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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 (39 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
276.1.h.a	$276$	$1$	276.h	276.h	$2$	$1$	$1$	$0.138$	$\Q$	$D_{2}$	$\Q(\sqrt{-23}) $, $\Q(\sqrt{-69}) $	$\Q(\sqrt{3}) $	✓	$4$	$0$	$-1$	$1$	$0$	$0$	$1$		$q-q^{2}+q^{3}+q^{4}-q^{6}-q^{8}+q^{9}+\cdots$
276.1.h.b	$276$	$1$	276.h	276.h	$2$	$1$	$1$	$0.138$	$\Q$	$D_{2}$	$\Q(\sqrt{-23}) $, $\Q(\sqrt{-69}) $	$\Q(\sqrt{3}) $	✓	$4$	$0$	$1$	$-1$	$0$	$0$	$1$		$q+q^{2}-q^{3}+q^{4}-q^{6}+q^{8}+q^{9}+\cdots$
1104.1.o.a	$1104$	$1$	1104.o	276.h	$2$	$2$	$2$	$0.551$	$\Q(\sqrt{2}) $	$D_{4}$	$\Q(\sqrt{-69}) $	None	✓	$4$	$0$	$0$	$-2$	$0$	$0$	$1$		$q-q^{3}-\beta q^{5}-\beta q^{7}+q^{9}+\beta q^{15}+\cdots$
1104.1.o.b	$1104$	$1$	1104.o	276.h	$2$	$2$	$2$	$0.551$	$\Q(\sqrt{2}) $	$D_{4}$	$\Q(\sqrt{-69}) $	None	✓	$4$	$0$	$0$	$2$	$0$	$0$	$1$		$q+q^{3}-\beta q^{5}+\beta q^{7}+q^{9}-\beta q^{15}+\cdots$
1380.1.b.a	$1380$	$1$	1380.b	1380.b	$2$	$2$	$2$	$0.689$	$\Q(\sqrt{-1}) $	$D_{2}$	$\Q(\sqrt{-5}) $, $\Q(\sqrt{-69}) $	$\Q(\sqrt{345}) $		$8$	$0$	$0$	$0$	$-2$	$0$	$1$		$q-iq^{2}-iq^{3}-q^{4}-q^{5}-q^{6}+iq^{7}+\cdots$
1380.1.b.b	$1380$	$1$	1380.b	1380.b	$2$	$2$	$2$	$0.689$	$\Q(\sqrt{-1}) $	$D_{2}$	$\Q(\sqrt{-15}) $, $\Q(\sqrt{-69}) $	$\Q(\sqrt{115}) $		$8$	$0$	$0$	$0$	$0$	$0$	$1$		$q-iq^{2}+iq^{3}-q^{4}-iq^{5}+q^{6}+iq^{8}+\cdots$
1380.1.b.c	$1380$	$1$	1380.b	1380.b	$2$	$2$	$2$	$0.689$	$\Q(\sqrt{-1}) $	$D_{2}$	$\Q(\sqrt{-15}) $, $\Q(\sqrt{-69}) $	$\Q(\sqrt{115}) $		$8$	$0$	$0$	$0$	$0$	$0$	$1$		$q+iq^{2}-iq^{3}-q^{4}-iq^{5}+q^{6}-iq^{8}+\cdots$
1380.1.b.d	$1380$	$1$	1380.b	1380.b	$2$	$2$	$2$	$0.689$	$\Q(\sqrt{-1}) $	$D_{2}$	$\Q(\sqrt{-5}) $, $\Q(\sqrt{-69}) $	$\Q(\sqrt{345}) $		$8$	$0$	$0$	$0$	$2$	$0$	$1$		$q-iq^{2}-iq^{3}-q^{4}+q^{5}-q^{6}-iq^{7}+\cdots$
1932.1.w.a	$1932$	$1$	1932.w	1932.w	$6$	$2$	$1$	$0.964$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-69}) $	None		$4$	$0$	$-1$	$-1$	$-1$	$1$	$1$		$q-\zeta_{6}q^{2}+\zeta_{6}^{2}q^{3}+\zeta_{6}^{2}q^{4}-\zeta_{6}q^{5}+\cdots$
1932.1.w.b	$1932$	$1$	1932.w	1932.w	$6$	$2$	$1$	$0.964$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-69}) $	None		$4$	$0$	$-1$	$-1$	$1$	$-1$	$1$		$q-\zeta_{6}q^{2}+\zeta_{6}^{2}q^{3}+\zeta_{6}^{2}q^{4}+\zeta_{6}q^{5}+\cdots$
1932.1.w.c	$1932$	$1$	1932.w	1932.w	$6$	$2$	$1$	$0.964$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-69}) $	None		$4$	$0$	$1$	$1$	$-1$	$-1$	$1$		$q+\zeta_{6}q^{2}-\zeta_{6}^{2}q^{3}+\zeta_{6}^{2}q^{4}-\zeta_{6}q^{5}+\cdots$
1932.1.w.d	$1932$	$1$	1932.w	1932.w	$6$	$2$	$1$	$0.964$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-69}) $	None		$4$	$0$	$1$	$1$	$1$	$1$	$1$		$q+\zeta_{6}q^{2}-\zeta_{6}^{2}q^{3}+\zeta_{6}^{2}q^{4}+\zeta_{6}q^{5}+\cdots$
1932.1.w.e	$1932$	$1$	1932.w	1932.w	$6$	$4$	$2$	$0.964$	$\Q(\zeta_{12})$	$D_{6}$	$\Q(\sqrt{-69}) $	None		$8$	$0$	$-2$	$2$	$0$	$0$	$1$		$q+\zeta_{12}^{4}q^{2}+\zeta_{12}^{2}q^{3}-\zeta_{12}^{2}q^{4}+\cdots$
1932.1.w.f	$1932$	$1$	1932.w	1932.w	$6$	$4$	$2$	$0.964$	$\Q(\zeta_{12})$	$D_{6}$	$\Q(\sqrt{-69}) $	None		$8$	$0$	$2$	$-2$	$0$	$0$	$1$		$q-\zeta_{12}^{4}q^{2}-\zeta_{12}^{2}q^{3}-\zeta_{12}^{2}q^{4}+\cdots$
2484.1.h.a	$2484$	$1$	2484.h	276.h	$2$	$1$	$1$	$1.240$	$\Q$	$D_{3}$	$\Q(\sqrt{-69}) $	None	✓	$2$	$0$	$-1$	$0$	$-2$	$-1$	$1$		$q-q^{2}+q^{4}-2q^{5}-q^{7}-q^{8}+2q^{10}+\cdots$
2484.1.h.b	$2484$	$1$	2484.h	276.h	$2$	$1$	$1$	$1.240$	$\Q$	$D_{3}$	$\Q(\sqrt{-69}) $	None	✓	$2$	$0$	$-1$	$0$	$2$	$1$	$1$		$q-q^{2}+q^{4}+2q^{5}+q^{7}-q^{8}-2q^{10}+\cdots$
2484.1.h.c	$2484$	$1$	2484.h	276.h	$2$	$1$	$1$	$1.240$	$\Q$	$D_{3}$	$\Q(\sqrt{-69}) $	None	✓	$2$	$0$	$1$	$0$	$-2$	$1$	$1$		$q+q^{2}+q^{4}-2q^{5}+q^{7}+q^{8}-2q^{10}+\cdots$
2484.1.h.d	$2484$	$1$	2484.h	276.h	$2$	$1$	$1$	$1.240$	$\Q$	$D_{3}$	$\Q(\sqrt{-69}) $	None	✓	$2$	$0$	$1$	$0$	$2$	$-1$	$1$		$q+q^{2}+q^{4}+2q^{5}-q^{7}+q^{8}+2q^{10}+\cdots$
2484.1.h.e	$2484$	$1$	2484.h	276.h	$2$	$2$	$2$	$1.240$	$\Q(\sqrt{3}) $	$D_{6}$	$\Q(\sqrt{-69}) $	None	✓	$4$	$0$	$-2$	$0$	$0$	$0$	$1$		$q-q^{2}+q^{4}-\beta q^{7}-q^{8}+q^{13}+\beta q^{14}+\cdots$
2484.1.h.f	$2484$	$1$	2484.h	276.h	$2$	$2$	$2$	$1.240$	$\Q(\sqrt{3}) $	$D_{6}$	$\Q(\sqrt{-69}) $	None	✓	$4$	$0$	$2$	$0$	$0$	$0$	$1$		$q+q^{2}+q^{4}-\beta q^{7}+q^{8}+q^{13}-\beta q^{14}+\cdots$
3588.1.e.i	$3588$	$1$	3588.e	3588.e	$2$	$4$	$4$	$1.791$	$\Q(\zeta_{8})$	$D_{4}$	$\Q(\sqrt{-69}) $	None		$8$	$0$	$0$	$-4$	$0$	$0$	$2$		$q+\zeta_{8}^{2}q^{2}-q^{3}-q^{4}+(-\zeta_{8}-\zeta_{8}^{3}+\cdots)q^{5}+\cdots$
3588.1.e.j	$3588$	$1$	3588.e	3588.e	$2$	$4$	$4$	$1.791$	$\Q(\zeta_{8})$	$D_{4}$	$\Q(\sqrt{-69}) $	None		$8$	$0$	$0$	$4$	$0$	$0$	$2$		$q-\zeta_{8}^{2}q^{2}+q^{3}-q^{4}+(-\zeta_{8}-\zeta_{8}^{3}+\cdots)q^{5}+\cdots$
3588.1.bd.e	$3588$	$1$	3588.bd	3588.ad	$6$	$8$	$4$	$1.791$	$\Q(\zeta_{24})$	$D_{12}$	$\Q(\sqrt{-69}) $	None		$8$	$0$	$0$	$-4$	$0$	$0$	$1$		$q-\zeta_{24}^{2}q^{2}+\zeta_{24}^{8}q^{3}+\zeta_{24}^{4}q^{4}+\cdots$
3588.1.bd.f	$3588$	$1$	3588.bd	3588.ad	$6$	$8$	$4$	$1.791$	$\Q(\zeta_{24})$	$D_{12}$	$\Q(\sqrt{-69}) $	None		$8$	$0$	$0$	$4$	$0$	$0$	$1$		$q+\zeta_{24}^{2}q^{2}-\zeta_{24}^{8}q^{3}+\zeta_{24}^{4}q^{4}+\cdots$
3588.1.bi.a	$3588$	$1$	3588.bi	3588.ai	$6$	$2$	$1$	$1.791$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-69}) $	None		$4$	$0$	$-1$	$-1$	$-2$	$-2$	$1$		$q+\zeta_{6}^{2}q^{2}+\zeta_{6}^{2}q^{3}-\zeta_{6}q^{4}-q^{5}+\cdots$
3588.1.bi.b	$3588$	$1$	3588.bi	3588.ai	$6$	$2$	$1$	$1.791$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-69}) $	None		$4$	$0$	$-1$	$-1$	$2$	$2$	$1$		$q+\zeta_{6}^{2}q^{2}+\zeta_{6}^{2}q^{3}-\zeta_{6}q^{4}+q^{5}+\cdots$
3588.1.bi.c	$3588$	$1$	3588.bi	3588.ai	$6$	$2$	$1$	$1.791$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-69}) $	None		$4$	$0$	$1$	$1$	$-2$	$2$	$1$		$q-\zeta_{6}^{2}q^{2}-\zeta_{6}^{2}q^{3}-\zeta_{6}q^{4}-q^{5}+\cdots$
3588.1.bi.d	$3588$	$1$	3588.bi	3588.ai	$6$	$2$	$1$	$1.791$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-69}) $	None		$4$	$0$	$1$	$1$	$2$	$-2$	$1$		$q-\zeta_{6}^{2}q^{2}-\zeta_{6}^{2}q^{3}-\zeta_{6}q^{4}+q^{5}+\cdots$
3588.1.bi.e	$3588$	$1$	3588.bi	3588.ai	$6$	$4$	$2$	$1.791$	$\Q(\zeta_{12})$	$D_{6}$	$\Q(\sqrt{-69}) $	None		$8$	$0$	$-2$	$2$	$0$	$0$	$3$		$q-\zeta_{12}^{2}q^{2}+\zeta_{12}^{2}q^{3}+\zeta_{12}^{4}q^{4}+\cdots$
3588.1.bi.f	$3588$	$1$	3588.bi	3588.ai	$6$	$4$	$2$	$1.791$	$\Q(\zeta_{12})$	$D_{6}$	$\Q(\sqrt{-69}) $	None		$8$	$0$	$2$	$-2$	$0$	$0$	$3$		$q+\zeta_{12}^{2}q^{2}-\zeta_{12}^{2}q^{3}+\zeta_{12}^{4}q^{4}+\cdots$
828.2.e.c	$828$	$2$	828.e	92.b	$2$	$8$	$8$	$6.612$	8.0.$\cdots$.2	$_{}$	$\Q(\sqrt{-69}) $	None		$8$	$0$	$0$	$0$	$0$	$0$	$2^{4}$	$\mathrm{U}(1)[D_{2}]$	$q+\beta _{2}q^{2}-2q^{4}-\beta _{4}q^{5}-\beta _{5}q^{7}-2\beta _{2}q^{8}+\cdots$
276.3.h.a	$276$	$3$	276.h	276.h	$2$	$2$	$2$	$7.520$	$\Q(\sqrt{6}) $	$_{}$	$\Q(\sqrt{-69}) $	None	✓	$4$	$0$	$-4$	$-6$	$0$	$0$	$1$	$\mathrm{U}(1)[D_{2}]$	$q-2q^{2}-3q^{3}+4q^{4}+3\beta q^{5}+6q^{6}+\cdots$
276.3.h.b	$276$	$3$	276.h	276.h	$2$	$2$	$2$	$7.520$	$\Q(\sqrt{46}) $	$_{}$	$\Q(\sqrt{-69}) $	None	✓	$4$	$0$	$-4$	$6$	$0$	$0$	$1$	$\mathrm{U}(1)[D_{2}]$	$q-2q^{2}+3q^{3}+4q^{4}+\beta q^{5}-6q^{6}+\cdots$
276.3.h.c	$276$	$3$	276.h	276.h	$2$	$2$	$2$	$7.520$	$\Q(\sqrt{46}) $	$_{}$	$\Q(\sqrt{-69}) $	None	✓	$4$	$0$	$4$	$-6$	$0$	$0$	$1$	$\mathrm{U}(1)[D_{2}]$	$q+2q^{2}-3q^{3}+4q^{4}+\beta q^{5}-6q^{6}+\cdots$
276.3.h.d	$276$	$3$	276.h	276.h	$2$	$2$	$2$	$7.520$	$\Q(\sqrt{6}) $	$_{}$	$\Q(\sqrt{-69}) $	None	✓	$4$	$0$	$4$	$6$	$0$	$0$	$1$	$\mathrm{U}(1)[D_{2}]$	$q+2q^{2}+3q^{3}+4q^{4}+3\beta q^{5}+6q^{6}+\cdots$
2208.2.m.b	$2208$	$2$	2208.m	69.c	$2$	$16$	$16$	$17.631$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	$_{}$	$\Q(\sqrt{-69}) $	None		$8$	$0$	$0$	$0$	$0$	$0$	$2^{28}$	$\mathrm{U}(1)[D_{2}]$	$q-\beta _{2}q^{3}-\beta _{13}q^{5}-\beta _{9}q^{7}-3q^{9}+\cdots$
3312.2.i.e	$3312$	$2$	3312.i	92.b	$2$	$8$	$8$	$26.446$	8.0.$\cdots$.105	$_{}$	$\Q(\sqrt{-69}) $	None		$8$	$0$	$0$	$0$	$0$	$0$	$2^{4}$	$\mathrm{U}(1)[D_{2}]$	$q+\beta _{4}q^{5}-\beta _{3}q^{7}-\beta _{1}q^{13}+(\beta _{4}+\beta _{7})q^{17}+\cdots$
1104.3.o.a	$1104$	$3$	1104.o	276.h	$2$	$4$	$4$	$30.082$	$\Q(\sqrt{3}, \sqrt{23})$	$_{}$	$\Q(\sqrt{-69}) $	None	✓	$4$	$0$	$0$	$-12$	$0$	$0$	$2^{6}$	$\mathrm{U}(1)[D_{2}]$	$q-3q^{3}+\beta _{1}q^{5}+\beta _{2}q^{7}+9q^{9}-\beta _{3}q^{13}+\cdots$
1104.3.o.b	$1104$	$3$	1104.o	276.h	$2$	$4$	$4$	$30.082$	$\Q(\sqrt{3}, \sqrt{23})$	$_{}$	$\Q(\sqrt{-69}) $	None	✓	$4$	$0$	$0$	$12$	$0$	$0$	$2^{6}$	$\mathrm{U}(1)[D_{2}]$	$q+3q^{3}+\beta _{1}q^{5}-\beta _{2}q^{7}+9q^{9}-\beta _{3}q^{13}+\cdots$

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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.