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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 (36 matches)

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Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Inner twists	Rank*	Traces				Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Inner twists	Rank*	$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
4140.2.a.a	$4140$	$2$	4140.a	1.a	$1$	$1$	$1$	$33.058$	$\Q$	None	✓	$1$	$0$	$0$	$0$	$-1$	$-4$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{5}-4q^{7}+2q^{13}-6q^{17}+2q^{19}+\cdots$
4140.2.a.b	$4140$	$2$	4140.a	1.a	$1$	$1$	$1$	$33.058$	$\Q$	None	✓	$1$	$1$	$0$	$0$	$-1$	$-3$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{5}-3q^{7}+2q^{11}-2q^{13}+7q^{17}+\cdots$
4140.2.a.c	$4140$	$2$	4140.a	1.a	$1$	$1$	$1$	$33.058$	$\Q$	None	✓	$1$	$1$	$0$	$0$	$-1$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{5}-2q^{7}+4q^{11}-2q^{13}-6q^{17}+\cdots$
4140.2.a.d	$4140$	$2$	4140.a	1.a	$1$	$1$	$1$	$33.058$	$\Q$	None	✓	$1$	$0$	$0$	$0$	$-1$	$-2$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{5}-2q^{7}+4q^{11}+q^{13}-4q^{19}+\cdots$
4140.2.a.e	$4140$	$2$	4140.a	1.a	$1$	$1$	$1$	$33.058$	$\Q$	None	✓	$1$	$1$	$0$	$0$	$1$	$-5$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{5}-5q^{7}+4q^{13}+3q^{17}-4q^{19}+\cdots$
4140.2.a.f	$4140$	$2$	4140.a	1.a	$1$	$1$	$1$	$33.058$	$\Q$	None	✓	$1$	$0$	$0$	$0$	$1$	$-4$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{5}-4q^{7}+6q^{11}-q^{13}+2q^{19}+\cdots$
4140.2.a.g	$4140$	$2$	4140.a	1.a	$1$	$1$	$1$	$33.058$	$\Q$	None	✓	$1$	$1$	$0$	$0$	$1$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{5}-2q^{7}-4q^{11}-2q^{13}+6q^{17}+\cdots$
4140.2.a.h	$4140$	$2$	4140.a	1.a	$1$	$1$	$1$	$33.058$	$\Q$	None	✓	$1$	$1$	$0$	$0$	$1$	$-1$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{5}-q^{7}-6q^{11}+6q^{13}-7q^{17}+\cdots$
4140.2.a.i	$4140$	$2$	4140.a	1.a	$1$	$1$	$1$	$33.058$	$\Q$	None	✓	$1$	$1$	$0$	$0$	$1$	$-1$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{5}-q^{7}-4q^{13}+3q^{17}-4q^{19}+\cdots$
4140.2.a.j	$4140$	$2$	4140.a	1.a	$1$	$1$	$1$	$33.058$	$\Q$	None	✓	$1$	$1$	$0$	$0$	$1$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{5}-6q^{13}-2q^{17}+6q^{19}+q^{23}+\cdots$
4140.2.a.k	$4140$	$2$	4140.a	1.a	$1$	$1$	$1$	$33.058$	$\Q$	None	✓	$1$	$1$	$0$	$0$	$1$	$2$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{5}+2q^{7}-3q^{13}-4q^{17}-4q^{19}+\cdots$
4140.2.a.l	$4140$	$2$	4140.a	1.a	$1$	$2$	$2$	$33.058$	$\Q(\sqrt{6}) $	None	✓	$1$	$1$	$0$	$0$	$-2$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{5}+(-1+\beta )q^{7}+\beta q^{11}+(2-\beta )q^{13}+\cdots$
4140.2.a.m	$4140$	$2$	4140.a	1.a	$1$	$2$	$2$	$33.058$	$\Q(\sqrt{17}) $	None	✓	$1$	$1$	$0$	$0$	$-2$	$1$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{5}+\beta q^{7}-2q^{11}+(-1-\beta )q^{13}+\cdots$
4140.2.a.n	$4140$	$2$	4140.a	1.a	$1$	$2$	$2$	$33.058$	$\Q(\sqrt{17}) $	None	✓	$1$	$1$	$0$	$0$	$-2$	$1$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{5}+\beta q^{7}-2\beta q^{11}+2q^{13}+(-2+\cdots)q^{17}+\cdots$
4140.2.a.o	$4140$	$2$	4140.a	1.a	$1$	$2$	$2$	$33.058$	$\Q(\sqrt{3}) $	None	✓	$1$	$0$	$0$	$0$	$-2$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{5}+(1+2\beta )q^{7}+(1+3\beta )q^{11}+(-5+\cdots)q^{13}+\cdots$
4140.2.a.p	$4140$	$2$	4140.a	1.a	$1$	$2$	$2$	$33.058$	$\Q(\sqrt{15}) $	None	✓	$1$	$0$	$0$	$0$	$-2$	$6$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{5}+3q^{7}+(-1-\beta )q^{11}+(1-\beta )q^{13}+\cdots$
4140.2.a.q	$4140$	$2$	4140.a	1.a	$1$	$2$	$2$	$33.058$	$\Q(\sqrt{6}) $	None	✓	$1$	$1$	$0$	$0$	$2$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{5}+(-1+\beta )q^{7}-\beta q^{11}+(2-\beta )q^{13}+\cdots$
4140.2.a.r	$4140$	$2$	4140.a	1.a	$1$	$2$	$2$	$33.058$	$\Q(\sqrt{6}) $	None	✓	$1$	$0$	$0$	$0$	$2$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{5}+q^{7}+(2-\beta )q^{11}-\beta q^{13}+(1+\cdots)q^{17}+\cdots$
4140.2.a.s	$4140$	$2$	4140.a	1.a	$1$	$3$	$3$	$33.058$	3.3.3144.1	None	✓	$1$	$0$	$0$	$0$	$3$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{5}+(1-\beta _{1})q^{7}+(-1-\beta _{2})q^{11}+\cdots$
4140.2.a.t	$4140$	$2$	4140.a	1.a	$1$	$5$	$5$	$33.058$	5.5.14345904.1	None	✓	$1$	$0$	$0$	$0$	$-5$	$4$	$-$	$2$	$\mathrm{SU}(2)$	$q-q^{5}+(1+\beta _{3})q^{7}+(-1+\beta _{4})q^{11}+\cdots$
4140.2.a.u	$4140$	$2$	4140.a	1.a	$1$	$5$	$5$	$33.058$	5.5.14345904.1	None	✓	$1$	$0$	$0$	$0$	$5$	$4$	$-$	$2$	$\mathrm{SU}(2)$	$q+q^{5}+(1+\beta _{3})q^{7}+(1-\beta _{4})q^{11}+(1+\cdots)q^{13}+\cdots$
4140.2.f.a	$4140$	$2$	4140.f	5.b	$2$	$6$	$6$	$33.058$	6.0.350464.1	None		$2$	$0$	$0$	$0$	$0$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q+(\beta _{1}-\beta _{4})q^{5}-\beta _{3}q^{7}+\beta _{1}q^{11}+(\beta _{3}+\cdots)q^{13}+\cdots$
4140.2.f.b	$4140$	$2$	4140.f	5.b	$2$	$12$	$12$	$33.058$	$\mathbb{Q}[x]/(x^{12} + \cdots)$	None		$2$	$0$	$0$	$0$	$0$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{8}q^{5}+(\beta _{1}+\beta _{6}-\beta _{10})q^{7}+(-1+\cdots)q^{11}+\cdots$
4140.2.f.c	$4140$	$2$	4140.f	5.b	$2$	$14$	$14$	$33.058$	$\mathbb{Q}[x]/(x^{14} + \cdots)$	None		$2$	$0$	$0$	$0$	$0$	$0$		$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{10}q^{5}+\beta _{13}q^{7}+(-1+\beta _{2}-\beta _{4}+\cdots)q^{11}+\cdots$
4140.2.f.d	$4140$	$2$	4140.f	5.b	$2$	$24$	$24$	$33.058$		None		$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
4140.2.i.a	$4140$	$2$	4140.i	69.c	$2$	$16$	$16$	$33.058$	$\mathbb{Q}[x]/(x^{16} + \cdots)$	None		$2$	$0$	$0$	$0$	$-16$	$0$		$2^{5}$	$\mathrm{SU}(2)[C_{2}]$	$q-q^{5}-\beta _{9}q^{7}+\beta _{1}q^{11}-\beta _{5}q^{13}+\cdots$
4140.2.i.b	$4140$	$2$	4140.i	69.c	$2$	$16$	$16$	$33.058$	$\mathbb{Q}[x]/(x^{16} + \cdots)$	None		$2$	$0$	$0$	$0$	$16$	$0$		$2^{5}$	$\mathrm{SU}(2)[C_{2}]$	$q+q^{5}-\beta _{9}q^{7}-\beta _{1}q^{11}-\beta _{5}q^{13}+\cdots$
4140.2.n.a	$4140$	$2$	4140.n	345.h	$2$	$16$	$16$	$33.058$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	$\Q(\sqrt{-115}) $		$8$	$0$	$0$	$0$	$0$	$0$		$2^{10}\cdot 3^{8}$	$\mathrm{U}(1)[D_{2}]$	$q+\beta _{2}q^{5}-\beta _{12}q^{7}+(\beta _{5}-\beta _{7})q^{17}+\cdots$
4140.2.n.b	$4140$	$2$	4140.n	345.h	$2$	$32$	$32$	$33.058$		None		$8$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
4140.2.s.a	$4140$	$2$	4140.s	15.e	$4$	$44$	$22$	$33.058$		None		$4$	$0$	$0$	$0$	$0$	$-12$			$\mathrm{SU}(2)[C_{4}]$
4140.2.s.b	$4140$	$2$	4140.s	15.e	$4$	$44$	$22$	$33.058$		None		$4$	$0$	$0$	$0$	$0$	$-4$			$\mathrm{SU}(2)[C_{4}]$
4140.3.c.a	$4140$	$3$	4140.c	15.d	$2$	$88$	$88$	$112.807$		None		$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
4140.3.d.a	$4140$	$3$	4140.d	23.b	$2$	$16$	$16$	$112.807$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	None		$2$	$0$	$0$	$0$	$0$	$0$		$2^{6}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{4}q^{5}-\beta _{7}q^{7}+(-2\beta _{4}+\beta _{9})q^{11}+\cdots$
4140.3.d.b	$4140$	$3$	4140.d	23.b	$2$	$32$	$32$	$112.807$		None		$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
4140.3.d.c	$4140$	$3$	4140.d	23.b	$2$	$32$	$32$	$112.807$		None		$2$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
4140.3.l.a	$4140$	$3$	4140.l	3.b	$2$	$56$	$56$	$112.807$		None		$2$	$0$	$0$	$0$	$0$	$32$			$\mathrm{SU}(2)[C_{2}]$

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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.