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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 (31 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
244.1.c.a	$244$	$1$	244.c	244.c	$2$	$1$	$1$	$0.122$	$\Q$	$D_{3}$	$\Q(\sqrt{-61}) $	None	✓	$2$	$0$	$-1$	$0$	$-1$	$1$	$1$		$q-q^{2}+q^{4}-q^{5}+q^{7}-q^{8}+q^{9}+\cdots$
244.1.c.b	$244$	$1$	244.c	244.c	$2$	$1$	$1$	$0.122$	$\Q$	$D_{3}$	$\Q(\sqrt{-61}) $	None	✓	$2$	$0$	$1$	$0$	$-1$	$-1$	$1$		$q+q^{2}+q^{4}-q^{5}-q^{7}+q^{8}+q^{9}+\cdots$
976.1.e.a	$976$	$1$	976.e	244.c	$2$	$1$	$1$	$0.487$	$\Q$	$D_{2}$	$\Q(\sqrt{-1}) $, $\Q(\sqrt{-61}) $	$\Q(\sqrt{61}) $	✓	$4$	$0$	$0$	$0$	$-2$	$0$	$1$		$q-2q^{5}+q^{9}+2q^{13}+3q^{25}+2q^{41}+\cdots$
976.1.e.b	$976$	$1$	976.e	244.c	$2$	$2$	$2$	$0.487$	$\Q(\sqrt{3}) $	$D_{6}$	$\Q(\sqrt{-61}) $	None	✓	$4$	$0$	$0$	$0$	$2$	$0$	$1$		$q+q^{5}-\beta q^{7}+q^{9}+\beta q^{11}-q^{13}+\cdots$
1220.1.g.d	$1220$	$1$	1220.g	1220.g	$2$	$2$	$2$	$0.609$	$\Q(\sqrt{-1}) $	$D_{2}$	$\Q(\sqrt{-5}) $, $\Q(\sqrt{-61}) $	$\Q(\sqrt{305}) $		$8$	$0$	$0$	$0$	$2$	$0$	$1$		$q-iq^{2}-q^{4}+q^{5}+iq^{7}+iq^{8}-q^{9}+\cdots$
1220.1.g.f	$1220$	$1$	1220.g	1220.g	$2$	$4$	$4$	$0.609$	$\Q(\zeta_{12})$	$D_{6}$	$\Q(\sqrt{-61}) $	None		$8$	$0$	$0$	$0$	$-2$	$0$	$1$		$q-\zeta_{12}^{3}q^{2}-q^{4}+\zeta_{12}^{4}q^{5}-\zeta_{12}^{3}q^{7}+\cdots$
1708.1.bh.a	$1708$	$1$	1708.bh	1708.ah	$6$	$6$	$3$	$0.852$	$\Q(\zeta_{18})$	$D_{9}$	$\Q(\sqrt{-61}) $	None		$4$	$0$	$-3$	$0$	$0$	$0$	$1$		$q+\zeta_{18}^{6}q^{2}-\zeta_{18}^{3}q^{4}+(\zeta_{18}^{4}+\zeta_{18}^{8}+\cdots)q^{5}+\cdots$
1708.1.bh.b	$1708$	$1$	1708.bh	1708.ah	$6$	$6$	$3$	$0.852$	$\Q(\zeta_{18})$	$D_{9}$	$\Q(\sqrt{-61}) $	None		$4$	$0$	$3$	$0$	$0$	$0$	$1$		$q-\zeta_{18}^{6}q^{2}-\zeta_{18}^{3}q^{4}+(\zeta_{18}^{4}+\zeta_{18}^{8}+\cdots)q^{5}+\cdots$
2196.1.h.a	$2196$	$1$	2196.h	244.c	$2$	$1$	$1$	$1.096$	$\Q$	$D_{2}$	$\Q(\sqrt{-183}) $, $\Q(\sqrt{-61}) $	$\Q(\sqrt{3}) $	✓	$4$	$0$	$-1$	$0$	$0$	$0$	$1$		$q-q^{2}+q^{4}-q^{8}+2q^{11}+2q^{13}+\cdots$
2196.1.h.b	$2196$	$1$	2196.h	244.c	$2$	$1$	$1$	$1.096$	$\Q$	$D_{3}$	$\Q(\sqrt{-61}) $	None	✓	$2$	$0$	$-1$	$0$	$1$	$-1$	$1$		$q-q^{2}+q^{4}+q^{5}-q^{7}-q^{8}-q^{10}+\cdots$
2196.1.h.c	$2196$	$1$	2196.h	244.c	$2$	$1$	$1$	$1.096$	$\Q$	$D_{2}$	$\Q(\sqrt{-183}) $, $\Q(\sqrt{-61}) $	$\Q(\sqrt{3}) $	✓	$4$	$0$	$1$	$0$	$0$	$0$	$1$		$q+q^{2}+q^{4}+q^{8}-2q^{11}+2q^{13}+\cdots$
2196.1.h.d	$2196$	$1$	2196.h	244.c	$2$	$1$	$1$	$1.096$	$\Q$	$D_{3}$	$\Q(\sqrt{-61}) $	None	✓	$2$	$0$	$1$	$0$	$1$	$1$	$1$		$q+q^{2}+q^{4}+q^{5}+q^{7}+q^{8}+q^{10}+\cdots$
2196.1.h.e	$2196$	$1$	2196.h	244.c	$2$	$2$	$2$	$1.096$	$\Q(\sqrt{3}) $	$D_{6}$	$\Q(\sqrt{-61}) $	None	✓	$4$	$0$	$-2$	$0$	$0$	$0$	$1$		$q-q^{2}+q^{4}-\beta q^{5}-\beta q^{7}-q^{8}+\beta q^{10}+\cdots$
2196.1.h.g	$2196$	$1$	2196.h	244.c	$2$	$2$	$2$	$1.096$	$\Q(\sqrt{3}) $	$D_{6}$	$\Q(\sqrt{-61}) $	None	✓	$4$	$0$	$2$	$0$	$0$	$0$	$1$		$q+q^{2}+q^{4}-\beta q^{5}+\beta q^{7}+q^{8}-\beta q^{10}+\cdots$
2684.1.bw.a	$2684$	$1$	2684.bw	2684.aw	$10$	$4$	$1$	$1.339$	$\Q(\zeta_{10})$	$D_{5}$	$\Q(\sqrt{-61}) $	None		$4$	$0$	$-1$	$0$	$3$	$-2$	$1$		$q+\zeta_{10}^{4}q^{2}-\zeta_{10}^{3}q^{4}+(1+\zeta_{10}^{2}+\cdots)q^{5}+\cdots$
2684.1.bw.b	$2684$	$1$	2684.bw	2684.aw	$10$	$4$	$1$	$1.339$	$\Q(\zeta_{10})$	$D_{5}$	$\Q(\sqrt{-61}) $	None		$4$	$0$	$1$	$0$	$3$	$2$	$1$		$q-\zeta_{10}^{4}q^{2}-\zeta_{10}^{3}q^{4}+(1+\zeta_{10}^{2}+\cdots)q^{5}+\cdots$
2684.1.bw.c	$2684$	$1$	2684.bw	2684.aw	$10$	$8$	$2$	$1.339$	$\Q(\zeta_{15})$	$D_{15}$	$\Q(\sqrt{-61}) $	None		$4$	$0$	$-2$	$0$	$-3$	$2$	$1$		$q+\zeta_{30}^{12}q^{2}-\zeta_{30}^{9}q^{4}+(\zeta_{30}^{10}-\zeta_{30}^{11}+\cdots)q^{5}+\cdots$
2684.1.bw.d	$2684$	$1$	2684.bw	2684.aw	$10$	$8$	$2$	$1.339$	$\Q(\zeta_{15})$	$D_{15}$	$\Q(\sqrt{-61}) $	None		$4$	$0$	$2$	$0$	$-3$	$-2$	$1$		$q-\zeta_{30}^{12}q^{2}-\zeta_{30}^{9}q^{4}+(\zeta_{30}^{10}-\zeta_{30}^{11}+\cdots)q^{5}+\cdots$
3172.1.b.c	$3172$	$1$	3172.b	3172.b	$2$	$2$	$2$	$1.583$	$\Q(\sqrt{-1}) $	$D_{2}$	$\Q(\sqrt{-13}) $, $\Q(\sqrt{-61}) $	$\Q(\sqrt{793}) $		$8$	$0$	$0$	$0$	$0$	$0$	$1$		$q-iq^{2}-q^{4}-iq^{7}+iq^{8}+q^{9}-iq^{11}+\cdots$
3172.1.b.d	$3172$	$1$	3172.b	3172.b	$2$	$4$	$4$	$1.583$	$\Q(\zeta_{12})$	$D_{6}$	$\Q(\sqrt{-61}) $	None		$8$	$0$	$0$	$0$	$0$	$0$	$1$		$q-\zeta_{12}^{3}q^{2}-q^{4}+(-\zeta_{12}^{2}-\zeta_{12}^{4}+\cdots)q^{5}+\cdots$
3172.1.bn.c	$3172$	$1$	3172.bn	3172.an	$6$	$12$	$6$	$1.583$	$\Q(\zeta_{36})$	$D_{18}$	$\Q(\sqrt{-61}) $	None		$8$	$0$	$0$	$0$	$0$	$0$	$1$		$q-\zeta_{36}^{3}q^{2}+\zeta_{36}^{6}q^{4}+(-\zeta_{36}^{4}-\zeta_{36}^{14}+\cdots)q^{5}+\cdots$
3172.1.bw.a	$3172$	$1$	3172.bw	3172.aw	$6$	$6$	$3$	$1.583$	$\Q(\zeta_{18})$	$D_{9}$	$\Q(\sqrt{-61}) $	None		$4$	$0$	$-3$	$0$	$0$	$0$	$1$		$q+\zeta_{18}^{6}q^{2}-\zeta_{18}^{3}q^{4}+(\zeta_{18}^{4}-\zeta_{18}^{5}+\cdots)q^{5}+\cdots$
3172.1.bw.b	$3172$	$1$	3172.bw	3172.aw	$6$	$6$	$3$	$1.583$	$\Q(\zeta_{18})$	$D_{9}$	$\Q(\sqrt{-61}) $	None		$4$	$0$	$3$	$0$	$0$	$0$	$1$		$q-\zeta_{18}^{6}q^{2}-\zeta_{18}^{3}q^{4}+(\zeta_{18}^{4}-\zeta_{18}^{5}+\cdots)q^{5}+\cdots$
3904.1.e.a	$3904$	$1$	3904.e	244.c	$2$	$1$	$1$	$1.948$	$\Q$	$D_{3}$	$\Q(\sqrt{-61}) $	None	✓	$2$	$0$	$0$	$0$	$1$	$-1$	$1$		$q+q^{5}-q^{7}+q^{9}+q^{11}+q^{13}-q^{23}+\cdots$
3904.1.e.b	$3904$	$1$	3904.e	244.c	$2$	$1$	$1$	$1.948$	$\Q$	$D_{3}$	$\Q(\sqrt{-61}) $	None	✓	$2$	$0$	$0$	$0$	$1$	$1$	$1$		$q+q^{5}+q^{7}+q^{9}-q^{11}+q^{13}+q^{23}+\cdots$
3904.1.e.c	$3904$	$1$	3904.e	244.c	$2$	$1$	$1$	$1.948$	$\Q$	$D_{2}$	$\Q(\sqrt{-1}) $, $\Q(\sqrt{-61}) $	$\Q(\sqrt{61}) $	✓	$4$	$0$	$0$	$0$	$2$	$0$	$1$		$q+2q^{5}+q^{9}-2q^{13}+3q^{25}+2q^{41}+\cdots$
3904.1.e.d	$3904$	$1$	3904.e	244.c	$2$	$2$	$2$	$1.948$	$\Q(\sqrt{3}) $	$D_{6}$	$\Q(\sqrt{-61}) $	None	✓	$4$	$0$	$0$	$0$	$-2$	$0$	$1$		$q-q^{5}-\beta q^{7}+q^{9}-\beta q^{11}+q^{13}+\cdots$
244.3.c.b	$244$	$3$	244.c	244.c	$2$	$3$	$3$	$6.649$	3.3.6588.1	$_{}$	$\Q(\sqrt{-61}) $	None	✓	$2$	$0$	$-6$	$0$	$0$	$0$	$1$	$\mathrm{U}(1)[D_{2}]$	$q-2q^{2}+4q^{4}+(2\beta _{1}+\beta _{2})q^{5}+(\beta _{1}+\cdots)q^{7}+\cdots$
244.3.c.c	$244$	$3$	244.c	244.c	$2$	$3$	$3$	$6.649$	3.3.6588.1	$_{}$	$\Q(\sqrt{-61}) $	None	✓	$2$	$0$	$6$	$0$	$0$	$0$	$1$	$\mathrm{U}(1)[D_{2}]$	$q+2q^{2}+4q^{4}+(2\beta _{1}+\beta _{2})q^{5}+(-\beta _{1}+\cdots)q^{7}+\cdots$
1952.2.h.b	$1952$	$2$	1952.h	61.b	$2$	$12$	$12$	$15.587$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	$_{}$	$\Q(\sqrt{-61}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$2^{16}$	$\mathrm{U}(1)[D_{2}]$	$q+\beta _{5}q^{5}+\beta _{6}q^{7}-3q^{9}+\beta _{4}q^{11}+\cdots$
976.3.e.a	$976$	$3$	976.e	244.c	$2$	$6$	$6$	$26.594$	6.6.2647506384.1	$_{}$	$\Q(\sqrt{-61}) $	None	✓	$4$	$0$	$0$	$0$	$0$	$0$	$2^{8}$	$\mathrm{U}(1)[D_{2}]$	$q+\beta _{2}q^{5}-\beta _{5}q^{7}+9q^{9}+(-2\beta _{3}-\beta _{5})q^{11}+\cdots$

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Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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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.