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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 (47 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
3311.1.h.a	$3311$	$1$	3311.h	3311.h	$2$	$1$	$1$	$1.652$	$\Q$	$D_{2}$	$\Q(\sqrt{-7}) $, $\Q(\sqrt{-3311}) $	$\Q(\sqrt{473}) $	✓	$4$	$0$	$-2$	$0$	$0$	$-1$		$1$		$q-2q^{2}+3q^{4}-q^{7}-4q^{8}-q^{9}-q^{11}+\cdots$
3311.1.h.b	$3311$	$1$	3311.h	3311.h	$2$	$1$	$1$	$1.652$	$\Q$	$D_{3}$	$\Q(\sqrt{-3311}) $	None	✓	$2$	$0$	$-1$	$-1$	$-1$	$1$		$1$		$q-q^{2}-q^{3}-q^{5}+q^{6}+q^{7}+q^{8}+\cdots$
3311.1.h.c	$3311$	$1$	3311.h	3311.h	$2$	$1$	$1$	$1.652$	$\Q$	$D_{3}$	$\Q(\sqrt{-3311}) $	None	✓	$2$	$0$	$-1$	$1$	$1$	$1$		$1$		$q-q^{2}+q^{3}+q^{5}-q^{6}+q^{7}+q^{8}+\cdots$
3311.1.h.d	$3311$	$1$	3311.h	3311.h	$2$	$1$	$1$	$1.652$	$\Q$	$D_{3}$	$\Q(\sqrt{-3311}) $	None	✓	$2$	$0$	$1$	$-1$	$-1$	$-1$		$1$		$q+q^{2}-q^{3}-q^{5}-q^{6}-q^{7}-q^{8}+\cdots$
3311.1.h.e	$3311$	$1$	3311.h	3311.h	$2$	$1$	$1$	$1.652$	$\Q$	$D_{3}$	$\Q(\sqrt{-3311}) $	None	✓	$2$	$0$	$1$	$1$	$1$	$-1$		$1$		$q+q^{2}+q^{3}+q^{5}+q^{6}-q^{7}-q^{8}+\cdots$
3311.1.h.f	$3311$	$1$	3311.h	3311.h	$2$	$1$	$1$	$1.652$	$\Q$	$D_{2}$	$\Q(\sqrt{-7}) $, $\Q(\sqrt{-3311}) $	$\Q(\sqrt{473}) $	✓	$4$	$0$	$2$	$0$	$0$	$1$		$1$		$q+2q^{2}+3q^{4}+q^{7}+4q^{8}-q^{9}-q^{11}+\cdots$
3311.1.h.g	$3311$	$1$	3311.h	3311.h	$2$	$2$	$2$	$1.652$	$\Q(\sqrt{-3}) $	$D_{6}$	None	$\Q(\sqrt{473}) $		$4$	$0$	$-2$	$0$	$0$	$-1$		$1$		$q-q^{2}+\zeta_{6}^{2}q^{7}+q^{8}-q^{9}-q^{11}+\cdots$
3311.1.h.h	$3311$	$1$	3311.h	3311.h	$2$	$2$	$2$	$1.652$	$\Q(\sqrt{3}) $	$D_{6}$	$\Q(\sqrt{-3311}) $	None	✓	$4$	$0$	$-2$	$0$	$0$	$2$		$1$		$q-q^{2}-\beta q^{3}-\beta q^{5}+\beta q^{6}+q^{7}+q^{8}+\cdots$
3311.1.h.i	$3311$	$1$	3311.h	3311.h	$2$	$2$	$2$	$1.652$	$\Q(\sqrt{3}) $	$D_{6}$	$\Q(\sqrt{-3311}) $	None	✓	$4$	$0$	$2$	$0$	$0$	$-2$		$1$		$q+q^{2}-\beta q^{3}-\beta q^{5}-\beta q^{6}-q^{7}-q^{8}+\cdots$
3311.1.h.j	$3311$	$1$	3311.h	3311.h	$2$	$2$	$2$	$1.652$	$\Q(\sqrt{-3}) $	$D_{6}$	None	$\Q(\sqrt{473}) $		$4$	$0$	$2$	$0$	$0$	$1$		$1$		$q+q^{2}-\zeta_{6}^{2}q^{7}-q^{8}-q^{9}-q^{11}+\cdots$
3311.1.h.k	$3311$	$1$	3311.h	3311.h	$2$	$3$	$3$	$1.652$	$\Q(\zeta_{18})^+$	$D_{9}$	$\Q(\sqrt{-3311}) $	None	✓	$2$	$0$	$0$	$0$	$0$	$-3$		$1$		$q+(-\beta _{1}+\beta _{2})q^{2}+\beta _{1}q^{3}+(1-\beta _{1}+\cdots)q^{4}+\cdots$
3311.1.h.l	$3311$	$1$	3311.h	3311.h	$2$	$3$	$3$	$1.652$	$\Q(\zeta_{18})^+$	$D_{9}$	$\Q(\sqrt{-3311}) $	None	✓	$2$	$0$	$0$	$0$	$0$	$3$		$1$		$q+(\beta _{1}-\beta _{2})q^{2}-\beta _{1}q^{3}+(1-\beta _{1})q^{4}+\cdots$
3311.1.h.m	$3311$	$1$	3311.h	3311.h	$2$	$3$	$3$	$1.652$	$\Q(\zeta_{18})^+$	$D_{9}$	$\Q(\sqrt{-3311}) $	None	✓	$2$	$0$	$0$	$0$	$0$	$-3$		$1$		$q+(-\beta _{1}+\beta _{2})q^{2}-\beta _{1}q^{3}+(1-\beta _{1}+\cdots)q^{4}+\cdots$
3311.1.h.n	$3311$	$1$	3311.h	3311.h	$2$	$3$	$3$	$1.652$	$\Q(\zeta_{18})^+$	$D_{9}$	$\Q(\sqrt{-3311}) $	None	✓	$2$	$0$	$0$	$0$	$0$	$3$		$1$		$q+(\beta _{1}-\beta _{2})q^{2}+\beta _{1}q^{3}+(1-\beta _{1})q^{4}+\cdots$
3311.1.h.o	$3311$	$1$	3311.h	3311.h	$2$	$6$	$6$	$1.652$	$\Q(\zeta_{36})^+$	$D_{18}$	$\Q(\sqrt{-3311}) $	None	✓	$4$	$0$	$0$	$0$	$0$	$-6$		$1$		$q+(-\beta _{2}-\beta _{4})q^{2}-\beta _{1}q^{3}+(1-\beta _{4}+\cdots)q^{4}+\cdots$
3311.1.h.p	$3311$	$1$	3311.h	3311.h	$2$	$6$	$6$	$1.652$	$\Q(\zeta_{36})^+$	$D_{18}$	$\Q(\sqrt{-3311}) $	None	✓	$4$	$0$	$0$	$0$	$0$	$6$		$1$		$q+(\beta _{2}+\beta _{4})q^{2}-\beta _{1}q^{3}+(1-\beta _{4})q^{4}+\cdots$
3311.1.bm.a	$3311$	$1$	3311.bm	3311.am	$6$	$2$	$1$	$1.652$	$\Q(\sqrt{-3}) $	$D_{6}$	$\Q(\sqrt{-7}) $	None		$4$	$0$	$-2$	$0$	$0$	$-1$		$1$		$q-q^{2}-\zeta_{6}q^{7}+q^{8}+\zeta_{6}q^{9}-q^{11}+\cdots$
3311.1.bm.b	$3311$	$1$	3311.bm	3311.am	$6$	$2$	$1$	$1.652$	$\Q(\sqrt{-3}) $	$D_{6}$	$\Q(\sqrt{-7}) $	None		$4$	$0$	$2$	$0$	$0$	$1$		$1$		$q+q^{2}+\zeta_{6}q^{7}-q^{8}+\zeta_{6}q^{9}-q^{11}+\cdots$
3311.1.bq.a	$3311$	$1$	3311.bq	3311.aq	$10$	$4$	$1$	$1.652$	$\Q(\zeta_{10})$	$D_{10}$	$\Q(\sqrt{-7}) $	None		$4$	$0$	$-2$	$0$	$0$	$-1$		$1$		$q+(\zeta_{10}^{2}+\zeta_{10}^{4})q^{2}+(-\zeta_{10}-\zeta_{10}^{3}+\cdots)q^{4}+\cdots$
3311.1.bq.b	$3311$	$1$	3311.bq	3311.aq	$10$	$4$	$1$	$1.652$	$\Q(\zeta_{10})$	$D_{10}$	$\Q(\sqrt{-7}) $	None		$4$	$0$	$2$	$0$	$0$	$1$		$1$		$q+(-\zeta_{10}^{2}-\zeta_{10}^{4})q^{2}+(-\zeta_{10}-\zeta_{10}^{3}+\cdots)q^{4}+\cdots$
3311.1.bx.a	$3311$	$1$	3311.bx	3311.ax	$14$	$6$	$1$	$1.652$	$\Q(\zeta_{14})$	$D_{14}$	$\Q(\sqrt{-7}) $	None		$4$	$0$	$-2$	$0$	$0$	$6$		$1$		$q+(\zeta_{14}^{4}-\zeta_{14}^{5})q^{2}+(-\zeta_{14}+\zeta_{14}^{2}+\cdots)q^{4}+\cdots$
3311.1.bx.b	$3311$	$1$	3311.bx	3311.ax	$14$	$6$	$1$	$1.652$	$\Q(\zeta_{14})$	$D_{14}$	$\Q(\sqrt{-7}) $	None		$4$	$0$	$2$	$0$	$0$	$-6$		$1$		$q+(-\zeta_{14}^{4}+\zeta_{14}^{5})q^{2}+(-\zeta_{14}+\zeta_{14}^{2}+\cdots)q^{4}+\cdots$
3311.1.cm.a	$3311$	$1$	3311.cm	3311.bm	$30$	$8$	$1$	$1.652$	$\Q(\zeta_{15})$	$D_{15}$	$\Q(\sqrt{-7}) $	None		$4$	$0$	$2$	$0$	$0$	$1$		$1$		$q+(\zeta_{30}^{2}+\zeta_{30}^{4})q^{2}+(\zeta_{30}^{4}+\zeta_{30}^{6}+\cdots)q^{4}+\cdots$
3311.1.cm.b	$3311$	$1$	3311.cm	3311.bm	$30$	$8$	$1$	$1.652$	$\Q(\zeta_{15})$	$D_{15}$	$\Q(\sqrt{-7}) $	None		$4$	$0$	$2$	$0$	$0$	$1$		$1$		$q+(-\zeta_{30}^{7}+\zeta_{30}^{14})q^{2}+(\zeta_{30}^{6}-\zeta_{30}^{13}+\cdots)q^{4}+\cdots$
3311.1.co.a	$3311$	$1$	3311.co	3311.bo	$30$	$8$	$1$	$1.652$	$\Q(\zeta_{15})$	$D_{30}$	$\Q(\sqrt{-7}) $	None		$4$	$0$	$-2$	$0$	$0$	$-1$		$1$		$q+(\zeta_{30}-\zeta_{30}^{2})q^{2}+(\zeta_{30}^{2}-\zeta_{30}^{3}+\cdots)q^{4}+\cdots$
3311.1.co.b	$3311$	$1$	3311.co	3311.bo	$30$	$8$	$1$	$1.652$	$\Q(\zeta_{15})$	$D_{30}$	$\Q(\sqrt{-7}) $	None		$4$	$0$	$2$	$0$	$0$	$1$		$1$		$q+(-\zeta_{30}^{7}-\zeta_{30}^{11})q^{2}+(-\zeta_{30}^{3}+\cdots)q^{4}+\cdots$
3311.1.dr.a	$3311$	$1$	3311.dr	3311.cr	$42$	$12$	$1$	$1.652$	$\Q(\zeta_{21})$	$D_{42}$	$\Q(\sqrt{-7}) $	None		$4$	$0$	$-2$	$0$	$0$	$6$		$1$		$q+(\zeta_{42}+\zeta_{42}^{17})q^{2}+(\zeta_{42}^{2}-\zeta_{42}^{13}+\cdots)q^{4}+\cdots$
3311.1.dr.b	$3311$	$1$	3311.dr	3311.cr	$42$	$12$	$1$	$1.652$	$\Q(\zeta_{21})$	$D_{42}$	$\Q(\sqrt{-7}) $	None		$4$	$0$	$2$	$0$	$0$	$-6$		$1$		$q+(-\zeta_{42}-\zeta_{42}^{17})q^{2}+(\zeta_{42}^{2}-\zeta_{42}^{13}+\cdots)q^{4}+\cdots$
3311.1.ev.a	$3311$	$1$	3311.ev	3311.dv	$70$	$24$	$1$	$1.652$	$\Q(\zeta_{35})$	$D_{35}$	$\Q(\sqrt{-7}) $	None		$4$	$0$	$2$	$0$	$0$	$-6$		$1$		$q+(\zeta_{70}^{16}-\zeta_{70}^{17})q^{2}+(\zeta_{70}^{32}-\zeta_{70}^{33}+\cdots)q^{4}+\cdots$
3311.1.ev.b	$3311$	$1$	3311.ev	3311.dv	$70$	$24$	$1$	$1.652$	$\Q(\zeta_{35})$	$D_{35}$	$\Q(\sqrt{-7}) $	None		$4$	$0$	$2$	$0$	$0$	$-6$		$1$		$q+(\zeta_{70}^{2}-\zeta_{70}^{31})q^{2}+(\zeta_{70}^{4}-\zeta_{70}^{27}+\cdots)q^{4}+\cdots$
3311.1.ex.a	$3311$	$1$	3311.ex	3311.dx	$70$	$24$	$1$	$1.652$	$\Q(\zeta_{35})$	$D_{70}$	$\Q(\sqrt{-7}) $	None		$4$	$0$	$-2$	$0$	$0$	$6$		$1$		$q+(\zeta_{70}^{23}+\zeta_{70}^{31})q^{2}+(-\zeta_{70}^{11}+\cdots)q^{4}+\cdots$
3311.1.ex.b	$3311$	$1$	3311.ex	3311.dx	$70$	$24$	$1$	$1.652$	$\Q(\zeta_{35})$	$D_{70}$	$\Q(\sqrt{-7}) $	None		$4$	$0$	$2$	$0$	$0$	$-6$		$1$		$q+(-\zeta_{70}^{3}+\zeta_{70}^{16})q^{2}+(\zeta_{70}^{6}-\zeta_{70}^{19}+\cdots)q^{4}+\cdots$
3311.1.gb.a	$3311$	$1$	3311.gb	3311.fb	$210$	$48$	$1$	$1.652$	$\Q(\zeta_{210})$	$D_{210}$	$\Q(\sqrt{-7}) $	None		$4$	$0$	$-2$	$0$	$0$	$6$		$1$		$q+(-\zeta_{210}^{43}-\zeta_{210}^{101})q^{2}+(-\zeta_{210}^{39}+\cdots)q^{4}+\cdots$
3311.1.gb.b	$3311$	$1$	3311.gb	3311.fb	$210$	$48$	$1$	$1.652$	$\Q(\zeta_{210})$	$D_{210}$	$\Q(\sqrt{-7}) $	None		$4$	$0$	$2$	$0$	$0$	$-6$		$1$		$q+(\zeta_{210}-\zeta_{210}^{38})q^{2}+(\zeta_{210}^{2}-\zeta_{210}^{39}+\cdots)q^{4}+\cdots$
3311.1.gd.a	$3311$	$1$	3311.gd	3311.fd	$210$	$48$	$1$	$1.652$	$\Q(\zeta_{210})$	$D_{105}$	$\Q(\sqrt{-7}) $	None		$4$	$0$	$-2$	$0$	$0$	$6$		$1$		$q+(\zeta_{210}^{2}+\zeta_{210}^{34})q^{2}+(\zeta_{210}^{4}+\zeta_{210}^{36}+\cdots)q^{4}+\cdots$
3311.1.gd.b	$3311$	$1$	3311.gd	3311.fd	$210$	$48$	$1$	$1.652$	$\Q(\zeta_{210})$	$D_{105}$	$\Q(\sqrt{-7}) $	None		$4$	$0$	$-2$	$0$	$0$	$6$		$1$		$q+(\zeta_{210}^{44}-\zeta_{210}^{97})q^{2}+(\zeta_{210}^{36}+\zeta_{210}^{88}+\cdots)q^{4}+\cdots$
3311.2.a.a	$3311$	$2$	3311.a	1.a	$1$	$1$	$1$	$26.438$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$1$	$2$	$-4$	$-1$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+2q^{3}-q^{4}-4q^{5}+2q^{6}-q^{7}+\cdots$
3311.2.a.b	$3311$	$2$	3311.a	1.a	$1$	$1$	$1$	$26.438$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$1$	$2$	$0$	$1$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+2q^{3}-q^{4}+2q^{6}+q^{7}-3q^{8}+\cdots$
3311.2.a.c	$3311$	$2$	3311.a	1.a	$1$	$1$	$1$	$26.438$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$2$	$1$	$-1$	$-1$	$+$	$1$	$\mathrm{SU}(2)$	$q+2q^{2}+q^{3}+2q^{4}-q^{5}+2q^{6}-q^{7}+\cdots$
3311.2.a.d	$3311$	$2$	3311.a	1.a	$1$	$15$	$15$	$26.438$	$\mathbb{Q}[x]/(x^{15} - \cdots)$	$_{}$	None	None	✓	$1$	$1$	$-2$	$-4$	$1$	$15$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}-\beta _{14}q^{3}+(1+\beta _{2})q^{4}-\beta _{7}q^{5}+\cdots$
3311.2.a.e	$3311$	$2$	3311.a	1.a	$1$	$16$	$16$	$26.438$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	$_{}$	None	None	✓	$1$	$1$	$-4$	$-3$	$-4$	$16$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+\beta _{14}q^{3}+\beta _{2}q^{4}-\beta _{11}q^{5}+\cdots$
3311.2.a.f	$3311$	$2$	3311.a	1.a	$1$	$18$	$18$	$26.438$	$\mathbb{Q}[x]/(x^{18} - \cdots)$	$_{}$	None	None	✓	$1$	$1$	$-4$	$3$	$4$	$-18$	$+$	$2^{2}$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}-\beta _{5}q^{3}+(1+\beta _{2})q^{4}-\beta _{6}q^{5}+\cdots$
3311.2.a.g	$3311$	$2$	3311.a	1.a	$1$	$19$	$19$	$26.438$	$\mathbb{Q}[x]/(x^{19} - \cdots)$	$_{}$	None	None	✓	$1$	$1$	$1$	$-9$	$-6$	$-19$	$+$	$2$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+\beta _{15}q^{3}+(1+\beta _{2})q^{4}+\beta _{3}q^{5}+\cdots$
3311.2.a.h	$3311$	$2$	3311.a	1.a	$1$	$32$	$32$	$26.438$		$_{}$	None	None	✓	$1$	$0$	$3$	$2$	$1$	$-32$	$-$		$\mathrm{SU}(2)$
3311.2.a.i	$3311$	$2$	3311.a	1.a	$1$	$35$	$35$	$26.438$		$_{}$	None	None	✓	$1$	$0$	$-5$	$3$	$16$	$-35$	$-$		$\mathrm{SU}(2)$
3311.2.a.j	$3311$	$2$	3311.a	1.a	$1$	$35$	$35$	$26.438$		$_{}$	None	None	✓	$1$	$0$	$2$	$-4$	$-1$	$35$	$-$		$\mathrm{SU}(2)$
3311.2.a.k	$3311$	$2$	3311.a	1.a	$1$	$38$	$38$	$26.438$		$_{}$	None	None	✓	$1$	$0$	$6$	$7$	$8$	$38$	$-$		$\mathrm{SU}(2)$

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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.