5$	$1.477$	5.5.973904.1	None	✓	✓	✓	✓	185.2.a.e	$1$	$0$	$2$	$3$	$-5$	$11$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{4}q^{2}+(1-\beta _{1})q^{3}+(2+\beta _{3})q^{4}+\cdots$
185.2.b.a	$185$	$2$	185.b	5.b	$2$	$18$	$18$	$1.477$	$\mathbb{Q}[x]/(x^{18} + \cdots)$	None		✓	✓	✓	185.2.b.a	$2$	$0$	$0$	$0$	$2$	$0$		$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	$q+(\beta _{1}+\beta _{13})q^{2}+(\beta _{12}-\beta _{13})q^{3}+(-2+\cdots)q^{4}+\cdots$
185.2.c.a	$185$	$2$	185.c	37.b	$2$	$2$	$2$	$1.477$	$\Q(\sqrt{-1}) $	None		✓			185.2.c.a	$2$	$0$	$0$	$2$	$0$	$2$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+q^{3}+2 q^{4}+i q^{5}+q^{7}-2 q^{9}+\cdots$
185.2.c.b	$185$	$2$	185.c	37.b	$2$	$12$	$12$	$1.477$	$\mathbb{Q}[x]/(x^{12} + \cdots)$	None		✓	✓		185.2.c.b	$2$	$0$	$0$	$2$	$0$	$-18$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{2}-\beta _{9}q^{3}+(-1+\beta _{9}+\beta _{10}+\cdots)q^{4}+\cdots$
185.2.d.a	$185$	$2$	185.d	185.d	$2$	$16$	$16$	$1.477$	$\mathbb{Q}[x]/(x^{16} + \cdots)$	None		✓	✓	✓	185.2.d.a	$4$	$0$	$0$	$0$	$0$	$0$		$2^{5}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{7}q^{2}-\beta _{9}q^{3}+(1-\beta _{2})q^{4}-\beta _{1}q^{5}+\cdots$
185.2.e.a	$185$	$2$	185.e	37.c	$3$	$14$	$7$	$1.477$	$\mathbb{Q}[x]/(x^{14} + \cdots)$	None		✓			185.2.e.a	$2$	$0$	$0$	$-2$	$-7$	$0$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-\beta _{1}+\beta _{4})q^{2}-\beta _{6}q^{3}+(\beta _{2}+\beta _{9}+\cdots)q^{4}+\cdots$
185.2.e.b	$185$	$2$	185.e	37.c	$3$	$14$	$7$	$1.477$	$\mathbb{Q}[x]/(x^{14} - \cdots)$	None		✓			185.2.e.b	$2$	$0$	$2$	$-2$	$7$	$2$		$3$	$\mathrm{SU}(2)[C_{3}]$	$q+\beta _{8}q^{2}+\beta _{6}q^{3}+(-1+\beta _{5}-\beta _{7}+\cdots)q^{4}+\cdots$
185.2.f.a	$185$	$2$	185.f	185.f	$4$	$2$	$1$	$1.477$	$\Q(\sqrt{-1}) $	None		✓			185.2.f.a	$2$	$0$	$0$	$-2$	$-4$	$-6$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q-i q^{2}+(-i-1)q^{3}+q^{4}+(i-2)q^{5}+\cdots$
185.2.f.b	$185$	$2$	185.f	185.f	$4$	$2$	$1$	$1.477$	$\Q(\sqrt{-1}) $	None		✓			185.2.f.b	$2$	$0$	$0$	$4$	$-4$	$0$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q-i q^{2}+(2 i+2)q^{3}+q^{4}+(i-2)q^{5}+\cdots$
185.2.f.c	$185$	$2$	185.f	185.f	$4$	$6$	$3$	$1.477$	6.0.350464.1	None		✓			185.2.f.c	$2$	$0$	$0$	$-2$	$2$	$-4$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q-\beta _{5}q^{2}+(-1+\beta _{1}-\beta _{3}-\beta _{4}+\beta _{5})q^{3}+\cdots$
185.2.f.d	$185$	$2$	185.f	185.f	$4$	$24$	$12$	$1.477$		None		✓	✓		185.2.f.d	$2$	$0$	$0$	$4$	$0$	$6$			$\mathrm{SU}(2)[C_{4}]$
185.2.k.a	$185$	$2$	185.k	185.k	$4$	$2$	$1$	$1.477$	$\Q(\sqrt{-1}) $	None		✓			185.2.f.b	$2$	$1$	$-2$	$-4$	$-2$	$0$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q-q^{2}+(2 i-2)q^{3}-q^{4}+(2 i-1)q^{5}+\cdots$
185.2.k.b	$185$	$2$	185.k	185.k	$4$	$2$	$1$	$1.477$	$\Q(\sqrt{-1}) $	None		✓			185.2.f.a	$2$	$0$	$-2$	$2$	$-2$	$-6$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q-q^{2}+(-i+1)q^{3}-q^{4}+(2 i-1)q^{5}+\cdots$
185.2.k.c	$185$	$2$	185.k	185.k	$4$	$6$	$3$	$1.477$	6.0.350464.1	None		✓			185.2.f.c	$2$	$0$	$-2$	$2$	$0$	$-4$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+\beta _{3}q^{2}+(1-\beta _{2}+\beta _{3}-\beta _{4}+\beta _{5})q^{3}+\cdots$
185.2.k.d	$185$	$2$	185.k	185.k	$4$	$24$	$12$	$1.477$		None		✓	✓		185.2.f.d	$2$	$0$	$4$	$-4$	$8$	$6$			$\mathrm{SU}(2)[C_{4}]$
185.2.l.a	$185$	$2$	185.l	185.l	$6$	$32$	$16$	$1.477$		None		✓	✓	✓	185.2.l.a	$4$	$0$	$0$	$0$	$3$	$0$			$\mathrm{SU}(2)[C_{6}]$
185.2.m.a	$185$	$2$	185.m	37.e	$6$	$28$	$14$	$1.477$		None		✓	✓	✓	185.2.m.a	$2$	$0$	$-6$	$-4$	$0$	$-2$			$\mathrm{SU}(2)[C_{6}]$
185.2.n.a	$185$	$2$	185.n	185.n	$6$	$36$	$18$	$1.477$		None		✓	✓	✓	185.2.n.a	$4$	$0$	$0$	$0$	$-2$	$0$			$\mathrm{SU}(2)[C_{6}]$
185.2.o.a	$185$	$2$	185.o	37.f	$9$	$36$	$6$	$1.477$		None		✓			185.2.o.a	$2$	$0$	$-3$	$0$	$0$	$6$			$\mathrm{SU}(2)[C_{9}]$
185.2.o.b	$185$	$2$	185.o	37.f	$9$	$36$	$6$	$1.477$		None		✓			185.2.o.b	$2$	$0$	$-3$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{9}]$
185.2.p.a	$185$	$2$	185.p	185.p	$12$	$68$	$17$	$1.477$		None		✓	✓	✓	185.2.p.a	$2$	$0$	$-4$	$-8$	$-10$	$-2$			$\mathrm{SU}(2)[C_{12}]$
185.2.u.a	$185$	$2$	185.u	185.u	$12$	$68$	$17$	$1.477$		None		✓	✓	✓	185.2.p.a	$2$	$0$	$-6$	$-4$	$0$	$-2$			$\mathrm{SU}(2)[C_{12}]$
185.2.v.a	$185$	$2$	185.v	185.v	$18$	$96$	$16$	$1.477$		None		✓	✓	✓	185.2.v.a	$4$	$0$	$0$	$0$	$-12$	$0$			$\mathrm{SU}(2)[C_{18}]$
185.2.w.a	$185$	$2$	185.w	37.h	$18$	$72$	$12$	$1.477$		None		✓	✓	✓	185.2.w.a	$2$	$0$	$6$	$0$	$0$	$-6$			$\mathrm{SU}(2)[C_{18}]$
185.2.x.a	$185$	$2$	185.x	185.x	$18$	$108$	$18$	$1.477$		None		✓	✓	✓	185.2.x.a	$4$	$0$	$0$	$0$	$-9$	$0$			$\mathrm{SU}(2)[C_{18}]$
185.2.z.a	$185$	$2$	185.z	185.z	$36$	$204$	$17$	$1.477$		None		✓	✓	✓	185.2.z.a	$2$	$0$	$-12$	$-6$	$-12$	$-12$			$\mathrm{SU}(2)[C_{36}]$
185.2.bc.a	$185$	$2$	185.bc	185.ac	$36$	$204$	$17$	$1.477$		None		✓	✓	✓	185.2.z.a	$2$	$0$	$-12$	$-18$	$-12$	$-12$			$\mathrm{SU}(2)[C_{36}]$
185.3.g.a	$185$	$3$	185.g	37.d	$4$	$48$	$24$	$5.041$		None		✓	✓	✓	185.3.g.a	$2$	$0$	$4$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{4}]$
185.3.h.a	$185$	$3$	185.h	185.h	$4$	$72$	$36$	$5.041$		None		✓	✓	✓	185.3.h.a	$4$	$0$	$0$	$-8$	$0$	$-4$			$\mathrm{SU}(2)[C_{4}]$
185.3.i.a	$185$	$3$	185.i	5.c	$4$	$72$	$36$	$5.041$		None		✓	✓	✓	185.3.i.a	$2$	$0$	$0$	$0$	$4$	$-4$			$\mathrm{SU}(2)[C_{4}]$
185.3.j.a	$185$	$3$	185.j	185.j	$4$	$72$	$36$	$5.041$		None		✓	✓	✓	185.3.j.a	$4$	$0$	$0$	$0$	$-6$	$0$			$\mathrm{SU}(2)[C_{4}]$
185.3.q.a	$185$	$3$	185.q	185.q	$12$	$144$	$36$	$5.041$		None		✓	✓	✓	185.3.q.a	$4$	$0$	$0$	$0$	$18$	$0$			$\mathrm{SU}(2)[C_{12}]$
185.3.r.a	$185$	$3$	185.r	185.r	$12$	$144$	$36$	$5.041$		None		✓	✓	✓	185.3.r.a	$4$	$0$	$-6$	$-4$	$-18$	$-2$			$\mathrm{SU}(2)[C_{12}]$
185.3.s.a	$185$	$3$	185.s	185.s	$12$	$144$	$36$	$5.041$		None		✓	✓	✓	185.3.s.a	$4$	$0$	$-6$	$0$	$2$	$-2$			$\mathrm{SU}(2)[C_{12}]$
185.3.t.a	$185$	$3$	185.t	37.g	$12$	$96$	$24$	$5.041$		None		✓	✓	✓	185.3.t.a	$2$	$0$	$-4$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{12}]$
185.3.y.a	$185$	$3$	185.y	185.y	$36$	$432$	$36$	$5.041$		None		✓	✓	✓	185.3.y.a	$4$	$0$	$-12$	$-6$	$0$	$-12$			$\mathrm{SU}(2)[C_{36}]$
185.3.ba.a	$185$	$3$	185.ba	185.aa	$36$	$432$	$36$	$5.041$		None		✓	✓	✓	185.3.ba.a	$4$	$0$	$0$	$0$	$-30$	$0$			$\mathrm{SU}(2)[C_{36}]$
185.3.bb.a	$185$	$3$	185.bb	37.i	$36$	$312$	$26$	$5.041$		None		✓	✓	✓	185.3.bb.a	$2$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{36}]$
185.3.bd.a	$185$	$3$	185.bd	185.ad	$36$	$432$	$36$	$5.041$		None		✓	✓	✓	185.3.bd.a	$4$	$0$	$-12$	$-18$	$-24$	$-12$			$\mathrm{SU}(2)[C_{36}]$
185.4.a.a	$185$	$4$	185.a	1.a	$1$	$7$	$7$	$10.915$	$\mathbb{Q}[x]/(x^{7} - \cdots)$	None	✓	✓	✓	✓	185.4.a.a	$1$	$1$	$-5$	$-6$	$35$	$-49$	$-$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta _{1})q^{2}+(-1-\beta _{1}+\beta _{3})q^{3}+\cdots$
185.4.a.b	$185$	$4$	185.a	1.a	$1$	$7$	$7$	$10.915$	$\mathbb{Q}[x]/(x^{7} - \cdots)$	None	✓	✓	✓	✓	185.4.a.b	$1$	$1$	$1$	$-8$	$-35$	$-77$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+(-1-\beta _{5})q^{3}+(2+\beta _{5}-\beta _{6})q^{4}+\cdots$
185.4.a.c	$185$	$4$	185.a	1.a	$1$	$10$	$10$	$10.915$	$\mathbb{Q}[x]/(x^{10} - \cdots)$	None	✓	✓	✓	✓	185.4.a.c	$1$	$0$	$7$	$4$	$-50$	$49$	$+$	$2^{3}$	$\mathrm{SU}(2)$	$q+(1-\beta _{1})q^{2}-\beta _{5}q^{3}+(5-\beta _{1}+\beta _{4}+\cdots)q^{4}+\cdots$
185.4.a.d	$185$	$4$	185.a	1.a	$1$	$12$	$12$	$10.915$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	None	✓	✓	✓	✓	185.4.a.d	$1$	$0$	$1$	$6$	$60$	$77$	$+$	$2^{5}$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+\beta _{3}q^{3}+(7+\beta _{2}-\beta _{3})q^{4}+\cdots$
185.4.b.a	$185$	$4$	185.b	5.b	$2$	$54$	$54$	$10.915$		None		✓	✓	✓	185.4.b.a	$2$	$0$	$0$	$0$	$-8$	$0$			$\mathrm{SU}(2)[C_{2}]$
185.4.c.a	$185$	$4$	185.c	37.b	$2$	$38$	$38$	$10.915$		None		✓	✓	✓	185.4.c.a	$2$	$0$	$0$	$0$	$0$	$-12$			$\mathrm{SU}(2)[C_{2}]$
185.4.d.a	$185$	$4$	185.d	185.d	$2$	$56$	$56$	$10.915$		None		✓	✓	✓	185.4.d.a	$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$

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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.