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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 (45 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
239.1.b.a	$239$	$1$	239.b	239.b	$2$	$1$	$1$	$0.119$	$\Q$	$D_{3}$	$\Q(\sqrt{-239}) $	None	✓	$2$	$0$	$-1$	$2$	$-1$	$0$	$1$		$q-q^{2}+2q^{3}-q^{5}-2q^{6}+q^{8}+3q^{9}+\cdots$
239.1.b.b	$239$	$1$	239.b	239.b	$2$	$2$	$2$	$0.119$	$\Q(\sqrt{5}) $	$D_{5}$	$\Q(\sqrt{-239}) $	None	✓	$2$	$0$	$-1$	$-1$	$-1$	$0$	$1$		$q+(-1+\beta )q^{2}+(-1+\beta )q^{3}+(1-\beta )q^{4}+\cdots$
239.1.b.c	$239$	$1$	239.b	239.b	$2$	$4$	$4$	$0.119$	$\Q(\zeta_{15})^+$	$D_{15}$	$\Q(\sqrt{-239}) $	None	✓	$2$	$0$	$1$	$-2$	$1$	$0$	$1$		$q+\beta _{1}q^{2}+(-1-\beta _{3})q^{3}+(1+\beta _{2})q^{4}+\cdots$
1195.1.c.a	$1195$	$1$	1195.c	1195.c	$2$	$1$	$1$	$0.596$	$\Q$	$D_{2}$	$\Q(\sqrt{-239}) $, $\Q(\sqrt{-1195}) $	$\Q(\sqrt{5}) $	✓	$4$	$0$	$0$	$0$	$1$	$0$	$1$		$q+q^{4}+q^{5}+q^{9}-2q^{11}+q^{16}+q^{20}+\cdots$
1195.1.c.b	$1195$	$1$	1195.c	1195.c	$2$	$2$	$2$	$0.596$	$\Q(\sqrt{-3}) $	$D_{6}$	$\Q(\sqrt{-239}) $	None		$4$	$0$	$0$	$0$	$-1$	$0$	$1$		$q+(\zeta_{6}+\zeta_{6}^{2})q^{2}+(-1-\zeta_{6}+\zeta_{6}^{2}+\cdots)q^{4}+\cdots$
1195.1.c.d	$1195$	$1$	1195.c	1195.c	$2$	$4$	$4$	$0.596$	$\Q(\zeta_{10})$	$D_{10}$	$\Q(\sqrt{-239}) $	None		$4$	$0$	$0$	$0$	$-1$	$0$	$1$		$q+(\zeta_{10}+\zeta_{10}^{4})q^{2}+(\zeta_{10}+\zeta_{10}^{4})q^{3}+\cdots$
1195.1.c.e	$1195$	$1$	1195.c	1195.c	$2$	$8$	$8$	$0.596$	$\Q(\zeta_{15})$	$D_{30}$	$\Q(\sqrt{-239}) $	None		$4$	$0$	$0$	$0$	$1$	$0$	$1$		$q+(\zeta_{30}^{4}+\zeta_{30}^{11})q^{2}+(-\zeta_{30}^{6}-\zeta_{30}^{9}+\cdots)q^{3}+\cdots$
1912.1.b.a	$1912$	$1$	1912.b	1912.b	$2$	$1$	$1$	$0.954$	$\Q$	$D_{2}$	$\Q(\sqrt{-239}) $, $\Q(\sqrt{-478}) $	$\Q(\sqrt{2}) $	✓	$4$	$0$	$1$	$0$	$0$	$0$	$1$		$q+q^{2}+q^{4}+q^{8}+q^{9}+q^{16}-2q^{17}+\cdots$
1912.1.b.c	$1912$	$1$	1912.b	1912.b	$2$	$2$	$2$	$0.954$	$\Q(\sqrt{-3}) $	$D_{6}$	$\Q(\sqrt{-239}) $	None		$4$	$0$	$-1$	$0$	$0$	$0$	$1$		$q+\zeta_{6}^{2}q^{2}-\zeta_{6}q^{4}+(-\zeta_{6}-\zeta_{6}^{2})q^{5}+\cdots$
1912.1.b.d	$1912$	$1$	1912.b	1912.b	$2$	$4$	$4$	$0.954$	$\Q(\zeta_{10})$	$D_{10}$	$\Q(\sqrt{-239}) $	None		$4$	$0$	$-1$	$0$	$0$	$0$	$1$		$q-\zeta_{10}^{3}q^{2}+(\zeta_{10}^{2}+\zeta_{10}^{3})q^{3}-\zeta_{10}q^{4}+\cdots$
1912.1.b.e	$1912$	$1$	1912.b	1912.b	$2$	$8$	$8$	$0.954$	$\Q(\zeta_{15})$	$D_{30}$	$\Q(\sqrt{-239}) $	None		$4$	$0$	$1$	$0$	$0$	$0$	$1$		$q-\zeta_{30}q^{2}+(-\zeta_{30}^{6}-\zeta_{30}^{9})q^{3}+\zeta_{30}^{2}q^{4}+\cdots$
2151.1.d.a	$2151$	$1$	2151.d	239.b	$2$	$1$	$1$	$1.073$	$\Q$	$D_{3}$	$\Q(\sqrt{-239}) $	None	✓	$2$	$0$	$1$	$0$	$1$	$0$	$1$		$q+q^{2}+q^{5}-q^{8}+q^{10}+q^{11}-q^{16}+\cdots$
2151.1.d.c	$2151$	$1$	2151.d	239.b	$2$	$2$	$2$	$1.073$	$\Q(\sqrt{5}) $	$D_{5}$	$\Q(\sqrt{-239}) $	None	✓	$2$	$0$	$1$	$0$	$1$	$0$	$1$		$q+(1-\beta )q^{2}+(1-\beta )q^{4}+(1-\beta )q^{5}+\cdots$
2151.1.d.e	$2151$	$1$	2151.d	239.b	$2$	$4$	$4$	$1.073$	$\Q(\zeta_{15})^+$	$D_{15}$	$\Q(\sqrt{-239}) $	None	✓	$2$	$0$	$-1$	$0$	$-1$	$0$	$1$		$q-\beta _{1}q^{2}+(1+\beta _{2})q^{4}+(-1+\beta _{1}-\beta _{3})q^{5}+\cdots$
2151.1.f.a	$2151$	$1$	2151.f	2151.f	$6$	$6$	$3$	$1.073$	$\Q(\zeta_{18})$	$D_{9}$	$\Q(\sqrt{-239}) $	None		$4$	$0$	$0$	$-3$	$0$	$0$	$3$		$q+(\zeta_{18}^{4}+\zeta_{18}^{8})q^{2}-\zeta_{18}^{3}q^{3}+(-\zeta_{18}^{3}+\cdots)q^{4}+\cdots$
2151.1.f.b	$2151$	$1$	2151.f	2151.f	$6$	$24$	$12$	$1.073$	$\Q(\zeta_{45})$	$D_{45}$	$\Q(\sqrt{-239}) $	None		$4$	$0$	$0$	$3$	$0$	$0$	$1$		$q+(-\zeta_{90}^{7}-\zeta_{90}^{23})q^{2}-\zeta_{90}^{3}q^{3}+\cdots$
2629.1.g.a	$2629$	$1$	2629.g	2629.g	$10$	$20$	$5$	$1.312$	$\Q(\zeta_{50})$	$D_{25}$	$\Q(\sqrt{-239}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q+(\zeta_{50}^{16}-\zeta_{50}^{19})q^{2}+(-\zeta_{50}^{9}-\zeta_{50}^{21}+\cdots)q^{3}+\cdots$
2629.1.g.b	$2629$	$1$	2629.g	2629.g	$10$	$40$	$10$	$1.312$	$\Q(\zeta_{75})$	$D_{75}$	$\Q(\sqrt{-239}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q+(\zeta_{150}^{4}-\zeta_{150}^{11})q^{2}+(-\zeta_{150}^{21}+\zeta_{150}^{24}+\cdots)q^{3}+\cdots$
2868.1.e.a	$2868$	$1$	2868.e	2868.e	$2$	$1$	$1$	$1.431$	$\Q$	$D_{2}$	$\Q(\sqrt{-239}) $, $\Q(\sqrt{-717}) $	$\Q(\sqrt{3}) $	✓	$4$	$0$	$-1$	$-1$	$0$	$0$	$1$		$q-q^{2}-q^{3}+q^{4}+q^{6}-q^{8}+q^{9}+\cdots$
2868.1.e.b	$2868$	$1$	2868.e	2868.e	$2$	$1$	$1$	$1.431$	$\Q$	$D_{2}$	$\Q(\sqrt{-239}) $, $\Q(\sqrt{-717}) $	$\Q(\sqrt{3}) $	✓	$4$	$0$	$1$	$1$	$0$	$0$	$1$		$q+q^{2}+q^{3}+q^{4}+q^{6}+q^{8}+q^{9}+\cdots$
2868.1.e.d	$2868$	$1$	2868.e	2868.e	$2$	$2$	$2$	$1.431$	$\Q(\sqrt{-3}) $	$D_{6}$	$\Q(\sqrt{-239}) $	None		$4$	$0$	$-1$	$2$	$0$	$0$	$1$		$q+\zeta_{6}^{2}q^{2}+q^{3}-\zeta_{6}q^{4}+(\zeta_{6}+\zeta_{6}^{2}+\cdots)q^{5}+\cdots$
2868.1.e.e	$2868$	$1$	2868.e	2868.e	$2$	$2$	$2$	$1.431$	$\Q(\sqrt{-3}) $	$D_{6}$	$\Q(\sqrt{-239}) $	None		$4$	$0$	$1$	$-2$	$0$	$0$	$1$		$q-\zeta_{6}^{2}q^{2}-q^{3}-\zeta_{6}q^{4}+(-\zeta_{6}-\zeta_{6}^{2}+\cdots)q^{5}+\cdots$
2868.1.e.g	$2868$	$1$	2868.e	2868.e	$2$	$4$	$4$	$1.431$	$\Q(\zeta_{10})$	$D_{10}$	$\Q(\sqrt{-239}) $	None		$4$	$0$	$-1$	$-1$	$0$	$0$	$1$		$q-\zeta_{10}^{3}q^{2}+\zeta_{10}^{2}q^{3}-\zeta_{10}q^{4}+(\zeta_{10}^{2}+\cdots)q^{5}+\cdots$
2868.1.e.h	$2868$	$1$	2868.e	2868.e	$2$	$4$	$4$	$1.431$	$\Q(\zeta_{10})$	$D_{10}$	$\Q(\sqrt{-239}) $	None		$4$	$0$	$1$	$1$	$0$	$0$	$1$		$q+\zeta_{10}q^{2}+\zeta_{10}q^{3}+\zeta_{10}^{2}q^{4}+(-\zeta_{10}+\cdots)q^{5}+\cdots$
2868.1.e.i	$2868$	$1$	2868.e	2868.e	$2$	$8$	$8$	$1.431$	$\Q(\zeta_{15})$	$D_{30}$	$\Q(\sqrt{-239}) $	None		$4$	$0$	$-1$	$2$	$0$	$0$	$1$		$q+\zeta_{30}^{11}q^{2}-\zeta_{30}^{6}q^{3}-\zeta_{30}^{7}q^{4}+\cdots$
2868.1.e.j	$2868$	$1$	2868.e	2868.e	$2$	$8$	$8$	$1.431$	$\Q(\zeta_{15})$	$D_{30}$	$\Q(\sqrt{-239}) $	None		$4$	$0$	$1$	$-2$	$0$	$0$	$1$		$q-\zeta_{30}q^{2}-\zeta_{30}^{9}q^{3}+\zeta_{30}^{2}q^{4}+(\zeta_{30}^{4}+\cdots)q^{5}+\cdots$
3585.1.i.a	$3585$	$1$	3585.i	3585.i	$4$	$2$	$1$	$1.789$	$\Q(\sqrt{-1}) $	$D_{4}$	$\Q(\sqrt{-239}) $	None		$4$	$0$	$-2$	$2$	$-2$	$0$	$1$		$q+(-1+i)q^{2}+q^{3}-iq^{4}-q^{5}+(-1+\cdots)q^{6}+\cdots$
3585.1.i.b	$3585$	$1$	3585.i	3585.i	$4$	$2$	$1$	$1.789$	$\Q(\sqrt{-1}) $	$D_{4}$	$\Q(\sqrt{-239}) $	None		$4$	$0$	$2$	$0$	$2$	$0$	$1$		$q+(1-i)q^{2}-iq^{3}-iq^{4}+q^{5}+(-1+\cdots)q^{6}+\cdots$
3585.1.i.c	$3585$	$1$	3585.i	3585.i	$4$	$4$	$2$	$1.789$	$\Q(\zeta_{12})$	$D_{12}$	$\Q(\sqrt{-239}) $	None		$4$	$0$	$-2$	$0$	$-2$	$0$	$1$		$q+(\zeta_{12}^{4}+\zeta_{12}^{5})q^{2}-\zeta_{12}^{3}q^{3}+(-\zeta_{12}^{2}+\cdots)q^{4}+\cdots$
3585.1.i.d	$3585$	$1$	3585.i	3585.i	$4$	$4$	$2$	$1.789$	$\Q(\zeta_{12})$	$D_{12}$	$\Q(\sqrt{-239}) $	None		$4$	$0$	$2$	$4$	$2$	$0$	$1$		$q+(-\zeta_{12}+\zeta_{12}^{2})q^{2}+q^{3}+(\zeta_{12}^{2}+\cdots)q^{4}+\cdots$
3585.1.i.e	$3585$	$1$	3585.i	3585.i	$4$	$8$	$4$	$1.789$	$\Q(\zeta_{20})$	$D_{20}$	$\Q(\sqrt{-239}) $	None		$4$	$0$	$-2$	$0$	$-2$	$0$	$1$		$q+(-\zeta_{20}+\zeta_{20}^{4})q^{2}-\zeta_{20}q^{3}+(\zeta_{20}^{2}+\cdots)q^{4}+\cdots$
3585.1.i.f	$3585$	$1$	3585.i	3585.i	$4$	$8$	$4$	$1.789$	$\Q(\zeta_{20})$	$D_{20}$	$\Q(\sqrt{-239}) $	None		$4$	$0$	$2$	$-2$	$2$	$0$	$1$		$q+(\zeta_{20}^{6}+\zeta_{20}^{9})q^{2}-\zeta_{20}^{6}q^{3}+(-\zeta_{20}^{2}+\cdots)q^{4}+\cdots$
3585.1.i.g	$3585$	$1$	3585.i	3585.i	$4$	$16$	$8$	$1.789$	$\Q(\zeta_{60})$	$D_{60}$	$\Q(\sqrt{-239}) $	None		$4$	$0$	$-2$	$-4$	$-2$	$0$	$1$		$q+(\zeta_{60}^{7}-\zeta_{60}^{8})q^{2}-\zeta_{60}^{18}q^{3}+(\zeta_{60}^{14}+\cdots)q^{4}+\cdots$
3585.1.i.h	$3585$	$1$	3585.i	3585.i	$4$	$16$	$8$	$1.789$	$\Q(\zeta_{60})$	$D_{60}$	$\Q(\sqrt{-239}) $	None		$4$	$0$	$2$	$0$	$2$	$0$	$1$		$q+(\zeta_{60}^{7}+\zeta_{60}^{8})q^{2}+\zeta_{60}^{27}q^{3}+(\zeta_{60}^{14}+\cdots)q^{4}+\cdots$
3824.1.h.a	$3824$	$1$	3824.h	239.b	$2$	$1$	$1$	$1.908$	$\Q$	$D_{3}$	$\Q(\sqrt{-239}) $	None	✓	$2$	$0$	$0$	$-2$	$-1$	$0$	$1$		$q-2q^{3}-q^{5}+3q^{9}+q^{11}+2q^{15}+\cdots$
3824.1.h.b	$3824$	$1$	3824.h	239.b	$2$	$2$	$2$	$1.908$	$\Q(\sqrt{5}) $	$D_{5}$	$\Q(\sqrt{-239}) $	None	✓	$2$	$0$	$0$	$1$	$-1$	$0$	$1$		$q+(1-\beta )q^{3}+(-1+\beta )q^{5}+(1-\beta )q^{9}+\cdots$
3824.1.h.c	$3824$	$1$	3824.h	239.b	$2$	$4$	$4$	$1.908$	$\Q(\zeta_{15})^+$	$D_{15}$	$\Q(\sqrt{-239}) $	None	✓	$2$	$0$	$0$	$2$	$1$	$0$	$1$		$q+(1+\beta _{3})q^{3}+\beta _{1}q^{5}+(1+\beta _{3})q^{9}+\cdots$
3824.1.l.a	$3824$	$1$	3824.l	3824.l	$4$	$2$	$1$	$1.908$	$\Q(\sqrt{-1}) $	$D_{4}$	$\Q(\sqrt{-239}) $	None		$4$	$0$	$-2$	$-2$	$-2$	$0$	$1$		$q-q^{2}+(-1+i)q^{3}+q^{4}+(-1-i+\cdots)q^{5}+\cdots$
3824.1.l.b	$3824$	$1$	3824.l	3824.l	$4$	$4$	$2$	$1.908$	$\Q(\zeta_{12})$	$D_{12}$	$\Q(\sqrt{-239}) $	None		$4$	$0$	$2$	$-4$	$2$	$0$	$1$		$q+\zeta_{12}^{2}q^{2}+(-1+\zeta_{12}^{3})q^{3}+\zeta_{12}^{4}q^{4}+\cdots$
3824.1.l.c	$3824$	$1$	3824.l	3824.l	$4$	$8$	$4$	$1.908$	$\Q(\zeta_{20})$	$D_{20}$	$\Q(\sqrt{-239}) $	None		$4$	$0$	$2$	$2$	$2$	$0$	$1$		$q-\zeta_{20}^{8}q^{2}+(\zeta_{20}^{2}-\zeta_{20}^{3})q^{3}-\zeta_{20}^{6}q^{4}+\cdots$
3824.1.l.d	$3824$	$1$	3824.l	3824.l	$4$	$16$	$8$	$1.908$	$\Q(\zeta_{60})$	$D_{60}$	$\Q(\sqrt{-239}) $	None		$4$	$0$	$-2$	$4$	$-2$	$0$	$1$		$q-\zeta_{60}^{8}q^{2}+(-\zeta_{60}^{3}-\zeta_{60}^{12})q^{3}+\cdots$
717.2.b.a	$717$	$2$	717.b	717.b	$2$	$30$	$30$	$5.725$		$_{}$	$\Q(\sqrt{-239}) $	None		$4$	$0$	$0$	$0$	$0$	$0$		$\mathrm{U}(1)[D_{2}]$
239.3.b.a	$239$	$3$	239.b	239.b	$2$	$15$	$15$	$6.512$	$\mathbb{Q}[x]/(x^{15} - \cdots)$	$_{}$	$\Q(\sqrt{-239}) $	None	✓	$2$	$0$	$0$	$0$	$0$	$0$	$3$	$\mathrm{U}(1)[D_{2}]$	$q+\beta _{2}q^{2}+\beta _{12}q^{3}+(4+\beta _{8}+\beta _{9})q^{4}+\cdots$
956.2.c.b	$956$	$2$	956.c	956.c	$2$	$30$	$30$	$7.634$		$_{}$	$\Q(\sqrt{-239}) $	None		$4$	$0$	$0$	$0$	$0$	$0$		$\mathrm{U}(1)[D_{2}]$
239.5.b.a	$239$	$5$	239.b	239.b	$2$	$15$	$15$	$24.705$	$\mathbb{Q}[x]/(x^{15} - \cdots)$	$_{}$	$\Q(\sqrt{-239}) $	None	✓	$2$	$0$	$0$	$0$	$0$	$0$	$3$	$\mathrm{U}(1)[D_{2}]$	$q+(\beta _{8}+\beta _{9})q^{2}+(\beta _{3}-2\beta _{6})q^{3}+(2^{4}+\cdots)q^{4}+\cdots$

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Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
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.