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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 (30 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
5148.2.a.a	$5148$	$2$	5148.a	1.a	$1$	$1$	$1$	$41.107$	$\Q$	None	✓	$1$	$0$	$0$	$0$	$-3$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q-3q^{5}+2q^{7}-q^{11}+q^{13}+2q^{19}+\cdots$
5148.2.a.b	$5148$	$2$	5148.a	1.a	$1$	$1$	$1$	$41.107$	$\Q$	None	✓	$1$	$0$	$0$	$0$	$-2$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{5}+q^{11}+q^{13}+6q^{17}+4q^{23}+\cdots$
5148.2.a.c	$5148$	$2$	5148.a	1.a	$1$	$1$	$1$	$41.107$	$\Q$	None	✓	$1$	$1$	$0$	$0$	$0$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{7}+q^{11}+q^{13}+2q^{17}+6q^{19}+\cdots$
5148.2.a.d	$5148$	$2$	5148.a	1.a	$1$	$1$	$1$	$41.107$	$\Q$	None	✓	$1$	$1$	$0$	$0$	$0$	$2$	$+$	$1$	$\mathrm{SU}(2)$	$q+2q^{7}+q^{11}+q^{13}-6q^{17}+2q^{19}+\cdots$
5148.2.a.e	$5148$	$2$	5148.a	1.a	$1$	$1$	$1$	$41.107$	$\Q$	None	✓	$1$	$0$	$0$	$0$	$2$	$-2$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{5}-2q^{7}-q^{11}+q^{13}+2q^{19}+\cdots$
5148.2.a.f	$5148$	$2$	5148.a	1.a	$1$	$1$	$1$	$41.107$	$\Q$	None	✓	$1$	$1$	$0$	$0$	$2$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+2q^{5}-q^{11}+q^{13}-6q^{17}-4q^{23}+\cdots$
5148.2.a.g	$5148$	$2$	5148.a	1.a	$1$	$2$	$2$	$41.107$	$\Q(\sqrt{21}) $	None	✓	$1$	$0$	$0$	$0$	$-4$	$5$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{5}+(2+\beta )q^{7}+q^{11}-q^{13}+4q^{17}+\cdots$
5148.2.a.h	$5148$	$2$	5148.a	1.a	$1$	$2$	$2$	$41.107$	$\Q(\sqrt{13}) $	None	✓	$1$	$1$	$0$	$0$	$0$	$-3$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1-\beta )q^{7}+q^{11}+q^{13}+2\beta q^{17}+\cdots$
5148.2.a.i	$5148$	$2$	5148.a	1.a	$1$	$2$	$2$	$41.107$	$\Q(\sqrt{3}) $	None	✓	$1$	$1$	$0$	$0$	$2$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+(1+\beta )q^{5}-q^{11}-q^{13}+(1-3\beta )q^{17}+\cdots$
5148.2.a.j	$5148$	$2$	5148.a	1.a	$1$	$2$	$2$	$41.107$	$\Q(\sqrt{2}) $	None	✓	$1$	$0$	$0$	$0$	$4$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+(2+\beta )q^{5}+2\beta q^{7}+q^{11}-q^{13}+\cdots$
5148.2.a.k	$5148$	$2$	5148.a	1.a	$1$	$2$	$2$	$41.107$	$\Q(\sqrt{21}) $	None	✓	$1$	$0$	$0$	$0$	$4$	$3$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{5}+(2-\beta )q^{7}-q^{11}+q^{13}+(-3+\cdots)q^{19}+\cdots$
5148.2.a.l	$5148$	$2$	5148.a	1.a	$1$	$3$	$3$	$41.107$	3.3.404.1	None	✓	$1$	$1$	$0$	$0$	$-4$	$-4$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1-2\beta _{1}+\beta _{2})q^{5}+(-2+\beta _{1}+\cdots)q^{7}+\cdots$
5148.2.a.m	$5148$	$2$	5148.a	1.a	$1$	$3$	$3$	$41.107$	3.3.564.1	None	✓	$1$	$1$	$0$	$0$	$-2$	$4$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta _{1})q^{5}+(1-\beta _{2})q^{7}-q^{11}+\cdots$
5148.2.a.n	$5148$	$2$	5148.a	1.a	$1$	$3$	$3$	$41.107$	3.3.1620.1	None	✓	$1$	$0$	$0$	$0$	$0$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{5}+\beta _{2}q^{7}+q^{11}-q^{13}+(-2+\cdots)q^{17}+\cdots$
5148.2.a.o	$5148$	$2$	5148.a	1.a	$1$	$3$	$3$	$41.107$	3.3.229.1	None	✓	$1$	$1$	$0$	$0$	$1$	$-7$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-\beta _{1}-\beta _{2})q^{5}+(-2-2\beta _{1}+\beta _{2})q^{7}+\cdots$
5148.2.a.p	$5148$	$2$	5148.a	1.a	$1$	$4$	$4$	$41.107$	4.4.82128.1	None	✓	$1$	$1$	$0$	$0$	$-4$	$2$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta _{1})q^{5}+(1-\beta _{1}+\beta _{2})q^{7}+\cdots$
5148.2.a.q	$5148$	$2$	5148.a	1.a	$1$	$4$	$4$	$41.107$	4.4.90996.1	None	✓	$1$	$0$	$0$	$0$	$-2$	$2$	$-$	$2$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{5}+(1+\beta _{2})q^{7}-q^{11}+q^{13}+\cdots$
5148.2.a.r	$5148$	$2$	5148.a	1.a	$1$	$4$	$4$	$41.107$	4.4.82128.1	None	✓	$1$	$0$	$0$	$0$	$4$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1-\beta _{1})q^{5}+(1-\beta _{1}+\beta _{2})q^{7}+q^{11}+\cdots$
5148.2.a.s	$5148$	$2$	5148.a	1.a	$1$	$5$	$5$	$41.107$	5.5.815952.1	None	✓	$1$	$1$	$0$	$0$	$-2$	$-2$	$+$	$2$	$\mathrm{SU}(2)$	$q-\beta _{4}q^{5}+\beta _{3}q^{7}+q^{11}-q^{13}+(-\beta _{1}+\cdots)q^{17}+\cdots$
5148.2.a.t	$5148$	$2$	5148.a	1.a	$1$	$5$	$5$	$41.107$	5.5.815952.1	None	✓	$1$	$0$	$0$	$0$	$2$	$-2$	$-$	$2$	$\mathrm{SU}(2)$	$q+\beta _{4}q^{5}+\beta _{3}q^{7}-q^{11}-q^{13}+(\beta _{1}+\cdots)q^{17}+\cdots$
5148.2.d.a	$5148$	$2$	5148.d	33.d	$2$	$48$	$48$	$41.107$		None		$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
5148.2.e.a	$5148$	$2$	5148.e	13.b	$2$	$2$	$2$	$41.107$	$\Q(\sqrt{-1}) $	None		$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+4iq^{7}+iq^{11}+(-3+2i)q^{13}+\cdots$
5148.2.e.b	$5148$	$2$	5148.e	13.b	$2$	$4$	$4$	$41.107$	$\Q(i, \sqrt{21})$	None		$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+(\beta _{1}-\beta _{2})q^{7}+\beta _{2}q^{11}+(2-3\beta _{2}+\cdots)q^{13}+\cdots$
5148.2.e.c	$5148$	$2$	5148.e	13.b	$2$	$8$	$8$	$41.107$	$\mathbb{Q}[x]/(x^{8} + \cdots)$	None		$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+(-\beta _{1}-\beta _{5}-\beta _{6}+\beta _{7})q^{5}+(\beta _{1}+\beta _{4}+\cdots)q^{7}+\cdots$
5148.2.e.d	$5148$	$2$	5148.e	13.b	$2$	$10$	$10$	$41.107$	$\mathbb{Q}[x]/(x^{10} - \cdots)$	None		$2$	$0$	$0$	$0$	$0$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{6}q^{5}-\beta _{9}q^{7}-\beta _{3}q^{11}+(\beta _{1}+\beta _{2}+\cdots)q^{13}+\cdots$
5148.2.e.e	$5148$	$2$	5148.e	13.b	$2$	$10$	$10$	$41.107$	$\mathbb{Q}[x]/(x^{10} - \cdots)$	None		$2$	$0$	$0$	$0$	$0$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{8}q^{5}+(\beta _{8}+\beta _{9})q^{7}+\beta _{7}q^{11}+(-\beta _{4}+\cdots)q^{13}+\cdots$
5148.2.e.f	$5148$	$2$	5148.e	13.b	$2$	$24$	$24$	$41.107$		None		$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
5148.2.p.a	$5148$	$2$	5148.p	429.e	$2$	$56$	$56$	$41.107$		None		$8$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
5148.2.ba.a	$5148$	$2$	5148.ba	39.f	$4$	$44$	$22$	$41.107$		None		$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{4}]$
5148.2.ba.b	$5148$	$2$	5148.ba	39.f	$4$	$44$	$22$	$41.107$		None		$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{4}]$

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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.