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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 251 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
99.1.h.a	$99$	$1$	99.h	99.h	$6$	$2$	$1$	$0.049$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-11}) $	None		$4$	$0$	$0$	$-1$	$1$	$0$		$1$		$q+\zeta_{6}^{2}q^{3}+\zeta_{6}^{2}q^{4}-\zeta_{6}^{2}q^{5}-\zeta_{6}q^{9}+\cdots$
99.2.a.a	$99$	$2$	99.a	1.a	$1$	$1$	$1$	$0.791$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$-1$	$0$	$-4$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{4}-4q^{5}-2q^{7}+3q^{8}+4q^{10}+\cdots$
99.2.a.b	$99$	$2$	99.a	1.a	$1$	$1$	$1$	$0.791$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$-1$	$0$	$2$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{4}+2q^{5}+4q^{7}+3q^{8}-2q^{10}+\cdots$
99.2.a.c	$99$	$2$	99.a	1.a	$1$	$1$	$1$	$0.791$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$1$	$0$	$4$	$-2$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{4}+4q^{5}-2q^{7}-3q^{8}+4q^{10}+\cdots$
99.2.a.d	$99$	$2$	99.a	1.a	$1$	$1$	$1$	$0.791$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$2$	$0$	$-1$	$-2$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{2}+2q^{4}-q^{5}-2q^{7}-2q^{10}+\cdots$
99.2.d.a	$99$	$2$	99.d	33.d	$2$	$4$	$4$	$0.791$	$\Q(\sqrt{-2}, \sqrt{3})$	$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{2}q^{2}+q^{4}-\beta _{1}q^{5}-\beta _{3}q^{7}+\beta _{2}q^{8}+\cdots$
99.2.e.a	$99$	$2$	99.e	9.c	$3$	$2$	$1$	$0.791$	$\Q(\sqrt{-3}) $	$_{}$	None	None		$2$	$0$	$-1$	$-3$	$-1$	$-4$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-1+\zeta_{6})q^{2}+(-2+\zeta_{6})q^{3}+\zeta_{6}q^{4}+\cdots$
99.2.e.b	$99$	$2$	99.e	9.c	$3$	$2$	$1$	$0.791$	$\Q(\sqrt{-3}) $	$_{}$	None	None		$2$	$0$	$0$	$-3$	$3$	$4$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-1-\zeta_{6})q^{3}+2\zeta_{6}q^{4}+3\zeta_{6}q^{5}+\cdots$
99.2.e.c	$99$	$2$	99.e	9.c	$3$	$2$	$1$	$0.791$	$\Q(\sqrt{-3}) $	$_{}$	None	None		$2$	$0$	$2$	$0$	$2$	$-4$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(2-2\zeta_{6})q^{2}+(1-2\zeta_{6})q^{3}-2\zeta_{6}q^{4}+\cdots$
99.2.e.d	$99$	$2$	99.e	9.c	$3$	$6$	$3$	$0.791$	$\Q(\zeta_{18})$	$_{}$	None	None		$2$	$0$	$0$	$0$	$-3$	$3$		$3$	$\mathrm{SU}(2)[C_{3}]$	$q+(\zeta_{18}^{2}-\zeta_{18}^{3}-\zeta_{18}^{4}+\zeta_{18}^{5})q^{2}+\cdots$
99.2.e.e	$99$	$2$	99.e	9.c	$3$	$8$	$4$	$0.791$	8.0.508277025.1	$_{}$	None	None		$2$	$0$	$-1$	$5$	$-4$	$-1$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-\beta _{2}-\beta _{7})q^{2}+(1+\beta _{7})q^{3}+(-2+\cdots)q^{4}+\cdots$
99.2.f.a	$99$	$2$	99.f	11.c	$5$	$4$	$1$	$0.791$	$\Q(\zeta_{10})$	$_{}$	None	None		$2$	$0$	$1$	$0$	$3$	$1$		$1$	$\mathrm{SU}(2)[C_{5}]$	$q+(-1+2\zeta_{10}-2\zeta_{10}^{2}+\zeta_{10}^{3})q^{2}+\cdots$
99.2.f.b	$99$	$2$	99.f	11.c	$5$	$4$	$1$	$0.791$	$\Q(\zeta_{10})$	$_{}$	None	None		$2$	$0$	$3$	$0$	$1$	$-3$		$1$	$\mathrm{SU}(2)[C_{5}]$	$q+(1-\zeta_{10}^{3})q^{2}+(1-\zeta_{10})q^{4}+(1-2\zeta_{10}+\cdots)q^{5}+\cdots$
99.2.f.c	$99$	$2$	99.f	11.c	$5$	$8$	$2$	$0.791$	8.0.484000000.9	$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$-6$		$1$	$\mathrm{SU}(2)[C_{5}]$	$q+\beta _{1}q^{2}+(1+2\beta _{2}+\beta _{3})q^{4}+(\beta _{4}+\beta _{7})q^{5}+\cdots$
99.2.g.a	$99$	$2$	99.g	99.g	$6$	$4$	$2$	$0.791$	$\Q(\sqrt{-3}, \sqrt{-11})$	$_{}$	$\Q(\sqrt{-11}) $	None		$4$	$0$	$0$	$-1$	$-9$	$0$		$1$	$\mathrm{U}(1)[D_{6}]$	$q-\beta _{1}q^{3}+(2-2\beta _{2})q^{4}+(-1-\beta _{1}+\cdots)q^{5}+\cdots$
99.2.g.b	$99$	$2$	99.g	99.g	$6$	$16$	$8$	$0.791$	$\mathbb{Q}[x]/(x^{16} + \cdots)$	$_{}$	None	None		$4$	$0$	$0$	$-6$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q+\beta _{1}q^{2}+(\beta _{6}-\beta _{7}+\beta _{9}+\beta _{12}+\beta _{13}+\cdots)q^{3}+\cdots$
99.2.j.a	$99$	$2$	99.j	33.f	$10$	$16$	$4$	$0.791$	$\mathbb{Q}[x]/(x^{16} + \cdots)$	$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{10}]$	$q+(\beta _{8}-\beta _{10}-\beta _{11}+\beta _{12}-\beta _{14}+2\beta _{15})q^{2}+\cdots$
99.2.m.a	$99$	$2$	99.m	99.m	$15$	$8$	$1$	$0.791$	$\Q(\zeta_{15})$	$_{}$	None	None		$4$	$0$	$-4$	$3$	$6$	$-1$		$1$	$\mathrm{SU}(2)[C_{15}]$	$q+(1-2\zeta_{15}^{2}+\zeta_{15}^{3}-\zeta_{15}^{4}+\zeta_{15}^{5}+\cdots)q^{2}+\cdots$
99.2.m.b	$99$	$2$	99.m	99.m	$15$	$72$	$9$	$0.791$		$_{}$	None	None		$4$	$0$	$-1$	$-12$	$-8$	$-2$			$\mathrm{SU}(2)[C_{15}]$
99.2.p.a	$99$	$2$	99.p	99.p	$30$	$80$	$10$	$0.791$		$_{}$	None	None		$4$	$0$	$-15$	$-3$	$-6$	$-5$			$\mathrm{SU}(2)[C_{30}]$
99.3.b.a	$99$	$3$	99.b	3.b	$2$	$8$	$8$	$2.698$	8.0.$\cdots$.6	$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$16$		$2^{6}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{2}q^{2}+(-2-\beta _{3})q^{4}+(\beta _{1}-\beta _{2}+\cdots)q^{5}+\cdots$
99.3.c.a	$99$	$3$	99.c	11.b	$2$	$1$	$1$	$2.698$	$\Q$	$_{}$	$\Q(\sqrt{-11}) $	None	✓	$2$	$0$	$0$	$0$	$1$	$0$		$1$	$\mathrm{U}(1)[D_{2}]$	$q+4q^{4}+q^{5}+11q^{11}+2^{4}q^{16}+4q^{20}+\cdots$
99.3.c.b	$99$	$3$	99.c	11.b	$2$	$4$	$4$	$2.698$	4.0.39744.5	$_{}$	None	None		$2$	$0$	$0$	$0$	$-4$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{3}q^{2}+(-5-2\beta _{1})q^{4}+(-1-3\beta _{1}+\cdots)q^{5}+\cdots$
99.3.c.c	$99$	$3$	99.c	11.b	$2$	$4$	$4$	$2.698$	$\Q(\sqrt{-3}, \sqrt{46})$	$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{2}q^{2}+q^{4}+\beta _{1}q^{5}-\beta _{3}q^{7}-5\beta _{2}q^{8}+\cdots$
99.3.h.a	$99$	$3$	99.h	99.h	$6$	$4$	$2$	$2.698$	$\Q(\sqrt{-3}, \sqrt{-11})$	$_{}$	$\Q(\sqrt{-11}) $	None		$4$	$0$	$0$	$5$	$-1$	$0$		$1$	$\mathrm{U}(1)[D_{6}]$	$q+(2\beta _{2}-\beta _{3})q^{3}-4\beta _{2}q^{4}+(3-6\beta _{1}+\cdots)q^{5}+\cdots$
99.3.h.b	$99$	$3$	99.h	99.h	$6$	$40$	$20$	$2.698$		$_{}$	None	None		$4$	$0$	$0$	$-6$	$2$	$0$			$\mathrm{SU}(2)[C_{6}]$
99.3.i.a	$99$	$3$	99.i	9.d	$6$	$40$	$20$	$2.698$		$_{}$	None	None		$2$	$0$	$0$	$-1$	$-9$	$2$			$\mathrm{SU}(2)[C_{6}]$
99.3.k.a	$99$	$3$	99.k	11.d	$10$	$4$	$1$	$2.698$	$\Q(\zeta_{10})$	$_{}$	None	None		$2$	$0$	$5$	$0$	$4$	$10$		$1$	$\mathrm{SU}(2)[C_{10}]$	$q+(2\zeta_{10}-2\zeta_{10}^{2}+\zeta_{10}^{3})q^{2}+(-4+\cdots)q^{4}+\cdots$
99.3.k.b	$99$	$3$	99.k	11.d	$10$	$16$	$4$	$2.698$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$30$		$2^{4}$	$\mathrm{SU}(2)[C_{10}]$	$q+\beta _{5}q^{2}+(-1-3\beta _{2}-\beta _{4}-\beta _{6}+\beta _{11}+\cdots)q^{4}+\cdots$
99.3.k.c	$99$	$3$	99.k	11.d	$10$	$16$	$4$	$2.698$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	$_{}$	None	None		$2$	$0$	$0$	$0$	$4$	$-30$		$1$	$\mathrm{SU}(2)[C_{10}]$	$q+(-1-\beta _{2}+\beta _{5}-\beta _{7}-\beta _{8})q^{2}+(-\beta _{1}+\cdots)q^{4}+\cdots$
99.3.l.a	$99$	$3$	99.l	33.h	$10$	$32$	$8$	$2.698$		$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$-16$			$\mathrm{SU}(2)[C_{10}]$
99.3.n.a	$99$	$3$	99.n	99.n	$30$	$176$	$22$	$2.698$		$_{}$	None	None		$4$	$0$	$-9$	$-3$	$-18$	$-3$			$\mathrm{SU}(2)[C_{30}]$
99.3.o.a	$99$	$3$	99.o	99.o	$30$	$176$	$22$	$2.698$		$_{}$	None	None		$4$	$0$	$-5$	$-9$	$-6$	$-5$			$\mathrm{SU}(2)[C_{30}]$
99.4.a.a	$99$	$4$	99.a	1.a	$1$	$1$	$1$	$5.841$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$1$	$0$	$4$	$-26$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-7q^{4}+4q^{5}-26q^{7}-15q^{8}+\cdots$
99.4.a.b	$99$	$4$	99.a	1.a	$1$	$1$	$1$	$5.841$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$5$	$0$	$14$	$-32$	$+$	$1$	$\mathrm{SU}(2)$	$q+5q^{2}+17q^{4}+14q^{5}-2^{5}q^{7}+45q^{8}+\cdots$
99.4.a.c	$99$	$4$	99.a	1.a	$1$	$2$	$2$	$5.841$	$\Q(\sqrt{3}) $	$_{}$	None	None	✓	$1$	$0$	$-2$	$0$	$-2$	$20$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta )q^{2}+(-4-2\beta )q^{4}+(-1+\cdots)q^{5}+\cdots$
99.4.a.d	$99$	$4$	99.a	1.a	$1$	$2$	$2$	$5.841$	$\Q(\sqrt{3}) $	$_{}$	None	None	✓	$1$	$1$	$-2$	$0$	$-20$	$-16$	$-$	$2$	$\mathrm{SU}(2)$	$q+(-1+\beta )q^{2}+(5-2\beta )q^{4}+(-10+\cdots)q^{5}+\cdots$
99.4.a.e	$99$	$4$	99.a	1.a	$1$	$2$	$2$	$5.841$	$\Q(\sqrt{33}) $	$_{}$	None	None	✓	$1$	$1$	$-1$	$0$	$-16$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta q^{2}+\beta q^{4}+(-10+4\beta )q^{5}+(2+\cdots)q^{7}+\cdots$
99.4.a.f	$99$	$4$	99.a	1.a	$1$	$2$	$2$	$5.841$	$\Q(\sqrt{97}) $	$_{}$	None	None	✓	$1$	$0$	$-1$	$0$	$14$	$24$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta q^{2}+(2^{4}+\beta )q^{4}+(6+2\beta )q^{5}+(14+\cdots)q^{7}+\cdots$
99.4.a.g	$99$	$4$	99.a	1.a	$1$	$2$	$2$	$5.841$	$\Q(\sqrt{3}) $	$_{}$	None	None	✓	$1$	$0$	$2$	$0$	$20$	$-16$	$+$	$2$	$\mathrm{SU}(2)$	$q+(1+\beta )q^{2}+(5+2\beta )q^{4}+(10-\beta )q^{5}+\cdots$
99.4.d.a	$99$	$4$	99.d	33.d	$2$	$2$	$2$	$5.841$	$\Q(\sqrt{-2}) $	$_{}$	None	None		$2$	$1$	$-6$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q-3q^{2}+q^{4}+14\beta q^{5}-12\beta q^{7}+21q^{8}+\cdots$
99.4.d.b	$99$	$4$	99.d	33.d	$2$	$2$	$2$	$5.841$	$\Q(\sqrt{-2}) $	$_{}$	None	None		$2$	$0$	$6$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+3q^{2}+q^{4}+14\beta q^{5}+12\beta q^{7}-21q^{8}+\cdots$
99.4.d.c	$99$	$4$	99.d	33.d	$2$	$8$	$8$	$5.841$	8.0.$\cdots$.4	$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$0$		$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{2}+(5+\beta _{3})q^{4}-5\beta _{6}q^{5}+(-2\beta _{4}+\cdots)q^{7}+\cdots$
99.4.e.a	$99$	$4$	99.e	9.c	$3$	$2$	$1$	$5.841$	$\Q(\sqrt{-3}) $	$_{}$	None	None		$2$	$0$	$4$	$-9$	$19$	$26$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(4-4\zeta_{6})q^{2}+(-6+3\zeta_{6})q^{3}-8\zeta_{6}q^{4}+\cdots$
99.4.e.b	$99$	$4$	99.e	9.c	$3$	$24$	$12$	$5.841$		$_{}$	None	None		$2$	$0$	$-4$	$6$	$2$	$8$			$\mathrm{SU}(2)[C_{3}]$
99.4.e.c	$99$	$4$	99.e	9.c	$3$	$34$	$17$	$5.841$		$_{}$	None	None		$2$	$0$	$0$	$5$	$3$	$-22$			$\mathrm{SU}(2)[C_{3}]$
99.4.f.a	$99$	$4$	99.f	11.c	$5$	$4$	$1$	$5.841$	$\Q(\zeta_{10})$	$_{}$	None	None		$2$	$0$	$-10$	$0$	$21$	$37$		$1$	$\mathrm{SU}(2)[C_{5}]$	$q+(-2-2\zeta_{10}+2\zeta_{10}^{2}+2\zeta_{10}^{3})q^{2}+\cdots$
99.4.f.b	$99$	$4$	99.f	11.c	$5$	$8$	$2$	$5.841$	8.0.682515625.5	$_{}$	None	None		$2$	$0$	$6$	$0$	$-9$	$3$		$1$	$\mathrm{SU}(2)[C_{5}]$	$q+(\beta _{1}+2\beta _{2}-\beta _{3}-\beta _{5}-\beta _{6})q^{2}+(2+\cdots)q^{4}+\cdots$
99.4.f.c	$99$	$4$	99.f	11.c	$5$	$8$	$2$	$5.841$	8.0.$\cdots$.1	$_{}$	None	None		$2$	$0$	$7$	$0$	$7$	$-35$		$1$	$\mathrm{SU}(2)[C_{5}]$	$q+(1-\beta _{1}-\beta _{2}+\beta _{4})q^{2}+(3-2\beta _{1}+\cdots)q^{4}+\cdots$
99.4.f.d	$99$	$4$	99.f	11.c	$5$	$12$	$3$	$5.841$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	$_{}$	None	None		$2$	$0$	$0$	$0$	$-28$	$12$		$1$	$\mathrm{SU}(2)[C_{5}]$	$q+(1+\beta _{3}+\beta _{5}+\beta _{6}+\beta _{7})q^{2}+(-1+\cdots)q^{4}+\cdots$

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Elliptic curves over $\Q$
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Genus 2 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.