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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 (40 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				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*	$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$	Coefficient ring index	Sato-Tate	$q$-expansion
780.1.o.a	$780$	$1$	780.o	195.e	$2$	$1$	$1$	$0.389$	$\Q$	$D_{3}$	$\Q(\sqrt{-195}) $	None	✓	$2$	$0$	$0$	$-1$	$-1$	$-1$	$1$		$q-q^{3}-q^{5}-q^{7}+q^{9}+q^{11}+q^{13}+\cdots$
780.1.o.b	$780$	$1$	780.o	195.e	$2$	$1$	$1$	$0.389$	$\Q$	$D_{3}$	$\Q(\sqrt{-195}) $	None	✓	$2$	$0$	$0$	$-1$	$1$	$1$	$1$		$q-q^{3}+q^{5}+q^{7}+q^{9}-q^{11}-q^{13}+\cdots$
780.1.o.c	$780$	$1$	780.o	195.e	$2$	$1$	$1$	$0.389$	$\Q$	$D_{3}$	$\Q(\sqrt{-195}) $	None	✓	$2$	$0$	$0$	$1$	$-1$	$1$	$1$		$q+q^{3}-q^{5}+q^{7}+q^{9}+q^{11}-q^{13}+\cdots$
780.1.o.d	$780$	$1$	780.o	195.e	$2$	$1$	$1$	$0.389$	$\Q$	$D_{3}$	$\Q(\sqrt{-195}) $	None	✓	$2$	$0$	$0$	$1$	$1$	$-1$	$1$		$q+q^{3}+q^{5}-q^{7}+q^{9}-q^{11}+q^{13}+\cdots$
1365.1.cz.a	$1365$	$1$	1365.cz	1365.bz	$6$	$2$	$1$	$0.681$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-195}) $	None		$4$	$0$	$0$	$-1$	$-1$	$2$	$1$		$q+\zeta_{6}^{2}q^{3}+\zeta_{6}^{2}q^{4}-\zeta_{6}q^{5}+q^{7}+\cdots$
1365.1.cz.b	$1365$	$1$	1365.cz	1365.bz	$6$	$2$	$1$	$0.681$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-195}) $	None		$4$	$0$	$0$	$-1$	$1$	$-2$	$1$		$q+\zeta_{6}^{2}q^{3}+\zeta_{6}^{2}q^{4}+\zeta_{6}q^{5}-q^{7}+\cdots$
1365.1.cz.c	$1365$	$1$	1365.cz	1365.bz	$6$	$2$	$1$	$0.681$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-195}) $	None		$4$	$0$	$0$	$1$	$-1$	$-2$	$1$		$q-\zeta_{6}^{2}q^{3}+\zeta_{6}^{2}q^{4}-\zeta_{6}q^{5}-q^{7}+\cdots$
1365.1.cz.d	$1365$	$1$	1365.cz	1365.bz	$6$	$2$	$1$	$0.681$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-195}) $	None		$4$	$0$	$0$	$1$	$1$	$2$	$1$		$q-\zeta_{6}^{2}q^{3}+\zeta_{6}^{2}q^{4}+\zeta_{6}q^{5}+q^{7}+\cdots$
1755.1.e.a	$1755$	$1$	1755.e	195.e	$2$	$1$	$1$	$0.876$	$\Q$	$D_{3}$	$\Q(\sqrt{-195}) $	None	✓	$2$	$0$	$0$	$0$	$-1$	$-1$	$1$		$q+q^{4}-q^{5}-q^{7}+q^{11}+q^{13}+q^{16}+\cdots$
1755.1.e.b	$1755$	$1$	1755.e	195.e	$2$	$1$	$1$	$0.876$	$\Q$	$D_{3}$	$\Q(\sqrt{-195}) $	None	✓	$2$	$0$	$0$	$0$	$-1$	$1$	$1$		$q+q^{4}-q^{5}+q^{7}+q^{11}-q^{13}+q^{16}+\cdots$
1755.1.e.c	$1755$	$1$	1755.e	195.e	$2$	$1$	$1$	$0.876$	$\Q$	$D_{3}$	$\Q(\sqrt{-195}) $	None	✓	$2$	$0$	$0$	$0$	$1$	$-1$	$1$		$q+q^{4}+q^{5}-q^{7}-q^{11}+q^{13}+q^{16}+\cdots$
1755.1.e.d	$1755$	$1$	1755.e	195.e	$2$	$1$	$1$	$0.876$	$\Q$	$D_{3}$	$\Q(\sqrt{-195}) $	None	✓	$2$	$0$	$0$	$0$	$1$	$1$	$1$		$q+q^{4}+q^{5}+q^{7}-q^{11}-q^{13}+q^{16}+\cdots$
2145.1.cn.a	$2145$	$1$	2145.cn	2145.bn	$10$	$4$	$1$	$1.070$	$\Q(\zeta_{10})$	$D_{5}$	$\Q(\sqrt{-195}) $	None		$4$	$0$	$0$	$-1$	$-1$	$-2$	$1$		$q-\zeta_{10}q^{3}+\zeta_{10}^{4}q^{4}-\zeta_{10}^{3}q^{5}+(-\zeta_{10}+\cdots)q^{7}+\cdots$
2145.1.cn.b	$2145$	$1$	2145.cn	2145.bn	$10$	$4$	$1$	$1.070$	$\Q(\zeta_{10})$	$D_{5}$	$\Q(\sqrt{-195}) $	None		$4$	$0$	$0$	$-1$	$1$	$2$	$1$		$q-\zeta_{10}q^{3}+\zeta_{10}^{4}q^{4}+\zeta_{10}^{3}q^{5}+(\zeta_{10}+\cdots)q^{7}+\cdots$
2145.1.cn.c	$2145$	$1$	2145.cn	2145.bn	$10$	$4$	$1$	$1.070$	$\Q(\zeta_{10})$	$D_{5}$	$\Q(\sqrt{-195}) $	None		$4$	$0$	$0$	$1$	$-1$	$2$	$1$		$q+\zeta_{10}q^{3}+\zeta_{10}^{4}q^{4}-\zeta_{10}^{3}q^{5}+(\zeta_{10}+\cdots)q^{7}+\cdots$
2145.1.cn.d	$2145$	$1$	2145.cn	2145.bn	$10$	$4$	$1$	$1.070$	$\Q(\zeta_{10})$	$D_{5}$	$\Q(\sqrt{-195}) $	None		$4$	$0$	$0$	$1$	$1$	$-2$	$1$		$q+\zeta_{10}q^{3}+\zeta_{10}^{4}q^{4}+\zeta_{10}^{3}q^{5}+(-\zeta_{10}+\cdots)q^{7}+\cdots$
2925.1.o.a	$2925$	$1$	2925.o	65.h	$4$	$4$	$2$	$1.460$	$\Q(\zeta_{8})$	$D_{2}$	$\Q(\sqrt{-3}) $, $\Q(\sqrt{-195}) $	$\Q(\sqrt{65}) $		$16$	$0$	$0$	$0$	$0$	$0$	$1$		$q-\zeta_{8}^{2}q^{4}-\zeta_{8}q^{7}+\zeta_{8}^{3}q^{13}-q^{16}+\cdots$
3120.1.be.a	$3120$	$1$	3120.be	195.e	$2$	$1$	$1$	$1.557$	$\Q$	$D_{3}$	$\Q(\sqrt{-195}) $	None	✓	$2$	$0$	$0$	$-1$	$-1$	$-1$	$1$		$q-q^{3}-q^{5}-q^{7}+q^{9}-q^{11}-q^{13}+\cdots$
3120.1.be.b	$3120$	$1$	3120.be	195.e	$2$	$1$	$1$	$1.557$	$\Q$	$D_{3}$	$\Q(\sqrt{-195}) $	None	✓	$2$	$0$	$0$	$-1$	$1$	$1$	$1$		$q-q^{3}+q^{5}+q^{7}+q^{9}+q^{11}+q^{13}+\cdots$
3120.1.be.c	$3120$	$1$	3120.be	195.e	$2$	$1$	$1$	$1.557$	$\Q$	$D_{3}$	$\Q(\sqrt{-195}) $	None	✓	$2$	$0$	$0$	$1$	$-1$	$1$	$1$		$q+q^{3}-q^{5}+q^{7}+q^{9}-q^{11}+q^{13}+\cdots$
3120.1.be.d	$3120$	$1$	3120.be	195.e	$2$	$1$	$1$	$1.557$	$\Q$	$D_{3}$	$\Q(\sqrt{-195}) $	None	✓	$2$	$0$	$0$	$1$	$1$	$-1$	$1$		$q+q^{3}+q^{5}-q^{7}+q^{9}+q^{11}-q^{13}+\cdots$
3315.1.b.a	$3315$	$1$	3315.b	3315.b	$2$	$2$	$2$	$1.654$	$\Q(\sqrt{-1}) $	$D_{2}$	$\Q(\sqrt{-51}) $, $\Q(\sqrt{-195}) $	$\Q(\sqrt{1105}) $		$8$	$0$	$0$	$0$	$0$	$0$	$1$		$q+iq^{3}+q^{4}-iq^{5}-q^{9}+iq^{11}+\cdots$
3315.1.b.b	$3315$	$1$	3315.b	3315.b	$2$	$2$	$2$	$1.654$	$\Q(\sqrt{-1}) $	$D_{2}$	$\Q(\sqrt{-51}) $, $\Q(\sqrt{-195}) $	$\Q(\sqrt{1105}) $		$8$	$0$	$0$	$0$	$0$	$0$	$1$		$q-iq^{3}+q^{4}-iq^{5}-q^{9}+iq^{11}+\cdots$
3315.1.cq.a	$3315$	$1$	3315.cq	3315.bq	$4$	$4$	$2$	$1.654$	$\Q(\zeta_{8})$	$D_{4}$	$\Q(\sqrt{-195}) $	None		$8$	$0$	$0$	$0$	$0$	$-4$	$1$		$q-\zeta_{8}q^{3}-q^{4}-\zeta_{8}q^{5}+(-1+\zeta_{8}^{2}+\cdots)q^{7}+\cdots$
3315.1.cq.b	$3315$	$1$	3315.cq	3315.bq	$4$	$4$	$2$	$1.654$	$\Q(\zeta_{8})$	$D_{4}$	$\Q(\sqrt{-195}) $	None		$8$	$0$	$0$	$0$	$0$	$4$	$1$		$q+\zeta_{8}q^{3}-q^{4}-\zeta_{8}q^{5}+(1-\zeta_{8}^{2})q^{7}+\cdots$
3315.1.dz.a	$3315$	$1$	3315.dz	3315.cz	$8$	$8$	$2$	$1.654$	$\Q(\zeta_{16})$	$D_{8}$	$\Q(\sqrt{-195}) $	None		$8$	$0$	$0$	$0$	$0$	$-8$	$1$		$q+\zeta_{16}^{3}q^{3}+\zeta_{16}^{4}q^{4}-\zeta_{16}^{7}q^{5}+\cdots$
3315.1.dz.b	$3315$	$1$	3315.dz	3315.cz	$8$	$8$	$2$	$1.654$	$\Q(\zeta_{16})$	$D_{8}$	$\Q(\sqrt{-195}) $	None		$8$	$0$	$0$	$0$	$0$	$8$	$1$		$q-\zeta_{16}^{3}q^{3}+\zeta_{16}^{4}q^{4}-\zeta_{16}^{7}q^{5}+\cdots$
3900.1.f.c	$3900$	$1$	3900.f	39.d	$2$	$2$	$2$	$1.946$	$\Q(\sqrt{-1}) $	$D_{3}$	$\Q(\sqrt{-195}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q-iq^{3}-iq^{7}-q^{9}-q^{11}-iq^{13}+\cdots$
3900.1.f.d	$3900$	$1$	3900.f	39.d	$2$	$2$	$2$	$1.946$	$\Q(\sqrt{-1}) $	$D_{3}$	$\Q(\sqrt{-195}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q+iq^{3}-iq^{7}-q^{9}+q^{11}-iq^{13}+\cdots$
585.2.h.e	$585$	$2$	585.h	65.d	$2$	$4$	$4$	$4.671$	$\Q(\sqrt{-5}, \sqrt{13})$	$_{}$	$\Q(\sqrt{-195}) $	None		$8$	$0$	$0$	$0$	$0$	$0$	$2^{2}$	$\mathrm{U}(1)[D_{2}]$	$q-2q^{4}-\beta _{1}q^{5}+\beta _{3}q^{7}+\beta _{1}q^{11}+\cdots$
195.3.e.a	$195$	$3$	195.e	195.e	$2$	$1$	$1$	$5.313$	$\Q$	$_{}$	$\Q(\sqrt{-195}) $	None	✓	$2$	$0$	$0$	$-3$	$-5$	$1$	$1$	$\mathrm{U}(1)[D_{2}]$	$q-3q^{3}+4q^{4}-5q^{5}+q^{7}+9q^{9}+\cdots$
195.3.e.b	$195$	$3$	195.e	195.e	$2$	$1$	$1$	$5.313$	$\Q$	$_{}$	$\Q(\sqrt{-195}) $	None	✓	$2$	$0$	$0$	$-3$	$5$	$-1$	$1$	$\mathrm{U}(1)[D_{2}]$	$q-3q^{3}+4q^{4}+5q^{5}-q^{7}+9q^{9}+\cdots$
195.3.e.c	$195$	$3$	195.e	195.e	$2$	$1$	$1$	$5.313$	$\Q$	$_{}$	$\Q(\sqrt{-195}) $	None	✓	$2$	$0$	$0$	$3$	$-5$	$-1$	$1$	$\mathrm{U}(1)[D_{2}]$	$q+3q^{3}+4q^{4}-5q^{5}-q^{7}+9q^{9}+\cdots$
195.3.e.d	$195$	$3$	195.e	195.e	$2$	$1$	$1$	$5.313$	$\Q$	$_{}$	$\Q(\sqrt{-195}) $	None	✓	$2$	$0$	$0$	$3$	$5$	$1$	$1$	$\mathrm{U}(1)[D_{2}]$	$q+3q^{3}+4q^{4}+5q^{5}+q^{7}+9q^{9}+\cdots$
975.2.s.b	$975$	$2$	975.s	195.s	$4$	$8$	$4$	$7.785$	8.0.$\cdots$.2	$_{}$	$\Q(\sqrt{-195}) $	None		$16$	$0$	$0$	$0$	$0$	$0$	$2^{4}$	$\mathrm{U}(1)[D_{4}]$	$q-\beta _{3}q^{3}+2\beta _{2}q^{4}+\beta _{1}q^{7}-3\beta _{2}q^{9}+\cdots$
2340.2.j.c	$2340$	$2$	2340.j	65.d	$2$	$8$	$8$	$18.685$	8.0.4569760000.1	$_{}$	$\Q(\sqrt{-195}) $	None		$8$	$0$	$0$	$0$	$0$	$0$	$2^{4}\cdot 3^{4}$	$\mathrm{U}(1)[D_{2}]$	$q-\beta _{5}q^{5}+\beta _{1}q^{7}+(-\beta _{2}-\beta _{5})q^{11}+\cdots$
780.3.o.a	$780$	$3$	780.o	195.e	$2$	$2$	$2$	$21.253$	$\Q(\sqrt{65}) $	$_{}$	$\Q(\sqrt{-195}) $	None	✓	$2$	$0$	$0$	$-6$	$-10$	$-1$	$3$	$\mathrm{U}(1)[D_{2}]$	$q-3q^{3}-5q^{5}+(-1-\beta )q^{7}+9q^{9}+\cdots$
780.3.o.b	$780$	$3$	780.o	195.e	$2$	$2$	$2$	$21.253$	$\Q(\sqrt{65}) $	$_{}$	$\Q(\sqrt{-195}) $	None	✓	$2$	$0$	$0$	$-6$	$10$	$1$	$3$	$\mathrm{U}(1)[D_{2}]$	$q-3q^{3}+5q^{5}+(1+\beta )q^{7}+9q^{9}+(9+\cdots)q^{11}+\cdots$
780.3.o.c	$780$	$3$	780.o	195.e	$2$	$2$	$2$	$21.253$	$\Q(\sqrt{65}) $	$_{}$	$\Q(\sqrt{-195}) $	None	✓	$2$	$0$	$0$	$6$	$-10$	$1$	$3$	$\mathrm{U}(1)[D_{2}]$	$q+3q^{3}-5q^{5}+(1+\beta )q^{7}+9q^{9}+(-9+\cdots)q^{11}+\cdots$
780.3.o.d	$780$	$3$	780.o	195.e	$2$	$2$	$2$	$21.253$	$\Q(\sqrt{65}) $	$_{}$	$\Q(\sqrt{-195}) $	None	✓	$2$	$0$	$0$	$6$	$10$	$-1$	$3$	$\mathrm{U}(1)[D_{2}]$	$q+3q^{3}+5q^{5}+(-1-\beta )q^{7}+9q^{9}+\cdots$

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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.