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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 (33 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
327.1.d.a	$327$	$1$	327.d	327.d	$2$	$1$	$1$	$0.163$	$\Q$	$D_{3}$	$\Q(\sqrt{-327}) $	None	✓	$2$	$0$	$-1$	$1$	$0$	$-1$	$1$		$q-q^{2}+q^{3}-q^{6}-q^{7}+q^{8}+q^{9}+\cdots$
327.1.d.b	$327$	$1$	327.d	327.d	$2$	$1$	$1$	$0.163$	$\Q$	$D_{2}$	$\Q(\sqrt{-3}) $, $\Q(\sqrt{-327}) $	$\Q(\sqrt{109}) $	✓	$4$	$0$	$0$	$-1$	$0$	$2$	$1$		$q-q^{3}-q^{4}+2q^{7}+q^{9}+q^{12}+q^{16}+\cdots$
327.1.d.c	$327$	$1$	327.d	327.d	$2$	$1$	$1$	$0.163$	$\Q$	$D_{3}$	$\Q(\sqrt{-327}) $	None	✓	$2$	$0$	$1$	$1$	$0$	$-1$	$1$		$q+q^{2}+q^{3}+q^{6}-q^{7}-q^{8}+q^{9}+\cdots$
327.1.d.d	$327$	$1$	327.d	327.d	$2$	$2$	$2$	$0.163$	$\Q(\sqrt{3}) $	$D_{6}$	$\Q(\sqrt{-327}) $	None	✓	$4$	$0$	$0$	$-2$	$0$	$-2$	$1$		$q-\beta q^{2}-q^{3}+2q^{4}+\beta q^{6}-q^{7}-\beta q^{8}+\cdots$
2289.1.ba.a	$2289$	$1$	2289.ba	2289.aa	$6$	$2$	$1$	$1.142$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-327}) $	None		$4$	$0$	$-2$	$-1$	$0$	$2$	$1$		$q-\zeta_{6}q^{2}+\zeta_{6}^{2}q^{3}+3\zeta_{6}^{2}q^{4}+2q^{6}+\cdots$
2289.1.ba.b	$2289$	$1$	2289.ba	2289.aa	$6$	$2$	$1$	$1.142$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-327}) $	None		$4$	$0$	$-1$	$-1$	$0$	$-1$	$1$		$q-\zeta_{6}q^{2}+\zeta_{6}^{2}q^{3}+q^{6}-\zeta_{6}q^{7}-q^{8}+\cdots$
2289.1.ba.c	$2289$	$1$	2289.ba	2289.aa	$6$	$2$	$1$	$1.142$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-327}) $	None		$4$	$0$	$-1$	$-1$	$0$	$-1$	$1$		$q-\zeta_{6}q^{2}+\zeta_{6}^{2}q^{3}+q^{6}+\zeta_{6}^{2}q^{7}+\cdots$
2289.1.ba.d	$2289$	$1$	2289.ba	2289.aa	$6$	$2$	$1$	$1.142$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-327}) $	None		$4$	$0$	$1$	$-1$	$0$	$-1$	$1$		$q+\zeta_{6}q^{2}+\zeta_{6}^{2}q^{3}-q^{6}+\zeta_{6}^{2}q^{7}+\cdots$
2289.1.ba.e	$2289$	$1$	2289.ba	2289.aa	$6$	$2$	$1$	$1.142$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-327}) $	None		$4$	$0$	$1$	$-1$	$0$	$-1$	$1$		$q+\zeta_{6}q^{2}+\zeta_{6}^{2}q^{3}-q^{6}-\zeta_{6}q^{7}+q^{8}+\cdots$
2289.1.ba.f	$2289$	$1$	2289.ba	2289.aa	$6$	$2$	$1$	$1.142$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-327}) $	None		$4$	$0$	$2$	$-1$	$0$	$2$	$1$		$q+\zeta_{6}q^{2}+\zeta_{6}^{2}q^{3}+3\zeta_{6}^{2}q^{4}-2q^{6}+\cdots$
2289.1.ba.g	$2289$	$1$	2289.ba	2289.aa	$6$	$4$	$2$	$1.142$	$\Q(\zeta_{12})$	$D_{6}$	$\Q(\sqrt{-327}) $	None		$8$	$0$	$0$	$2$	$0$	$-2$	$3$		$q+(\zeta_{12}^{3}+\zeta_{12}^{5})q^{2}+\zeta_{12}^{2}q^{3}+(-1+\cdots)q^{4}+\cdots$
2289.1.ba.h	$2289$	$1$	2289.ba	2289.aa	$6$	$4$	$2$	$1.142$	$\Q(\zeta_{12})$	$D_{6}$	$\Q(\sqrt{-327}) $	None		$8$	$0$	$0$	$2$	$0$	$-2$	$3$		$q+(-\zeta_{12}^{3}-\zeta_{12}^{5})q^{2}+\zeta_{12}^{2}q^{3}+\cdots$
2289.1.ba.i	$2289$	$1$	2289.ba	2289.aa	$6$	$4$	$2$	$1.142$	$\Q(\zeta_{12})$	$D_{6}$	$\Q(\sqrt{-327}) $	None		$8$	$0$	$0$	$2$	$0$	$4$	$3$		$q+\zeta_{12}^{2}q^{3}+\zeta_{12}^{2}q^{4}+q^{7}+\zeta_{12}^{4}q^{9}+\cdots$
2616.1.o.e	$2616$	$1$	2616.o	2616.o	$2$	$4$	$4$	$1.306$	$\Q(\zeta_{8})$	$D_{4}$	$\Q(\sqrt{-327}) $	None		$8$	$0$	$0$	$0$	$0$	$8$	$1$		$q-\zeta_{8}q^{2}-\zeta_{8}^{2}q^{3}+\zeta_{8}^{2}q^{4}+\zeta_{8}^{3}q^{6}+\cdots$
2616.1.o.f	$2616$	$1$	2616.o	2616.o	$2$	$8$	$8$	$1.306$	$\Q(\zeta_{24})$	$D_{12}$	$\Q(\sqrt{-327}) $	None		$8$	$0$	$0$	$0$	$0$	$-8$	$1$		$q-\zeta_{24}q^{2}+\zeta_{24}^{6}q^{3}+\zeta_{24}^{2}q^{4}-\zeta_{24}^{7}q^{6}+\cdots$
2943.1.d.a	$2943$	$1$	2943.d	327.d	$2$	$3$	$3$	$1.469$	$\Q(\zeta_{18})^+$	$D_{9}$	$\Q(\sqrt{-327}) $	None	✓	$2$	$0$	$0$	$0$	$0$	$0$	$1$		$q-\beta _{1}q^{2}+(1+\beta _{2})q^{4}-\beta _{1}q^{7}+(-1+\cdots)q^{8}+\cdots$
2943.1.d.b	$2943$	$1$	2943.d	327.d	$2$	$3$	$3$	$1.469$	$\Q(\zeta_{18})^+$	$D_{9}$	$\Q(\sqrt{-327}) $	None	✓	$2$	$0$	$0$	$0$	$0$	$0$	$1$		$q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}-\beta _{1}q^{7}+(1+\beta _{1}+\cdots)q^{8}+\cdots$
2943.1.d.c	$2943$	$1$	2943.d	327.d	$2$	$6$	$6$	$1.469$	$\Q(\zeta_{36})^+$	$D_{18}$	$\Q(\sqrt{-327}) $	None	✓	$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q-\beta _{1}q^{2}+(1+\beta _{2})q^{4}-\beta _{4}q^{7}+(-\beta _{1}+\cdots)q^{8}+\cdots$
3597.1.x.a	$3597$	$1$	3597.x	3597.x	$10$	$4$	$1$	$1.795$	$\Q(\zeta_{10})$	$D_{5}$	$\Q(\sqrt{-327}) $	None		$4$	$0$	$-2$	$-1$	$0$	$3$	$1$		$q+(\zeta_{10}^{2}+\zeta_{10}^{4})q^{2}+\zeta_{10}^{4}q^{3}+(-\zeta_{10}+\cdots)q^{4}+\cdots$
3597.1.x.b	$3597$	$1$	3597.x	3597.x	$10$	$4$	$1$	$1.795$	$\Q(\zeta_{10})$	$D_{5}$	$\Q(\sqrt{-327}) $	None		$4$	$0$	$2$	$-1$	$0$	$3$	$1$		$q+(-\zeta_{10}^{2}-\zeta_{10}^{4})q^{2}+\zeta_{10}^{4}q^{3}+\cdots$
3597.1.x.c	$3597$	$1$	3597.x	3597.x	$10$	$8$	$2$	$1.795$	$\Q(\zeta_{15})$	$D_{15}$	$\Q(\sqrt{-327}) $	None		$4$	$0$	$-2$	$-2$	$0$	$-3$	$5$		$q+(\zeta_{30}^{7}+\zeta_{30}^{11})q^{2}+\zeta_{30}^{12}q^{3}+\cdots$
3597.1.x.d	$3597$	$1$	3597.x	3597.x	$10$	$8$	$2$	$1.795$	$\Q(\zeta_{20})$	$D_{10}$	$\Q(\sqrt{-327}) $	None		$8$	$0$	$0$	$2$	$0$	$6$	$1$		$q+(-\zeta_{20}^{3}-\zeta_{20}^{9})q^{2}-\zeta_{20}^{8}q^{3}+\cdots$
3597.1.x.e	$3597$	$1$	3597.x	3597.x	$10$	$8$	$2$	$1.795$	$\Q(\zeta_{15})$	$D_{15}$	$\Q(\sqrt{-327}) $	None		$4$	$0$	$2$	$-2$	$0$	$-3$	$5$		$q+(-\zeta_{30}^{7}-\zeta_{30}^{11})q^{2}+\zeta_{30}^{12}q^{3}+\cdots$
3597.1.x.f	$3597$	$1$	3597.x	3597.x	$10$	$16$	$4$	$1.795$	$\Q(\zeta_{60})$	$D_{30}$	$\Q(\sqrt{-327}) $	None		$8$	$0$	$0$	$4$	$0$	$-6$	$1$		$q+(\zeta_{60}^{7}-\zeta_{60}^{11})q^{2}-\zeta_{60}^{12}q^{3}+\cdots$
3924.1.g.a	$3924$	$1$	3924.g	436.c	$2$	$1$	$1$	$1.958$	$\Q$	$D_{2}$	$\Q(\sqrt{-327}) $, $\Q(\sqrt{-109}) $	$\Q(\sqrt{3}) $	✓	$4$	$0$	$-1$	$0$	$0$	$0$	$1$		$q-q^{2}+q^{4}-q^{8}-2q^{11}+q^{16}+2q^{22}+\cdots$
3924.1.g.c	$3924$	$1$	3924.g	436.c	$2$	$1$	$1$	$1.958$	$\Q$	$D_{2}$	$\Q(\sqrt{-327}) $, $\Q(\sqrt{-109}) $	$\Q(\sqrt{3}) $	✓	$4$	$0$	$1$	$0$	$0$	$0$	$1$		$q+q^{2}+q^{4}+q^{8}+2q^{11}+q^{16}+2q^{22}+\cdots$
3924.1.g.f	$3924$	$1$	3924.g	436.c	$2$	$2$	$2$	$1.958$	$\Q(\sqrt{-3}) $	$D_{6}$	$\Q(\sqrt{-327}) $	None		$4$	$0$	$-1$	$0$	$0$	$0$	$1$		$q+\zeta_{6}^{2}q^{2}-\zeta_{6}q^{4}+(\zeta_{6}+\zeta_{6}^{2})q^{7}+\cdots$
3924.1.g.g	$3924$	$1$	3924.g	436.c	$2$	$2$	$2$	$1.958$	$\Q(\sqrt{-1}) $	$D_{2}$	$\Q(\sqrt{-1}) $, $\Q(\sqrt{-327}) $	$\Q(\sqrt{327}) $		$8$	$0$	$0$	$0$	$0$	$0$	$1$		$q-iq^{2}-q^{4}+iq^{8}+q^{16}+iq^{17}+\cdots$
3924.1.g.h	$3924$	$1$	3924.g	436.c	$2$	$2$	$2$	$1.958$	$\Q(\sqrt{-3}) $	$D_{6}$	$\Q(\sqrt{-327}) $	None		$4$	$0$	$1$	$0$	$0$	$0$	$1$		$q-\zeta_{6}^{2}q^{2}-\zeta_{6}q^{4}+(\zeta_{6}+\zeta_{6}^{2})q^{7}+\cdots$
3924.1.g.j	$3924$	$1$	3924.g	436.c	$2$	$4$	$4$	$1.958$	$\Q(\zeta_{12})$	$D_{6}$	$\Q(\sqrt{-327}) $	None		$8$	$0$	$0$	$0$	$0$	$0$	$1$		$q-\zeta_{12}q^{2}+\zeta_{12}^{2}q^{4}+(\zeta_{12}^{2}+\zeta_{12}^{4}+\cdots)q^{7}+\cdots$
981.2.c.g	$981$	$2$	981.c	109.b	$2$	$12$	$12$	$7.833$	$\mathbb{Q}[x]/(x^{12} + \cdots)$	$_{}$	$\Q(\sqrt{-327}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$2^{6}$	$\mathrm{U}(1)[D_{2}]$	$q+\beta _{1}q^{2}+(-2+\beta _{2})q^{4}+\beta _{7}q^{7}+(-2\beta _{1}+\cdots)q^{8}+\cdots$
327.3.d.a	$327$	$3$	327.d	327.d	$2$	$6$	$6$	$8.910$	6.6.8496685269.1	$_{}$	$\Q(\sqrt{-327}) $	None	✓	$4$	$0$	$0$	$-18$	$0$	$0$	$2^{3}$	$\mathrm{U}(1)[D_{2}]$	$q+\beta _{1}q^{2}-3q^{3}+(4+\beta _{2}+\beta _{4})q^{4}+\cdots$
327.3.d.b	$327$	$3$	327.d	327.d	$2$	$6$	$6$	$8.910$	6.6.$\cdots$.2	$_{}$	$\Q(\sqrt{-327}) $	None	✓	$4$	$0$	$0$	$18$	$0$	$0$	$1$	$\mathrm{U}(1)[D_{2}]$	$q+\beta _{1}q^{2}+3q^{3}+(4+\beta _{3}-\beta _{4})q^{4}+\cdots$

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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.