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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 (19 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
371.1.c.a	$371$	$1$	371.c	371.c	$2$	$1$	$1$	$0.185$	$\Q$	$D_{2}$	$\Q(\sqrt{-7}) $, $\Q(\sqrt{-371}) $	$\Q(\sqrt{53}) $	✓	$4$	$0$	$0$	$0$	$0$	$1$	$1$		$q+q^{4}+q^{7}-q^{9}-2q^{11}+q^{16}-q^{25}+\cdots$
371.1.c.b	$371$	$1$	371.c	371.c	$2$	$2$	$2$	$0.185$	$\Q(\sqrt{2}) $	$D_{4}$	$\Q(\sqrt{-371}) $	None	✓	$4$	$0$	$0$	$0$	$0$	$-2$	$1$		$q-\beta q^{3}+q^{4}+\beta q^{5}-q^{7}+q^{9}-\beta q^{12}+\cdots$
1484.1.h.a	$1484$	$1$	1484.h	371.c	$2$	$1$	$1$	$0.741$	$\Q$	$D_{3}$	$\Q(\sqrt{-371}) $	None	✓	$2$	$0$	$0$	$-2$	$1$	$1$	$1$		$q-2q^{3}+q^{5}+q^{7}+3q^{9}-q^{11}-2q^{15}+\cdots$
1484.1.h.b	$1484$	$1$	1484.h	371.c	$2$	$1$	$1$	$0.741$	$\Q$	$D_{3}$	$\Q(\sqrt{-371}) $	None	✓	$2$	$0$	$0$	$2$	$-1$	$1$	$1$		$q+2q^{3}-q^{5}+q^{7}+3q^{9}-q^{11}-2q^{15}+\cdots$
1484.1.h.c	$1484$	$1$	1484.h	371.c	$2$	$2$	$2$	$0.741$	$\Q(\sqrt{3}) $	$D_{6}$	$\Q(\sqrt{-371}) $	None	✓	$4$	$0$	$0$	$0$	$0$	$2$	$1$		$q-\beta q^{5}+q^{7}-q^{9}+q^{11}+\beta q^{19}+\cdots$
1484.1.h.d	$1484$	$1$	1484.h	371.c	$2$	$4$	$4$	$0.741$	$\Q(\zeta_{24})^+$	$D_{12}$	$\Q(\sqrt{-371}) $	None	✓	$4$	$0$	$0$	$0$	$0$	$-4$	$1$		$q+(-\beta _{1}-\beta _{3})q^{3}-\beta _{1}q^{5}-q^{7}+q^{9}+\cdots$
1855.1.g.e	$1855$	$1$	1855.g	1855.g	$2$	$8$	$8$	$0.926$	$\Q(\zeta_{16})$	$D_{8}$	$\Q(\sqrt{-371}) $	None		$8$	$0$	$0$	$0$	$0$	$0$	$1$		$q+(\zeta_{16}^{3}+\zeta_{16}^{5})q^{3}-q^{4}-\zeta_{16}q^{5}+\cdots$
2597.1.i.b	$2597$	$1$	2597.i	371.i	$6$	$2$	$1$	$1.296$	$\Q(\sqrt{-3}) $	$D_{2}$	$\Q(\sqrt{-7}) $, $\Q(\sqrt{-371}) $	$\Q(\sqrt{53}) $		$8$	$0$	$0$	$0$	$0$	$0$	$1$		$q+\zeta_{6}^{2}q^{4}+\zeta_{6}q^{9}-\zeta_{6}^{2}q^{11}-\zeta_{6}q^{16}+\cdots$
2597.1.i.c	$2597$	$1$	2597.i	371.i	$6$	$4$	$2$	$1.296$	$\Q(\sqrt{2}, \sqrt{-3})$	$D_{4}$	$\Q(\sqrt{-371}) $	None		$8$	$0$	$0$	$0$	$0$	$0$	$1$		$q-\beta _{1}q^{3}+(-1-\beta _{2})q^{4}+(-\beta _{1}-\beta _{3})q^{5}+\cdots$
3339.1.e.a	$3339$	$1$	3339.e	371.c	$2$	$1$	$1$	$1.666$	$\Q$	$D_{2}$	$\Q(\sqrt{-7}) $, $\Q(\sqrt{-371}) $	$\Q(\sqrt{53}) $	✓	$4$	$0$	$0$	$0$	$0$	$1$	$1$		$q+q^{4}+q^{7}+2q^{11}+q^{16}-q^{25}+\cdots$
3339.1.e.c	$3339$	$1$	3339.e	371.c	$2$	$2$	$2$	$1.666$	$\Q(\sqrt{2}) $	$D_{4}$	$\Q(\sqrt{-371}) $	None	✓	$4$	$0$	$0$	$0$	$0$	$-2$	$1$		$q+q^{4}-\beta q^{5}-q^{7}+q^{16}+\beta q^{19}+\cdots$
3339.1.bf.a	$3339$	$1$	3339.bf	3339.af	$6$	$2$	$1$	$1.666$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-371}) $	None		$4$	$0$	$0$	$-1$	$1$	$-1$	$1$		$q+\zeta_{6}^{2}q^{3}+\zeta_{6}^{2}q^{4}-\zeta_{6}^{2}q^{5}-\zeta_{6}q^{7}+\cdots$
3339.1.bf.b	$3339$	$1$	3339.bf	3339.af	$6$	$2$	$1$	$1.666$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-371}) $	None		$4$	$0$	$0$	$1$	$-1$	$-1$	$1$		$q-\zeta_{6}^{2}q^{3}+\zeta_{6}^{2}q^{4}+\zeta_{6}^{2}q^{5}-\zeta_{6}q^{7}+\cdots$
3339.1.bf.d	$3339$	$1$	3339.bf	3339.af	$6$	$4$	$2$	$1.666$	$\Q(\zeta_{12})$	$D_{6}$	$\Q(\sqrt{-371}) $	None		$8$	$0$	$0$	$0$	$0$	$-2$	$1$		$q+\zeta_{12}^{5}q^{3}-\zeta_{12}^{2}q^{4}+(\zeta_{12}+\zeta_{12}^{3}+\cdots)q^{5}+\cdots$
3339.1.bf.f	$3339$	$1$	3339.bf	3339.af	$6$	$8$	$4$	$1.666$	$\Q(\zeta_{24})$	$D_{12}$	$\Q(\sqrt{-371}) $	None		$8$	$0$	$0$	$0$	$0$	$4$	$1$		$q-\zeta_{24}^{7}q^{3}-\zeta_{24}^{4}q^{4}+(\zeta_{24}^{9}-\zeta_{24}^{11}+\cdots)q^{5}+\cdots$
371.3.c.b	$371$	$3$	371.c	371.c	$2$	$4$	$4$	$10.109$	4.4.314608.1	$_{}$	$\Q(\sqrt{-371}) $	None	✓	$4$	$0$	$0$	$0$	$0$	$-28$	$2^{2}$	$\mathrm{U}(1)[D_{2}]$	$q-\beta _{1}q^{3}+4q^{4}+(-\beta _{1}+\beta _{2})q^{5}-7q^{7}+\cdots$
371.3.c.c	$371$	$3$	371.c	371.c	$2$	$4$	$4$	$10.109$	4.4.664832.1	$_{}$	$\Q(\sqrt{-371}) $	None	✓	$4$	$0$	$0$	$0$	$0$	$28$	$1$	$\mathrm{U}(1)[D_{2}]$	$q+\beta _{1}q^{3}+4q^{4}+(-\beta _{1}-\beta _{2})q^{5}+7q^{7}+\cdots$
1484.3.h.a	$1484$	$3$	1484.h	371.c	$2$	$8$	$8$	$40.436$	8.8.$\cdots$.3	$_{}$	$\Q(\sqrt{-371}) $	None	✓	$4$	$0$	$0$	$0$	$0$	$-56$	$2^{8}$	$\mathrm{U}(1)[D_{2}]$	$q+\beta _{5}q^{3}+(\beta _{1}-\beta _{5})q^{5}-7q^{7}+(9+3\beta _{2}+\cdots)q^{9}+\cdots$
1484.3.h.b	$1484$	$3$	1484.h	371.c	$2$	$8$	$8$	$40.436$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	$_{}$	$\Q(\sqrt{-371}) $	None	✓	$4$	$0$	$0$	$0$	$0$	$56$	$2^{5}\cdot 3^{2}$	$\mathrm{U}(1)[D_{2}]$	$q+\beta _{5}q^{3}+(\beta _{4}+\beta _{5})q^{5}+7q^{7}+(9+\beta _{2}+\cdots)q^{9}+\cdots$

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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.