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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 (1-50 of 143 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
999.1.d.a	$999$	$1$	999.d	111.d	$2$	$1$	$1$	$0.499$	$\Q$	$D_{3}$	$\Q(\sqrt{-111}) $	None	✓	$2$	$0$	$-2$	$0$	$1$	$-1$		$1$		$q-2q^{2}+3q^{4}+q^{5}-q^{7}-4q^{8}-2q^{10}+\cdots$
999.1.d.b	$999$	$1$	999.d	111.d	$2$	$1$	$1$	$0.499$	$\Q$	$D_{3}$	$\Q(\sqrt{-111}) $	None	✓	$2$	$0$	$2$	$0$	$-1$	$-1$		$1$		$q+2q^{2}+3q^{4}-q^{5}-q^{7}+4q^{8}-2q^{10}+\cdots$
999.1.d.c	$999$	$1$	999.d	111.d	$2$	$2$	$2$	$0.499$	$\Q(\sqrt{3}) $	$D_{6}$	$\Q(\sqrt{-111}) $	None	✓	$4$	$0$	$0$	$0$	$0$	$2$		$1$		$q-q^{4}-\beta q^{5}+q^{7}+q^{16}+\beta q^{17}+\cdots$
999.1.d.d	$999$	$1$	999.d	111.d	$2$	$4$	$4$	$0.499$	$\Q(\zeta_{24})^+$	$D_{12}$	$\Q(\sqrt{-111}) $	None	✓	$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q+(-\beta _{1}-\beta _{3})q^{2}+q^{4}-\beta _{1}q^{5}-\beta _{2}q^{7}+\cdots$
999.1.ce.a	$999$	$1$	999.ce	111.n	$18$	$6$	$1$	$0.499$	$\Q(\zeta_{18})$	$D_{18}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$0$	$0$	$-6$		$1$		$q+\zeta_{18}^{5}q^{4}+(-1+\zeta_{18}^{7})q^{7}+(\zeta_{18}^{4}+\cdots)q^{13}+\cdots$
999.1.cq.a	$999$	$1$	999.cq	111.p	$18$	$6$	$1$	$0.499$	$\Q(\zeta_{18})$	$D_{9}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$0$	$0$	$6$		$1$		$q+\zeta_{18}^{4}q^{4}+(1+\zeta_{18}^{2})q^{7}+(-\zeta_{18}^{3}+\cdots)q^{13}+\cdots$
999.1.dq.a	$999$	$1$	999.dq	37.i	$36$	$12$	$1$	$0.499$	$\Q(\zeta_{36})$	$D_{36}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{36}^{17}q^{4}+(\zeta_{36}^{9}-\zeta_{36}^{13})q^{7}+\cdots$
999.2.a.a	$999$	$2$	999.a	1.a	$1$	$1$	$1$	$7.977$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$-1$	$0$	$-1$	$-1$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{4}-q^{5}-q^{7}+3q^{8}+q^{10}+\cdots$
999.2.a.b	$999$	$2$	999.a	1.a	$1$	$1$	$1$	$7.977$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$1$	$0$	$1$	$-1$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{4}+q^{5}-q^{7}-3q^{8}+q^{10}+\cdots$
999.2.a.c	$999$	$2$	999.a	1.a	$1$	$2$	$2$	$7.977$	$\Q(\sqrt{3}) $	$_{}$	None	None	✓	$2$	$1$	$0$	$0$	$0$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{2}+q^{4}-\beta q^{5}-q^{7}-\beta q^{8}-3q^{10}+\cdots$
999.2.a.d	$999$	$2$	999.a	1.a	$1$	$2$	$2$	$7.977$	$\Q(\sqrt{7}) $	$_{}$	None	None	✓	$2$	$0$	$0$	$0$	$0$	$-2$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{2}+5q^{4}+\beta q^{5}-q^{7}+3\beta q^{8}+\cdots$
999.2.a.e	$999$	$2$	999.a	1.a	$1$	$6$	$6$	$7.977$	6.6.30815981.1	$_{}$	None	None	✓	$1$	$1$	$-3$	$0$	$-4$	$-1$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta _{1})q^{2}+(1-\beta _{1}-\beta _{3}+\beta _{4}+\cdots)q^{4}+\cdots$
999.2.a.f	$999$	$2$	999.a	1.a	$1$	$6$	$6$	$7.977$	6.6.11335869.1	$_{}$	None	None	✓	$1$	$1$	$-3$	$0$	$-4$	$-1$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta _{1})q^{2}+(1-\beta _{1}+\beta _{2})q^{4}+\cdots$
999.2.a.g	$999$	$2$	999.a	1.a	$1$	$6$	$6$	$7.977$	6.6.30815981.1	$_{}$	None	None	✓	$1$	$0$	$3$	$0$	$4$	$-1$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1-\beta _{1})q^{2}+(1-\beta _{1}-\beta _{3}+\beta _{4})q^{4}+\cdots$
999.2.a.h	$999$	$2$	999.a	1.a	$1$	$6$	$6$	$7.977$	6.6.11335869.1	$_{}$	None	None	✓	$1$	$0$	$3$	$0$	$4$	$-1$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1-\beta _{1})q^{2}+(1-\beta _{1}+\beta _{2})q^{4}+(1+\cdots)q^{5}+\cdots$
999.2.a.i	$999$	$2$	999.a	1.a	$1$	$8$	$8$	$7.977$	8.8.$\cdots$.1	$_{}$	None	None	✓	$2$	$0$	$0$	$0$	$0$	$8$	$-$	$2^{2}$	$\mathrm{SU}(2)$	$q+\beta _{3}q^{2}+(1-\beta _{4}+\beta _{6})q^{4}+(-\beta _{2}+\cdots)q^{5}+\cdots$
999.2.a.j	$999$	$2$	999.a	1.a	$1$	$10$	$10$	$7.977$	$\mathbb{Q}[x]/(x^{10} - \cdots)$	$_{}$	None	None	✓	$2$	$0$	$0$	$0$	$0$	$6$	$-$	$2^{4}$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}+\beta _{5}q^{5}+(1-\beta _{4}+\cdots)q^{7}+\cdots$
999.2.c.a	$999$	$2$	999.c	37.b	$2$	$2$	$2$	$7.977$	$\Q(\sqrt{-3}) $	$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$2$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q-\zeta_{6}q^{2}-q^{4}-\zeta_{6}q^{5}+q^{7}-\zeta_{6}q^{8}+\cdots$
999.2.c.b	$999$	$2$	999.c	37.b	$2$	$2$	$2$	$7.977$	$\Q(\sqrt{-3}) $	$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$2$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q-\zeta_{6}q^{2}-q^{4}-\zeta_{6}q^{5}+q^{7}-\zeta_{6}q^{8}+\cdots$
999.2.c.c	$999$	$2$	999.c	37.b	$2$	$2$	$2$	$7.977$	$\Q(\sqrt{-1}) $	$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$-6$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+iq^{2}+q^{4}-iq^{5}-3q^{7}+3iq^{8}+\cdots$
999.2.c.d	$999$	$2$	999.c	37.b	$2$	$2$	$2$	$7.977$	$\Q(\sqrt{-1}) $	$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$-6$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+iq^{2}+q^{4}-iq^{5}-3q^{7}+3iq^{8}+\cdots$
999.2.c.e	$999$	$2$	999.c	37.b	$2$	$2$	$2$	$7.977$	$\Q(\sqrt{-3}) $	$_{}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$0$	$0$	$2$		$3$	$\mathrm{U}(1)[D_{2}]$	$q+2q^{4}+q^{7}+(-1+2\zeta_{6})q^{13}+4q^{16}+\cdots$
999.2.c.f	$999$	$2$	999.c	37.b	$2$	$8$	$8$	$7.977$	8.0.$\cdots$.1	$_{}$	$\Q(\sqrt{-111}) $	None		$4$	$0$	$0$	$0$	$0$	$0$		$2^{2}\cdot 3^{2}$	$\mathrm{U}(1)[D_{2}]$	$q-\beta _{4}q^{2}+(-2+\beta _{7})q^{4}-\beta _{3}q^{5}+\beta _{7}q^{7}+\cdots$
999.2.c.g	$999$	$2$	999.c	37.b	$2$	$8$	$8$	$7.977$	8.0.$\cdots$.1	$_{}$	$\Q(\sqrt{-111}) $	None		$4$	$0$	$0$	$0$	$0$	$0$		$2^{2}\cdot 3$	$\mathrm{U}(1)[D_{2}]$	$q+\beta _{4}q^{2}+(-2+\beta _{7})q^{4}+\beta _{2}q^{5}+(\beta _{3}+\cdots)q^{7}+\cdots$
999.2.c.h	$999$	$2$	999.c	37.b	$2$	$12$	$12$	$7.977$	$\mathbb{Q}[x]/(x^{12} + \cdots)$	$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$2$		$3^{4}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{2}+(-1+\beta _{2})q^{4}-\beta _{10}q^{5}+\cdots$
999.2.c.i	$999$	$2$	999.c	37.b	$2$	$12$	$12$	$7.977$	$\mathbb{Q}[x]/(x^{12} + \cdots)$	$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$2$		$3^{4}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{2}+(-1+\beta _{2})q^{4}-\beta _{10}q^{5}+\cdots$
999.2.e.a	$999$	$2$	999.e	9.c	$3$	$36$	$18$	$7.977$		$_{}$	None	None		$2$	$0$	$-4$	$0$	$-6$	$0$			$\mathrm{SU}(2)[C_{3}]$
999.2.e.b	$999$	$2$	999.e	9.c	$3$	$36$	$18$	$7.977$		$_{}$	None	None		$2$	$0$	$6$	$0$	$10$	$0$			$\mathrm{SU}(2)[C_{3}]$
999.2.f.a	$999$	$2$	999.f	37.c	$3$	$2$	$1$	$7.977$	$\Q(\sqrt{-3}) $	$_{}$	None	None		$2$	$1$	$-1$	$0$	$-4$	$4$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-1+\zeta_{6})q^{2}+\zeta_{6}q^{4}-4\zeta_{6}q^{5}+\cdots$
999.2.f.b	$999$	$2$	999.f	37.c	$3$	$2$	$1$	$7.977$	$\Q(\sqrt{-3}) $	$_{}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$0$	$0$	$-5$		$1$	$\mathrm{U}(1)[D_{3}]$	$q+2\zeta_{6}q^{4}-5\zeta_{6}q^{7}+7\zeta_{6}q^{13}+(-4+\cdots)q^{16}+\cdots$
999.2.f.c	$999$	$2$	999.f	37.c	$3$	$2$	$1$	$7.977$	$\Q(\sqrt{-3}) $	$_{}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$0$	$0$	$4$		$1$	$\mathrm{U}(1)[D_{3}]$	$q+2\zeta_{6}q^{4}+4\zeta_{6}q^{7}-2\zeta_{6}q^{13}+(-4+\cdots)q^{16}+\cdots$
999.2.f.d	$999$	$2$	999.f	37.c	$3$	$2$	$1$	$7.977$	$\Q(\sqrt{-3}) $	$_{}$	None	None		$2$	$0$	$1$	$0$	$4$	$4$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(1-\zeta_{6})q^{2}+\zeta_{6}q^{4}+4\zeta_{6}q^{5}+4\zeta_{6}q^{7}+\cdots$
999.2.f.e	$999$	$2$	999.f	37.c	$3$	$22$	$11$	$7.977$		$_{}$	None	None		$2$	$0$	$-1$	$0$	$-4$	$-5$			$\mathrm{SU}(2)[C_{3}]$
999.2.f.f	$999$	$2$	999.f	37.c	$3$	$22$	$11$	$7.977$		$_{}$	None	None		$2$	$0$	$1$	$0$	$4$	$-5$			$\mathrm{SU}(2)[C_{3}]$
999.2.f.g	$999$	$2$	999.f	37.c	$3$	$24$	$12$	$7.977$		$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$-4$			$\mathrm{SU}(2)[C_{3}]$
999.2.f.h	$999$	$2$	999.f	37.c	$3$	$24$	$12$	$7.977$		$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$8$			$\mathrm{SU}(2)[C_{3}]$
999.2.g.a	$999$	$2$	999.g	333.g	$3$	$72$	$36$	$7.977$		$_{}$	None	None		$2$	$0$	$-1$	$0$	$1$	$0$			$\mathrm{SU}(2)[C_{3}]$
999.2.h.a	$999$	$2$	999.h	333.h	$3$	$72$	$36$	$7.977$		$_{}$	None	None		$2$	$0$	$2$	$0$	$-2$	$0$			$\mathrm{SU}(2)[C_{3}]$
999.2.j.a	$999$	$2$	999.j	111.g	$4$	$4$	$2$	$7.977$	$\Q(\zeta_{12})$	$_{}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$0$	$0$	$0$		$3^{2}$	$\mathrm{U}(1)[D_{4}]$	$q+2\zeta_{12}q^{4}+(-\zeta_{12}+2\zeta_{12}^{3})q^{7}+\cdots$
999.2.j.b	$999$	$2$	999.j	111.g	$4$	$8$	$4$	$7.977$	8.0.56070144.2	$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$-8$		$2^{6}$	$\mathrm{SU}(2)[C_{4}]$	$q-\beta _{1}q^{2}+(-2\beta _{2}-\beta _{5})q^{4}+\beta _{3}q^{5}+\cdots$
999.2.j.c	$999$	$2$	999.j	111.g	$4$	$40$	$20$	$7.977$		$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$8$			$\mathrm{SU}(2)[C_{4}]$
999.2.j.d	$999$	$2$	999.j	111.g	$4$	$48$	$24$	$7.977$		$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{4}]$
999.2.k.a	$999$	$2$	999.k	333.k	$6$	$2$	$1$	$7.977$	$\Q(\sqrt{-3}) $	$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$-1$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q+(-1+2\zeta_{6})q^{2}-q^{4}+(-1+\zeta_{6})q^{7}+\cdots$
999.2.k.b	$999$	$2$	999.k	333.k	$6$	$4$	$2$	$7.977$	$\Q(\sqrt{-3}, \sqrt{-7})$	$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$3$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q+(\beta _{1}-\beta _{3})q^{2}+(-1+\beta _{1}+\beta _{3})q^{4}+\cdots$
999.2.k.c	$999$	$2$	999.k	333.k	$6$	$66$	$33$	$7.977$		$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{6}]$
999.2.q.a	$999$	$2$	999.q	333.q	$6$	$8$	$4$	$7.977$	8.0.592240896.6	$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$0$		$3$	$\mathrm{SU}(2)[C_{6}]$	$q+\beta _{3}q^{2}-\beta _{1}q^{4}+(\beta _{4}-\beta _{5})q^{5}+(-1+\cdots)q^{7}+\cdots$
999.2.q.b	$999$	$2$	999.q	333.q	$6$	$12$	$6$	$7.977$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$-2$		$3^{2}$	$\mathrm{SU}(2)[C_{6}]$	$q-\beta _{5}q^{2}+(2-2\beta _{4}-\beta _{6})q^{4}+\beta _{1}q^{5}+\cdots$
999.2.q.c	$999$	$2$	999.q	333.q	$6$	$52$	$26$	$7.977$		$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$-2$			$\mathrm{SU}(2)[C_{6}]$
999.2.s.a	$999$	$2$	999.s	37.e	$6$	$2$	$1$	$7.977$	$\Q(\sqrt{-3}) $	$_{}$	None	None		$2$	$1$	$-3$	$0$	$-6$	$2$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q+(-1-\zeta_{6})q^{2}+\zeta_{6}q^{4}+(-4+2\zeta_{6})q^{5}+\cdots$
999.2.s.b	$999$	$2$	999.s	37.e	$6$	$2$	$1$	$7.977$	$\Q(\sqrt{-3}) $	$_{}$	$\Q(\sqrt{-3}) $	None		$4$	$1$	$0$	$0$	$0$	$-4$		$1$	$\mathrm{U}(1)[D_{6}]$	$q-2\zeta_{6}q^{4}-4\zeta_{6}q^{7}+(-8+4\zeta_{6})q^{13}+\cdots$

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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.