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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 (20 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
391.1.c.a	$391$	$1$	391.c	391.c	$2$	$3$	$3$	$0.195$	$\Q(\zeta_{14})^+$	$D_{7}$	$\Q(\sqrt{-391}) $	None	✓	$2$	$0$	$-1$	$0$	$-1$	$-1$	$1$		$q-\beta _{1}q^{2}+(1+\beta _{2})q^{4}-\beta _{1}q^{5}+(-1+\cdots)q^{7}+\cdots$
391.1.c.b	$391$	$1$	391.c	391.c	$2$	$3$	$3$	$0.195$	$\Q(\zeta_{14})^+$	$D_{7}$	$\Q(\sqrt{-391}) $	None	✓	$2$	$0$	$-1$	$0$	$1$	$1$	$1$		$q-\beta _{1}q^{2}+(1+\beta _{2})q^{4}+\beta _{1}q^{5}+(1-\beta _{1}+\cdots)q^{7}+\cdots$
1955.1.d.e	$1955$	$1$	1955.d	1955.d	$2$	$2$	$2$	$0.976$	$\Q(\sqrt{-1}) $	$D_{2}$	$\Q(\sqrt{-115}) $, $\Q(\sqrt{-391}) $	$\Q(\sqrt{85}) $		$8$	$0$	$0$	$0$	$0$	$0$	$1$		$q+q^{4}-iq^{5}-iq^{7}-q^{9}+q^{16}+iq^{17}+\cdots$
1955.1.d.f	$1955$	$1$	1955.d	1955.d	$2$	$12$	$12$	$0.976$	$\Q(\zeta_{28})$	$D_{14}$	$\Q(\sqrt{-391}) $	None		$8$	$0$	$0$	$0$	$0$	$0$	$1$		$q+(-\zeta_{28}^{2}-\zeta_{28}^{12})q^{2}+(-1+\zeta_{28}^{4}+\cdots)q^{4}+\cdots$
2737.1.q.a	$2737$	$1$	2737.q	2737.q	$6$	$2$	$1$	$1.366$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-391}) $	None		$4$	$0$	$1$	$0$	$-2$	$-1$	$1$		$q+\zeta_{6}q^{2}-\zeta_{6}q^{5}+\zeta_{6}^{2}q^{7}+q^{8}-\zeta_{6}q^{9}+\cdots$
2737.1.q.b	$2737$	$1$	2737.q	2737.q	$6$	$2$	$1$	$1.366$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-391}) $	None		$4$	$0$	$1$	$0$	$2$	$1$	$1$		$q+\zeta_{6}q^{2}+\zeta_{6}q^{5}-\zeta_{6}^{2}q^{7}+q^{8}-\zeta_{6}q^{9}+\cdots$
2737.1.q.c	$2737$	$1$	2737.q	2737.q	$6$	$12$	$6$	$1.366$	$\Q(\zeta_{21})$	$D_{21}$	$\Q(\sqrt{-391}) $	None		$4$	$0$	$-1$	$0$	$-2$	$-1$	$1$		$q+(-\zeta_{42}^{9}-\zeta_{42}^{19})q^{2}+(-\zeta_{42}^{7}+\cdots)q^{4}+\cdots$
2737.1.q.d	$2737$	$1$	2737.q	2737.q	$6$	$12$	$6$	$1.366$	$\Q(\zeta_{21})$	$D_{21}$	$\Q(\sqrt{-391}) $	None		$4$	$0$	$-1$	$0$	$2$	$1$	$1$		$q+(\zeta_{42}^{10}+\zeta_{42}^{18})q^{2}+(-\zeta_{42}^{7}-\zeta_{42}^{15}+\cdots)q^{4}+\cdots$
3128.1.l.a	$3128$	$1$	3128.l	3128.l	$2$	$1$	$1$	$1.561$	$\Q$	$D_{2}$	$\Q(\sqrt{-391}) $, $\Q(\sqrt{-782}) $	$\Q(\sqrt{2}) $	✓	$4$	$0$	$-1$	$0$	$0$	$-2$	$1$		$q-q^{2}+q^{4}-2q^{7}-q^{8}-q^{9}+2q^{14}+\cdots$
3128.1.l.b	$3128$	$1$	3128.l	3128.l	$2$	$1$	$1$	$1.561$	$\Q$	$D_{2}$	$\Q(\sqrt{-391}) $, $\Q(\sqrt{-782}) $	$\Q(\sqrt{2}) $	✓	$4$	$0$	$-1$	$0$	$0$	$2$	$1$		$q-q^{2}+q^{4}+2q^{7}-q^{8}-q^{9}-2q^{14}+\cdots$
3128.1.l.i	$3128$	$1$	3128.l	3128.l	$2$	$6$	$6$	$1.561$	$\Q(\zeta_{14})$	$D_{14}$	$\Q(\sqrt{-391}) $	None		$4$	$0$	$1$	$0$	$0$	$-2$	$1$		$q+\zeta_{14}^{3}q^{2}+\zeta_{14}^{6}q^{4}+(-\zeta_{14}^{3}-\zeta_{14}^{4}+\cdots)q^{5}+\cdots$
3128.1.l.j	$3128$	$1$	3128.l	3128.l	$2$	$6$	$6$	$1.561$	$\Q(\zeta_{14})$	$D_{14}$	$\Q(\sqrt{-391}) $	None		$4$	$0$	$1$	$0$	$0$	$2$	$1$		$q+\zeta_{14}^{3}q^{2}+\zeta_{14}^{6}q^{4}+(\zeta_{14}^{3}+\zeta_{14}^{4}+\cdots)q^{5}+\cdots$
3519.1.h.a	$3519$	$1$	3519.h	391.c	$2$	$1$	$1$	$1.756$	$\Q$	$D_{2}$	$\Q(\sqrt{-51}) $, $\Q(\sqrt{-391}) $	$\Q(\sqrt{69}) $	✓	$4$	$0$	$0$	$0$	$-2$	$0$	$1$		$q-q^{4}-2q^{5}-2q^{11}-2q^{13}+q^{16}+\cdots$
3519.1.h.b	$3519$	$1$	3519.h	391.c	$2$	$1$	$1$	$1.756$	$\Q$	$D_{2}$	$\Q(\sqrt{-51}) $, $\Q(\sqrt{-391}) $	$\Q(\sqrt{69}) $	✓	$4$	$0$	$0$	$0$	$2$	$0$	$1$		$q-q^{4}+2q^{5}+2q^{11}-2q^{13}+q^{16}+\cdots$
3519.1.h.c	$3519$	$1$	3519.h	391.c	$2$	$3$	$3$	$1.756$	$\Q(\zeta_{14})^+$	$D_{7}$	$\Q(\sqrt{-391}) $	None	✓	$2$	$0$	$1$	$0$	$-1$	$1$	$1$		$q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}-\beta _{1}q^{5}+(1-\beta _{1}+\cdots)q^{7}+\cdots$
3519.1.h.d	$3519$	$1$	3519.h	391.c	$2$	$3$	$3$	$1.756$	$\Q(\zeta_{14})^+$	$D_{7}$	$\Q(\sqrt{-391}) $	None	✓	$2$	$0$	$1$	$0$	$1$	$-1$	$1$		$q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}+\beta _{1}q^{5}+(-1+\cdots)q^{7}+\cdots$
3519.1.h.e	$3519$	$1$	3519.h	391.c	$2$	$6$	$6$	$1.756$	$\Q(\zeta_{28})^+$	$D_{14}$	$\Q(\sqrt{-391}) $	None	✓	$4$	$0$	$0$	$0$	$-2$	$0$	$1$		$q-\beta _{3}q^{2}+(1+\beta _{4})q^{4}+(-1+\beta _{2}+\beta _{4}+\cdots)q^{5}+\cdots$
3519.1.h.f	$3519$	$1$	3519.h	391.c	$2$	$6$	$6$	$1.756$	$\Q(\zeta_{28})^+$	$D_{14}$	$\Q(\sqrt{-391}) $	None	✓	$4$	$0$	$0$	$0$	$2$	$0$	$1$		$q+\beta _{3}q^{2}+(1+\beta _{4})q^{4}+(1-\beta _{2}-\beta _{4}+\cdots)q^{5}+\cdots$
391.3.c.a	$391$	$3$	391.c	391.c	$2$	$7$	$7$	$10.654$	$\mathbb{Q}[x]/(x^{7} - \cdots)$	$_{}$	$\Q(\sqrt{-391}) $	None	✓	$2$	$0$	$0$	$0$	$0$	$0$	$1$	$\mathrm{U}(1)[D_{2}]$	$q+\beta _{2}q^{2}+(4+\beta _{3}+\beta _{4})q^{4}-\beta _{5}q^{5}+\cdots$
391.3.c.b	$391$	$3$	391.c	391.c	$2$	$7$	$7$	$10.654$	$\mathbb{Q}[x]/(x^{7} - \cdots)$	$_{}$	$\Q(\sqrt{-391}) $	None	✓	$2$	$0$	$0$	$0$	$0$	$0$	$1$	$\mathrm{U}(1)[D_{2}]$	$q+\beta _{2}q^{2}+(4+\beta _{3}+\beta _{4})q^{4}+\beta _{5}q^{5}+\cdots$

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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.