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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
392.1.g.a	$392$	$1$	392.g	8.d	$2$	$1$	$1$	$0.196$	$\Q$	$D_{2}$	$\Q(\sqrt{-7}) $, $\Q(\sqrt{-2}) $	$\Q(\sqrt{14}) $	✓	$4$	$0$	$1$	$0$	$0$	$0$	$1$		$q+q^{2}+q^{4}+q^{8}-q^{9}-2q^{11}+q^{16}+\cdots$
392.1.k.a	$392$	$1$	392.k	56.k	$6$	$2$	$1$	$0.196$	$\Q(\sqrt{-3}) $	$D_{2}$	$\Q(\sqrt{-7}) $, $\Q(\sqrt{-2}) $	$\Q(\sqrt{14}) $		$8$	$0$	$-1$	$0$	$0$	$0$	$1$		$q-\zeta_{6}q^{2}+\zeta_{6}^{2}q^{4}+q^{8}+\zeta_{6}q^{9}-\zeta_{6}^{2}q^{11}+\cdots$
1568.1.g.a	$1568$	$1$	1568.g	8.d	$2$	$1$	$1$	$0.783$	$\Q$	$D_{2}$	$\Q(\sqrt{-7}) $, $\Q(\sqrt{-2}) $	$\Q(\sqrt{14}) $	✓	$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q-q^{9}+2q^{11}+q^{25}+2q^{43}-2q^{67}+\cdots$
1568.1.o.a	$1568$	$1$	1568.o	56.k	$6$	$2$	$1$	$0.783$	$\Q(\sqrt{-3}) $	$D_{2}$	$\Q(\sqrt{-7}) $, $\Q(\sqrt{-2}) $	$\Q(\sqrt{14}) $		$8$	$0$	$0$	$0$	$0$	$0$	$1$		$q-\zeta_{6}^{2}q^{9}-\zeta_{6}q^{11}-\zeta_{6}q^{25}+q^{43}+\cdots$
1736.1.n.a	$1736$	$1$	1736.n	1736.n	$2$	$1$	$1$	$0.866$	$\Q$	$D_{2}$	$\Q(\sqrt{-31}) $, $\Q(\sqrt{-434}) $	$\Q(\sqrt{14}) $	✓	$4$	$0$	$-1$	$0$	$-2$	$-1$	$1$		$q-q^{2}+q^{4}-2q^{5}-q^{7}-q^{8}-q^{9}+\cdots$
1736.1.n.b	$1736$	$1$	1736.n	1736.n	$2$	$1$	$1$	$0.866$	$\Q$	$D_{2}$	$\Q(\sqrt{-31}) $, $\Q(\sqrt{-434}) $	$\Q(\sqrt{14}) $	✓	$4$	$0$	$-1$	$0$	$2$	$1$	$1$		$q-q^{2}+q^{4}+2q^{5}+q^{7}-q^{8}-q^{9}+\cdots$
1736.1.dj.a	$1736$	$1$	1736.dj	1736.cj	$10$	$4$	$1$	$0.866$	$\Q(\zeta_{10})$	$D_{10}$	None	$\Q(\sqrt{14}) $		$4$	$0$	$1$	$0$	$-2$	$-1$	$1$		$q+\zeta_{10}^{3}q^{2}-\zeta_{10}q^{4}+(-\zeta_{10}+\zeta_{10}^{4}+\cdots)q^{5}+\cdots$
1736.1.dj.b	$1736$	$1$	1736.dj	1736.cj	$10$	$4$	$1$	$0.866$	$\Q(\zeta_{10})$	$D_{10}$	None	$\Q(\sqrt{14}) $		$4$	$0$	$1$	$0$	$2$	$1$	$1$		$q+\zeta_{10}^{3}q^{2}-\zeta_{10}q^{4}+(\zeta_{10}-\zeta_{10}^{4}+\cdots)q^{5}+\cdots$
2240.1.c.a	$2240$	$1$	2240.c	280.c	$2$	$2$	$2$	$1.118$	$\Q(\sqrt{-1}) $	$D_{2}$	$\Q(\sqrt{-35}) $, $\Q(\sqrt{-10}) $	$\Q(\sqrt{14}) $		$8$	$0$	$0$	$0$	$0$	$-2$	$1$		$q-iq^{5}-q^{7}+q^{9}+iq^{11}+iq^{13}+\cdots$
2240.1.c.b	$2240$	$1$	2240.c	280.c	$2$	$2$	$2$	$1.118$	$\Q(\sqrt{-1}) $	$D_{2}$	$\Q(\sqrt{-35}) $, $\Q(\sqrt{-10}) $	$\Q(\sqrt{14}) $		$8$	$0$	$0$	$0$	$0$	$2$	$1$		$q-iq^{5}+q^{7}+q^{9}-iq^{11}+iq^{13}+\cdots$
2632.1.b.a	$2632$	$1$	2632.b	2632.b	$2$	$1$	$1$	$1.314$	$\Q$	$D_{2}$	$\Q(\sqrt{-47}) $, $\Q(\sqrt{-658}) $	$\Q(\sqrt{14}) $	✓	$4$	$0$	$-1$	$0$	$0$	$-1$	$1$		$q-q^{2}+q^{4}-q^{7}-q^{8}+q^{9}+q^{14}+\cdots$
2632.1.b.b	$2632$	$1$	2632.b	2632.b	$2$	$1$	$1$	$1.314$	$\Q$	$D_{2}$	$\Q(\sqrt{-47}) $, $\Q(\sqrt{-658}) $	$\Q(\sqrt{14}) $	✓	$4$	$0$	$-1$	$0$	$0$	$1$	$1$		$q-q^{2}+q^{4}+q^{7}-q^{8}+q^{9}-q^{14}+\cdots$
3080.1.bc.a	$3080$	$1$	3080.bc	3080.ac	$2$	$1$	$1$	$1.537$	$\Q$	$D_{2}$	$\Q(\sqrt{-55}) $, $\Q(\sqrt{-770}) $	$\Q(\sqrt{14}) $	✓	$4$	$0$	$-1$	$0$	$-1$	$1$	$1$		$q-q^{2}+q^{4}-q^{5}+q^{7}-q^{8}-q^{9}+\cdots$
3080.1.bc.b	$3080$	$1$	3080.bc	3080.ac	$2$	$1$	$1$	$1.537$	$\Q$	$D_{2}$	$\Q(\sqrt{-55}) $, $\Q(\sqrt{-770}) $	$\Q(\sqrt{14}) $	✓	$4$	$0$	$-1$	$0$	$1$	$-1$	$1$		$q-q^{2}+q^{4}+q^{5}-q^{7}-q^{8}-q^{9}+\cdots$
3080.1.bc.c	$3080$	$1$	3080.bc	3080.ac	$2$	$1$	$1$	$1.537$	$\Q$	$D_{2}$	$\Q(\sqrt{-55}) $, $\Q(\sqrt{-770}) $	$\Q(\sqrt{14}) $	✓	$4$	$0$	$1$	$0$	$-1$	$-1$	$1$		$q+q^{2}+q^{4}-q^{5}-q^{7}+q^{8}-q^{9}+\cdots$
3080.1.bc.d	$3080$	$1$	3080.bc	3080.ac	$2$	$1$	$1$	$1.537$	$\Q$	$D_{2}$	$\Q(\sqrt{-55}) $, $\Q(\sqrt{-770}) $	$\Q(\sqrt{14}) $	✓	$4$	$0$	$1$	$0$	$1$	$1$	$1$		$q+q^{2}+q^{4}+q^{5}+q^{7}+q^{8}-q^{9}+\cdots$
3528.1.g.a	$3528$	$1$	3528.g	8.d	$2$	$1$	$1$	$1.761$	$\Q$	$D_{2}$	$\Q(\sqrt{-7}) $, $\Q(\sqrt{-2}) $	$\Q(\sqrt{14}) $	✓	$4$	$0$	$-1$	$0$	$0$	$0$	$1$		$q-q^{2}+q^{4}-q^{8}+2q^{11}+q^{16}-2q^{22}+\cdots$
3528.1.bx.a	$3528$	$1$	3528.bx	56.k	$6$	$2$	$1$	$1.761$	$\Q(\sqrt{-3}) $	$D_{2}$	$\Q(\sqrt{-7}) $, $\Q(\sqrt{-2}) $	$\Q(\sqrt{14}) $		$8$	$0$	$1$	$0$	$0$	$0$	$1$		$q+\zeta_{6}q^{2}+\zeta_{6}^{2}q^{4}-q^{8}+\zeta_{6}^{2}q^{11}+\cdots$
3584.1.c.b	$3584$	$1$	3584.c	7.b	$2$	$4$	$4$	$1.789$	$\Q(\zeta_{8})$	$D_{4}$	None	$\Q(\sqrt{14}) $		$8$	$0$	$0$	$0$	$0$	$0$	$2$		$q+(-\zeta_{8}-\zeta_{8}^{3})q^{5}+\zeta_{8}^{2}q^{7}+q^{9}+\cdots$
3584.1.h.b	$3584$	$1$	3584.h	56.h	$2$	$4$	$4$	$1.789$	$\Q(\zeta_{8})$	$D_{4}$	None	$\Q(\sqrt{14}) $		$8$	$0$	$0$	$0$	$0$	$0$	$2$		$q+(\zeta_{8}-\zeta_{8}^{3})q^{5}+\zeta_{8}^{2}q^{7}-q^{9}+(\zeta_{8}+\cdots)q^{11}+\cdots$

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Elliptic 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.