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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 (24 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
164.1.d.a	$164$	$1$	164.d	164.d	$2$	$1$	$1$	$0.082$	$\Q$	$D_{2}$	$\Q(\sqrt{-1}) $, $\Q(\sqrt{-41}) $	$\Q(\sqrt{41}) $	✓	$4$	$0$	$1$	$0$	$-2$	$0$	$1$		$q+q^{2}+q^{4}-2q^{5}+q^{8}-q^{9}-2q^{10}+\cdots$
328.1.c.a	$328$	$1$	328.c	328.c	$2$	$1$	$1$	$0.164$	$\Q$	$D_{2}$	$\Q(\sqrt{-2}) $, $\Q(\sqrt{-82}) $	$\Q(\sqrt{41}) $	✓	$4$	$0$	$-1$	$0$	$0$	$0$	$1$		$q-q^{2}+q^{4}-q^{8}+q^{9}+q^{16}-q^{18}+\cdots$
656.1.m.a	$656$	$1$	656.m	656.m	$4$	$2$	$1$	$0.327$	$\Q(\sqrt{-1}) $	$D_{4}$	None	$\Q(\sqrt{41}) $		$4$	$0$	$0$	$0$	$2$	$0$	$1$		$q-iq^{2}-q^{4}+(1+i)q^{5}+iq^{8}+iq^{9}+\cdots$
820.1.e.a	$820$	$1$	820.e	820.e	$2$	$1$	$1$	$0.409$	$\Q$	$D_{2}$	$\Q(\sqrt{-5}) $, $\Q(\sqrt{-205}) $	$\Q(\sqrt{41}) $	✓	$4$	$0$	$-1$	$0$	$-1$	$0$	$1$		$q-q^{2}+q^{4}-q^{5}-q^{8}+q^{9}+q^{10}+\cdots$
820.1.e.b	$820$	$1$	820.e	820.e	$2$	$1$	$1$	$0.409$	$\Q$	$D_{2}$	$\Q(\sqrt{-5}) $, $\Q(\sqrt{-205}) $	$\Q(\sqrt{41}) $	✓	$4$	$0$	$1$	$0$	$-1$	$0$	$1$		$q+q^{2}+q^{4}-q^{5}+q^{8}+q^{9}-q^{10}+\cdots$
943.1.b.a	$943$	$1$	943.b	943.b	$2$	$1$	$1$	$0.471$	$\Q$	$D_{2}$	$\Q(\sqrt{-23}) $, $\Q(\sqrt{-943}) $	$\Q(\sqrt{41}) $	✓	$4$	$0$	$-2$	$0$	$0$	$0$	$1$		$q-2q^{2}+3q^{4}-4q^{8}+q^{9}+5q^{16}+\cdots$
1271.1.d.a	$1271$	$1$	1271.d	1271.d	$2$	$1$	$1$	$0.634$	$\Q$	$D_{2}$	$\Q(\sqrt{-31}) $, $\Q(\sqrt{-1271}) $	$\Q(\sqrt{41}) $	✓	$4$	$0$	$-2$	$0$	$2$	$0$	$1$		$q-2q^{2}+3q^{4}+2q^{5}-4q^{8}-q^{9}+\cdots$
1312.1.c.a	$1312$	$1$	1312.c	328.c	$2$	$1$	$1$	$0.655$	$\Q$	$D_{2}$	$\Q(\sqrt{-2}) $, $\Q(\sqrt{-82}) $	$\Q(\sqrt{41}) $	✓	$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q+q^{9}+q^{25}-q^{41}+2q^{43}-q^{49}+\cdots$
1312.1.bg.a	$1312$	$1$	1312.bg	1312.ag	$8$	$4$	$1$	$0.655$	$\Q(\zeta_{8})$	$D_{8}$	None	$\Q(\sqrt{41}) $		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q-\zeta_{8}^{3}q^{2}-\zeta_{8}^{2}q^{4}+(-\zeta_{8}^{2}-\zeta_{8}^{3}+\cdots)q^{5}+\cdots$
1476.1.h.a	$1476$	$1$	1476.h	164.d	$2$	$1$	$1$	$0.737$	$\Q$	$D_{2}$	$\Q(\sqrt{-1}) $, $\Q(\sqrt{-41}) $	$\Q(\sqrt{41}) $	✓	$4$	$0$	$-1$	$0$	$2$	$0$	$1$		$q-q^{2}+q^{4}+2q^{5}-q^{8}-2q^{10}+q^{16}+\cdots$
1640.1.j.a	$1640$	$1$	1640.j	1640.j	$2$	$1$	$1$	$0.818$	$\Q$	$D_{2}$	$\Q(\sqrt{-10}) $, $\Q(\sqrt{-410}) $	$\Q(\sqrt{41}) $	✓	$4$	$0$	$-1$	$0$	$-1$	$0$	$1$		$q-q^{2}+q^{4}-q^{5}-q^{8}-q^{9}+q^{10}+\cdots$
1640.1.j.b	$1640$	$1$	1640.j	1640.j	$2$	$1$	$1$	$0.818$	$\Q$	$D_{2}$	$\Q(\sqrt{-10}) $, $\Q(\sqrt{-410}) $	$\Q(\sqrt{41}) $	✓	$4$	$0$	$1$	$0$	$1$	$0$	$1$		$q+q^{2}+q^{4}+q^{5}+q^{8}-q^{9}+q^{10}+\cdots$
1763.1.c.b	$1763$	$1$	1763.c	1763.c	$2$	$1$	$1$	$0.880$	$\Q$	$D_{2}$	$\Q(\sqrt{-43}) $, $\Q(\sqrt{-1763}) $	$\Q(\sqrt{41}) $	✓	$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q+q^{4}-q^{9}+q^{16}+2q^{23}+q^{25}+\cdots$
1845.1.o.a	$1845$	$1$	1845.o	205.g	$4$	$2$	$1$	$0.921$	$\Q(\sqrt{-1}) $	$D_{4}$	None	$\Q(\sqrt{41}) $		$4$	$0$	$-2$	$0$	$0$	$0$	$1$		$q+(-1-i)q^{2}+iq^{4}+iq^{5}-q^{8}+\cdots$
1845.1.o.b	$1845$	$1$	1845.o	205.g	$4$	$2$	$1$	$0.921$	$\Q(\sqrt{-1}) $	$D_{4}$	None	$\Q(\sqrt{41}) $		$4$	$0$	$2$	$0$	$0$	$0$	$1$		$q+(1+i)q^{2}+iq^{4}-iq^{5}+q^{8}+(1+\cdots)q^{10}+\cdots$
2419.1.b.a	$2419$	$1$	2419.b	2419.b	$2$	$1$	$1$	$1.207$	$\Q$	$D_{2}$	$\Q(\sqrt{-59}) $, $\Q(\sqrt{-2419}) $	$\Q(\sqrt{41}) $	✓	$4$	$0$	$0$	$0$	$-2$	$0$	$1$		$q+q^{4}-2q^{5}+q^{9}+q^{16}-2q^{20}+\cdots$
2501.1.j.a	$2501$	$1$	2501.j	2501.j	$4$	$2$	$1$	$1.248$	$\Q(\sqrt{-1}) $	$D_{4}$	None	$\Q(\sqrt{41}) $		$4$	$0$	$2$	$0$	$0$	$0$	$1$		$q+(1-i)q^{2}-iq^{4}+iq^{5}+q^{8}-q^{9}+\cdots$
2624.1.h.a	$2624$	$1$	2624.h	164.d	$2$	$1$	$1$	$1.310$	$\Q$	$D_{2}$	$\Q(\sqrt{-1}) $, $\Q(\sqrt{-41}) $	$\Q(\sqrt{41}) $	✓	$4$	$0$	$0$	$0$	$2$	$0$	$1$		$q+2q^{5}-q^{9}+3q^{25}+2q^{37}+q^{41}+\cdots$
2624.1.m.a	$2624$	$1$	2624.m	656.m	$4$	$2$	$1$	$1.310$	$\Q(\sqrt{-1}) $	$D_{4}$	None	$\Q(\sqrt{41}) $		$4$	$0$	$0$	$0$	$2$	$0$	$1$		$q+(1+i)q^{5}+iq^{9}+iq^{25}+iq^{31}+\cdots$
2624.1.cj.a	$2624$	$1$	2624.cj	2624.bj	$16$	$8$	$1$	$1.310$	$\Q(\zeta_{16})$	$D_{16}$	None	$\Q(\sqrt{41}) $		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q+\zeta_{16}^{5}q^{2}-\zeta_{16}^{2}q^{4}+(-\zeta_{16}+\zeta_{16}^{6}+\cdots)q^{5}+\cdots$
2952.1.h.a	$2952$	$1$	2952.h	328.c	$2$	$1$	$1$	$1.473$	$\Q$	$D_{2}$	$\Q(\sqrt{-2}) $, $\Q(\sqrt{-82}) $	$\Q(\sqrt{41}) $	✓	$4$	$0$	$1$	$0$	$0$	$0$	$1$		$q+q^{2}+q^{4}+q^{8}+q^{16}+q^{25}+q^{32}+\cdots$
3280.1.ce.a	$3280$	$1$	3280.ce	3280.be	$4$	$2$	$1$	$1.637$	$\Q(\sqrt{-1}) $	$D_{4}$	None	$\Q(\sqrt{41}) $		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q+iq^{2}-q^{4}+iq^{5}-iq^{8}-iq^{9}+\cdots$
3280.1.ce.b	$3280$	$1$	3280.ce	3280.be	$4$	$2$	$1$	$1.637$	$\Q(\sqrt{-1}) $	$D_{4}$	None	$\Q(\sqrt{41}) $		$4$	$0$	$0$	$0$	$2$	$0$	$1$		$q-iq^{2}-q^{4}+q^{5}+iq^{8}-iq^{9}-iq^{10}+\cdots$
3403.1.b.a	$3403$	$1$	3403.b	3403.b	$2$	$1$	$1$	$1.698$	$\Q$	$D_{2}$	$\Q(\sqrt{-83}) $, $\Q(\sqrt{-3403}) $	$\Q(\sqrt{41}) $	✓	$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q+q^{4}+q^{9}+q^{16}-2q^{23}+q^{25}+\cdots$

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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.