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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 182 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
93.1.l.a	$93$	$1$	93.l	93.l	$10$	$4$	$1$	$0.046$	$\Q(\zeta_{10})$	$D_{5}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$-1$	$0$	$-2$		$1$		$q-\zeta_{10}q^{3}-\zeta_{10}^{3}q^{4}+(\zeta_{10}^{2}+\zeta_{10}^{4}+\cdots)q^{7}+\cdots$
93.2.a.a	$93$	$2$	93.a	1.a	$1$	$2$	$2$	$0.743$	$\Q(\sqrt{5}) $	$_{}$	None	None	✓	$1$	$1$	$-3$	$-2$	$-4$	$-4$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1-\beta )q^{2}-q^{3}+3\beta q^{4}+(-3+\cdots)q^{5}+\cdots$
93.2.a.b	$93$	$2$	93.a	1.a	$1$	$3$	$3$	$0.743$	3.3.229.1	$_{}$	None	None	✓	$1$	$0$	$0$	$3$	$-2$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+q^{3}+(1+\beta _{2})q^{4}+(-1+\beta _{1}+\cdots)q^{5}+\cdots$
93.2.c.a	$93$	$2$	93.c	93.c	$2$	$8$	$8$	$0.743$	8.0.$\cdots$.2	$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$-8$		$3^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{5}q^{2}+\beta _{6}q^{3}+\beta _{3}q^{4}+\beta _{1}q^{5}+\cdots$
93.2.e.a	$93$	$2$	93.e	31.c	$3$	$4$	$2$	$0.743$	$\Q(\sqrt{2}, \sqrt{-3})$	$_{}$	None	None		$2$	$0$	$0$	$2$	$4$	$4$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+\beta _{3}q^{2}+(1+\beta _{2})q^{3}+(-\beta _{1}-2\beta _{2}+\cdots)q^{5}+\cdots$
93.2.e.b	$93$	$2$	93.e	31.c	$3$	$6$	$3$	$0.743$	6.0.591408.1	$_{}$	None	None		$2$	$0$	$0$	$-3$	$-4$	$-4$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+\beta _{3}q^{2}-\beta _{4}q^{3}+(1-\beta _{2}+\beta _{3})q^{4}+\cdots$
93.2.f.a	$93$	$2$	93.f	31.d	$5$	$8$	$2$	$0.743$	$\Q(\zeta_{15})$	$_{}$	None	None		$2$	$0$	$3$	$2$	$-6$	$9$		$5$	$\mathrm{SU}(2)[C_{5}]$	$q+(1-\zeta_{15}+\zeta_{15}^{3})q^{2}+(1+\zeta_{15}^{2}+\cdots)q^{3}+\cdots$
93.2.f.b	$93$	$2$	93.f	31.d	$5$	$16$	$4$	$0.743$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	$_{}$	None	None		$2$	$0$	$-3$	$-4$	$6$	$-7$		$1$	$\mathrm{SU}(2)[C_{5}]$	$q-\beta _{1}q^{2}+\beta _{8}q^{3}+(-1-\beta _{8}-\beta _{9}+\cdots)q^{4}+\cdots$
93.2.g.a	$93$	$2$	93.g	93.g	$6$	$2$	$1$	$0.743$	$\Q(\sqrt{-3}) $	$_{}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$-3$	$0$	$4$		$1$	$\mathrm{U}(1)[D_{6}]$	$q+(-1-\zeta_{6})q^{3}+2q^{4}+(4-4\zeta_{6})q^{7}+\cdots$
93.2.g.b	$93$	$2$	93.g	93.g	$6$	$2$	$1$	$0.743$	$\Q(\sqrt{-3}) $	$_{}$	None	None		$2$	$0$	$0$	$0$	$3$	$1$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q+(1-2\zeta_{6})q^{2}+(-1+2\zeta_{6})q^{3}-q^{4}+\cdots$
93.2.g.c	$93$	$2$	93.g	93.g	$6$	$2$	$1$	$0.743$	$\Q(\sqrt{-3}) $	$_{}$	None	None		$2$	$0$	$0$	$3$	$-3$	$1$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q+(-1+2\zeta_{6})q^{2}+(2-\zeta_{6})q^{3}-q^{4}+\cdots$
93.2.g.d	$93$	$2$	93.g	93.g	$6$	$4$	$2$	$0.743$	$\Q(\sqrt{2}, \sqrt{-3})$	$_{}$	None	None		$4$	$0$	$0$	$-6$	$0$	$-4$		$3$	$\mathrm{SU}(2)[C_{6}]$	$q+\beta _{2}q^{2}+(-1+\beta _{1})q^{3}-4q^{4}+\beta _{3}q^{5}+\cdots$
93.2.g.e	$93$	$2$	93.g	93.g	$6$	$4$	$2$	$0.743$	$\Q(\sqrt{-3}, \sqrt{-11})$	$_{}$	None	None		$2$	$0$	$0$	$1$	$-3$	$-1$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q+(-\beta _{1}+\beta _{2}+\beta _{3})q^{2}+(1-\beta _{1}-\beta _{2}+\cdots)q^{3}+\cdots$
93.2.g.f	$93$	$2$	93.g	93.g	$6$	$4$	$2$	$0.743$	$\Q(\sqrt{-3}, \sqrt{-11})$	$_{}$	None	None		$2$	$0$	$0$	$2$	$3$	$-1$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q+(-\beta _{1}+\beta _{2}+\beta _{3})q^{2}+(1-\beta _{1}+\beta _{3})q^{3}+\cdots$
93.2.k.a	$93$	$2$	93.k	93.k	$10$	$32$	$8$	$0.743$		$_{}$	None	None		$4$	$0$	$0$	$-5$	$0$	$8$			$\mathrm{SU}(2)[C_{10}]$
93.2.m.a	$93$	$2$	93.m	31.g	$15$	$16$	$2$	$0.743$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	$_{}$	None	None		$2$	$0$	$0$	$-2$	$6$	$-9$		$1$	$\mathrm{SU}(2)[C_{15}]$	$q+(-\beta _{7}+\beta _{12}+\beta _{13})q^{2}+(-1+\beta _{2}+\cdots)q^{3}+\cdots$
93.2.m.b	$93$	$2$	93.m	31.g	$15$	$24$	$3$	$0.743$		$_{}$	None	None		$2$	$0$	$0$	$3$	$-6$	$-1$			$\mathrm{SU}(2)[C_{15}]$
93.2.p.a	$93$	$2$	93.p	93.p	$30$	$8$	$1$	$0.743$	$\Q(\zeta_{15})$	$_{}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$3$	$0$	$-4$		$1$	$\mathrm{U}(1)[D_{30}]$	$q+(\zeta_{15}^{2}+2\zeta_{15}^{7})q^{3}+2\zeta_{15}^{6}q^{4}+\cdots$
93.2.p.b	$93$	$2$	93.p	93.p	$30$	$64$	$8$	$0.743$		$_{}$	None	None		$4$	$0$	$0$	$-10$	$0$	$-26$			$\mathrm{SU}(2)[C_{30}]$
93.3.b.a	$93$	$3$	93.b	3.b	$2$	$20$	$20$	$2.534$	$\mathbb{Q}[x]/(x^{20} + \cdots)$	$_{}$	None	None		$2$	$0$	$0$	$-4$	$0$	$0$		$2^{2}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{2}+\beta _{6}q^{3}+(-2+\beta _{2})q^{4}+\beta _{11}q^{5}+\cdots$
93.3.d.a	$93$	$3$	93.d	31.b	$2$	$2$	$2$	$2.534$	$\Q(\sqrt{-3}) $	$_{}$	None	None		$2$	$0$	$-6$	$0$	$-12$	$4$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q-3q^{2}-\zeta_{6}q^{3}+5q^{4}-6q^{5}+3\zeta_{6}q^{6}+\cdots$
93.3.d.b	$93$	$3$	93.d	31.b	$2$	$8$	$8$	$2.534$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	$_{}$	None	None		$2$	$0$	$6$	$0$	$12$	$-20$		$2^{4}\cdot 3$	$\mathrm{SU}(2)[C_{2}]$	$q+(1+\beta _{5})q^{2}+\beta _{1}q^{3}+(2-\beta _{2}+\beta _{5}+\cdots)q^{4}+\cdots$
93.3.h.a	$93$	$3$	93.h	93.h	$6$	$2$	$1$	$2.534$	$\Q(\sqrt{-3}) $	$_{}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$3$	$0$	$-2$		$1$	$\mathrm{U}(1)[D_{6}]$	$q+3\zeta_{6}q^{3}+4q^{4}-2\zeta_{6}q^{7}+(-9+9\zeta_{6})q^{9}+\cdots$
93.3.h.b	$93$	$3$	93.h	93.h	$6$	$36$	$18$	$2.534$		$_{}$	None	None		$4$	$0$	$0$	$-2$	$0$	$-14$			$\mathrm{SU}(2)[C_{6}]$
93.3.i.a	$93$	$3$	93.i	31.e	$6$	$10$	$5$	$2.534$	$\mathbb{Q}[x]/(x^{10} + \cdots)$	$_{}$	None	None		$2$	$0$	$-6$	$15$	$0$	$-1$		$3^{3}$	$\mathrm{SU}(2)[C_{6}]$	$q+(-1-\beta _{8}-\beta _{9})q^{2}+(1+\beta _{2})q^{3}+\cdots$
93.3.i.b	$93$	$3$	93.i	31.e	$6$	$12$	$6$	$2.534$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	$_{}$	None	None		$2$	$0$	$6$	$-18$	$0$	$9$		$3^{2}$	$\mathrm{SU}(2)[C_{6}]$	$q+(1-\beta _{3})q^{2}+(-2+\beta _{5})q^{3}+(3-\beta _{2}+\cdots)q^{4}+\cdots$
93.3.j.a	$93$	$3$	93.j	31.f	$10$	$40$	$10$	$2.534$		$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$-4$			$\mathrm{SU}(2)[C_{10}]$
93.3.l.a	$93$	$3$	93.l	93.l	$10$	$8$	$2$	$2.534$	8.0.3844000000.4	$_{}$	None	None		$4$	$0$	$0$	$-6$	$0$	$24$		$1$	$\mathrm{SU}(2)[C_{10}]$	$q+\beta _{1}q^{2}-3\beta _{3}q^{3}+(-2-3\beta _{2}+2\beta _{3}+\cdots)q^{4}+\cdots$
93.3.l.b	$93$	$3$	93.l	93.l	$10$	$72$	$18$	$2.534$		$_{}$	None	None		$4$	$0$	$0$	$5$	$0$	$-54$			$\mathrm{SU}(2)[C_{10}]$
93.3.n.a	$93$	$3$	93.n	31.h	$30$	$40$	$5$	$2.534$		$_{}$	None	None		$2$	$0$	$6$	$-15$	$0$	$11$			$\mathrm{SU}(2)[C_{30}]$
93.3.n.b	$93$	$3$	93.n	31.h	$30$	$48$	$6$	$2.534$		$_{}$	None	None		$2$	$0$	$-6$	$18$	$0$	$1$			$\mathrm{SU}(2)[C_{30}]$
93.3.o.a	$93$	$3$	93.o	93.o	$30$	$8$	$1$	$2.534$	$\Q(\zeta_{15})$	$_{}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$-3$	$0$	$2$		$1$	$\mathrm{U}(1)[D_{30}]$	$q-3\zeta_{15}^{4}q^{3}+(-4\zeta_{15}^{2}-4\zeta_{15}^{7})q^{4}+\cdots$
93.3.o.b	$93$	$3$	93.o	93.o	$30$	$144$	$18$	$2.534$		$_{}$	None	None		$4$	$0$	$0$	$-8$	$0$	$14$			$\mathrm{SU}(2)[C_{30}]$
93.4.a.a	$93$	$4$	93.a	1.a	$1$	$1$	$1$	$5.487$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$3$	$-3$	$-9$	$-34$	$-$	$1$	$\mathrm{SU}(2)$	$q+3q^{2}-3q^{3}+q^{4}-9q^{5}-9q^{6}+\cdots$
93.4.a.b	$93$	$4$	93.a	1.a	$1$	$2$	$2$	$5.487$	$\Q(\sqrt{29}) $	$_{}$	None	None	✓	$1$	$1$	$-5$	$-6$	$8$	$-4$	$-$	$1$	$\mathrm{SU}(2)$	$q+(-2-\beta )q^{2}-3q^{3}+(3+5\beta )q^{4}+\cdots$
93.4.a.c	$93$	$4$	93.a	1.a	$1$	$2$	$2$	$5.487$	$\Q(\sqrt{17}) $	$_{}$	None	None	✓	$1$	$1$	$-3$	$6$	$-8$	$-37$	$-$	$1$	$\mathrm{SU}(2)$	$q+(-1-\beta )q^{2}+3q^{3}+(-3+3\beta )q^{4}+\cdots$
93.4.a.d	$93$	$4$	93.a	1.a	$1$	$2$	$2$	$5.487$	$\Q(\sqrt{41}) $	$_{}$	None	None	✓	$1$	$1$	$-1$	$-6$	$-11$	$29$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta q^{2}-3q^{3}+(2+\beta )q^{4}+(-7+3\beta )q^{5}+\cdots$
93.4.a.e	$93$	$4$	93.a	1.a	$1$	$3$	$3$	$5.487$	3.3.2089.1	$_{}$	None	None	✓	$1$	$0$	$3$	$-9$	$8$	$19$	$+$	$1$	$\mathrm{SU}(2)$	$q+(1+\beta _{1})q^{2}-3q^{3}+(1+3\beta _{1}+2\beta _{2})q^{4}+\cdots$
93.4.a.f	$93$	$4$	93.a	1.a	$1$	$6$	$6$	$5.487$	$\mathbb{Q}[x]/(x^{6} - \cdots)$	$_{}$	None	None	✓	$1$	$0$	$3$	$18$	$12$	$47$	$+$	$1$	$\mathrm{SU}(2)$	$q+(1-\beta _{1})q^{2}+3q^{3}+(6+\beta _{2})q^{4}+(2+\cdots)q^{5}+\cdots$
93.4.c.a	$93$	$4$	93.c	93.c	$2$	$2$	$2$	$5.487$	$\Q(\sqrt{-3}) $	$_{}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$0$	$0$	$40$		$2\cdot 3$	$\mathrm{U}(1)[D_{2}]$	$q-\zeta_{6}q^{3}+8q^{4}+20q^{7}-3^{3}q^{9}-8\zeta_{6}q^{12}+\cdots$
93.4.c.b	$93$	$4$	93.c	93.c	$2$	$28$	$28$	$5.487$		$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$-64$			$\mathrm{SU}(2)[C_{2}]$
93.4.e.a	$93$	$4$	93.e	31.c	$3$	$14$	$7$	$5.487$	$\mathbb{Q}[x]/(x^{14} - \cdots)$	$_{}$	None	None		$2$	$0$	$-6$	$-21$	$-4$	$-17$		$2^{4}$	$\mathrm{SU}(2)[C_{3}]$	$q-\beta _{2}q^{2}+3\beta _{3}q^{3}+(3-\beta _{4})q^{4}+(-1+\cdots)q^{5}+\cdots$
93.4.e.b	$93$	$4$	93.e	31.c	$3$	$18$	$9$	$5.487$	$\mathbb{Q}[x]/(x^{18} - \cdots)$	$_{}$	None	None		$2$	$0$	$6$	$27$	$4$	$-9$		$2^{4}\cdot 3$	$\mathrm{SU}(2)[C_{3}]$	$q+\beta _{3}q^{2}+3\beta _{4}q^{3}+(5-\beta _{2})q^{4}+(\beta _{5}+\cdots)q^{5}+\cdots$
93.4.f.a	$93$	$4$	93.f	31.d	$5$	$32$	$8$	$5.487$		$_{}$	None	None		$2$	$0$	$0$	$-24$	$-54$	$-25$			$\mathrm{SU}(2)[C_{5}]$
93.4.f.b	$93$	$4$	93.f	31.d	$5$	$32$	$8$	$5.487$		$_{}$	None	None		$2$	$0$	$0$	$24$	$54$	$-25$			$\mathrm{SU}(2)[C_{5}]$
93.4.g.a	$93$	$4$	93.g	93.g	$6$	$60$	$30$	$5.487$		$_{}$	None	None		$4$	$0$	$0$	$-3$	$0$	$24$			$\mathrm{SU}(2)[C_{6}]$
93.4.k.a	$93$	$4$	93.k	93.k	$10$	$8$	$2$	$5.487$	$\Q(\zeta_{15})$	$_{}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$0$	$0$	$-40$		$2^{4}\cdot 3^{4}$	$\mathrm{U}(1)[D_{10}]$	$q+\zeta_{15}^{6}q^{3}+8\zeta_{15}^{2}q^{4}+(-10-10\zeta_{15}^{2}+\cdots)q^{7}+\cdots$
93.4.k.b	$93$	$4$	93.k	93.k	$10$	$112$	$28$	$5.487$		$_{}$	None	None		$4$	$0$	$0$	$-5$	$0$	$24$			$\mathrm{SU}(2)[C_{10}]$
93.4.m.a	$93$	$4$	93.m	31.g	$15$	$56$	$7$	$5.487$		$_{}$	None	None		$2$	$0$	$6$	$21$	$54$	$32$			$\mathrm{SU}(2)[C_{15}]$
93.4.m.b	$93$	$4$	93.m	31.g	$15$	$72$	$9$	$5.487$		$_{}$	None	None		$2$	$0$	$-6$	$-27$	$-54$	$24$			$\mathrm{SU}(2)[C_{15}]$

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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.