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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 (44 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				Fricke sign	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*	$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
2096.1.h.a	$2096$	$1$	2096.h	131.b	$2$	$1$	$1$	$1.046$	$\Q$	$D_{3}$	$\Q(\sqrt{-131}) $	None	✓	$2$	$0$	$0$	$1$	$2$	$1$		$1$		$q+q^{3}+2q^{5}+q^{7}-2q^{11}-q^{13}+\cdots$
2096.1.h.b	$2096$	$1$	2096.h	131.b	$2$	$2$	$2$	$1.046$	$\Q(\sqrt{5}) $	$D_{5}$	$\Q(\sqrt{-131}) $	None	✓	$2$	$0$	$0$	$1$	$-1$	$1$		$1$		$q+(1-\beta )q^{3}-\beta q^{5}+\beta q^{7}+(1-\beta )q^{9}+\cdots$
2096.1.h.c	$2096$	$1$	2096.h	131.b	$2$	$2$	$2$	$1.046$	$\Q(\sqrt{-2}) $	$S_{4}$	None	None		$2$	$0$	$0$	$2$	$0$	$2$		$1$		$q+q^{3}+q^{7}+q^{13}-\beta q^{17}+\beta q^{19}+\cdots$
2096.1.h.d	$2096$	$1$	2096.h	131.b	$2$	$4$	$4$	$1.046$	$\Q(\zeta_{15})^+$	$D_{15}$	$\Q(\sqrt{-131}) $	None	✓	$2$	$0$	$0$	$-1$	$-2$	$-1$		$1$		$q-\beta _{1}q^{3}+\beta _{3}q^{5}+(\beta _{2}+\beta _{3})q^{7}+(1+\cdots)q^{9}+\cdots$
2096.1.i.a	$2096$	$1$	2096.i	2096.i	$4$	$4$	$2$	$1.046$	$\Q(\zeta_{8})$	$S_{4}$	None	None		$4$	$0$	$0$	$-4$	$0$	$0$		$1$		$q-\zeta_{8}q^{2}+(-1+\zeta_{8}^{2})q^{3}+\zeta_{8}^{2}q^{4}+\cdots$
2096.1.q.a	$2096$	$1$	2096.q	524.g	$10$	$8$	$2$	$1.046$	$\Q(\zeta_{20})$	$A_{5}$	None	None		$4$	$0$	$0$	$0$	$2$	$0$		$1$		$q-\zeta_{20}q^{3}-\zeta_{20}^{8}q^{5}+(-\zeta_{20}-\zeta_{20}^{5}+\cdots)q^{7}+\cdots$
2096.2.a.a	$2096$	$2$	2096.a	1.a	$1$	$1$	$1$	$16.737$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$0$	$-1$	$-2$	$-1$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-2q^{5}-q^{7}-2q^{9}+4q^{11}+\cdots$
2096.2.a.b	$2096$	$2$	2096.a	1.a	$1$	$1$	$1$	$16.737$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$0$	$-1$	$-2$	$3$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-2q^{5}+3q^{7}-2q^{9}+q^{13}+\cdots$
2096.2.a.c	$2096$	$2$	2096.a	1.a	$1$	$1$	$1$	$16.737$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$0$	$0$	$0$	$5$	$+$	$1$	$\mathrm{SU}(2)$	$q+5q^{7}-3q^{9}-2q^{11}-2q^{13}-6q^{17}+\cdots$
2096.2.a.d	$2096$	$2$	2096.a	1.a	$1$	$1$	$1$	$16.737$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$0$	$1$	$-2$	$1$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-2q^{5}+q^{7}-2q^{9}-3q^{13}+\cdots$
2096.2.a.e	$2096$	$2$	2096.a	1.a	$1$	$1$	$1$	$16.737$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$0$	$2$	$-2$	$-1$	$+$	$1$	$\mathrm{SU}(2)$	$q+2q^{3}-2q^{5}-q^{7}+q^{9}-2q^{11}+\cdots$
2096.2.a.f	$2096$	$2$	2096.a	1.a	$1$	$1$	$1$	$16.737$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$0$	$2$	$-2$	$3$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{3}-2q^{5}+3q^{7}+q^{9}+6q^{11}+\cdots$
2096.2.a.g	$2096$	$2$	2096.a	1.a	$1$	$2$	$2$	$16.737$	$\Q(\sqrt{5}) $	$_{}$	None	None	✓	$1$	$1$	$0$	$-3$	$-1$	$1$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1-\beta )q^{3}-\beta q^{5}+\beta q^{7}+(-1+\cdots)q^{9}+\cdots$
2096.2.a.h	$2096$	$2$	2096.a	1.a	$1$	$2$	$2$	$16.737$	$\Q(\sqrt{5}) $	$_{}$	None	None	✓	$1$	$1$	$0$	$-1$	$1$	$3$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta q^{3}+(1-\beta )q^{5}+(1+\beta )q^{7}+(-2+\cdots)q^{9}+\cdots$
2096.2.a.i	$2096$	$2$	2096.a	1.a	$1$	$2$	$2$	$16.737$	$\Q(\sqrt{2}) $	$_{}$	None	None	✓	$1$	$0$	$0$	$0$	$4$	$-2$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{3}+(2+\beta )q^{5}+(-1+\beta )q^{7}-q^{9}+\cdots$
2096.2.a.j	$2096$	$2$	2096.a	1.a	$1$	$2$	$2$	$16.737$	$\Q(\sqrt{13}) $	$_{}$	None	None	✓	$1$	$1$	$0$	$1$	$-5$	$-3$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{3}+(-3+\beta )q^{5}+(-1-\beta )q^{7}+\cdots$
2096.2.a.k	$2096$	$2$	2096.a	1.a	$1$	$2$	$2$	$16.737$	$\Q(\sqrt{3}) $	$_{}$	None	None	✓	$1$	$1$	$0$	$2$	$2$	$-4$	$+$	$1$	$\mathrm{SU}(2)$	$q+(1+\beta )q^{3}+(1-\beta )q^{5}+(-2-\beta )q^{7}+\cdots$
2096.2.a.l	$2096$	$2$	2096.a	1.a	$1$	$2$	$2$	$16.737$	$\Q(\sqrt{5}) $	$_{}$	None	None	✓	$1$	$0$	$0$	$3$	$1$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1+\beta )q^{3}+\beta q^{5}+\beta q^{7}+(-1+3\beta )q^{9}+\cdots$
2096.2.a.m	$2096$	$2$	2096.a	1.a	$1$	$4$	$4$	$16.737$	4.4.3981.1	$_{}$	None	None	✓	$1$	$1$	$0$	$-3$	$2$	$-7$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1-\beta _{3})q^{3}+(\beta _{1}+\beta _{2}-\beta _{3})q^{5}+\cdots$
2096.2.a.n	$2096$	$2$	2096.a	1.a	$1$	$4$	$4$	$16.737$	4.4.123336.1	$_{}$	None	None	✓	$1$	$1$	$0$	$-1$	$-3$	$1$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{3}+(-1+\beta _{1})q^{5}+\beta _{3}q^{7}+(3+\cdots)q^{9}+\cdots$
2096.2.a.o	$2096$	$2$	2096.a	1.a	$1$	$5$	$5$	$16.737$	5.5.592456.1	$_{}$	None	None	✓	$1$	$1$	$0$	$-2$	$3$	$-4$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{3}+(1-\beta _{3})q^{5}+(-1-\beta _{4})q^{7}+\cdots$
2096.2.a.p	$2096$	$2$	2096.a	1.a	$1$	$5$	$5$	$16.737$	5.5.703228.1	$_{}$	None	None	✓	$1$	$0$	$0$	$-1$	$1$	$3$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta _{3}q^{3}+(\beta _{2}+\beta _{4})q^{5}+(1-\beta _{2})q^{7}+\cdots$
2096.2.a.q	$2096$	$2$	2096.a	1.a	$1$	$8$	$8$	$16.737$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	$_{}$	None	None	✓	$1$	$0$	$0$	$0$	$5$	$-6$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{5}q^{3}+(1-\beta _{4})q^{5}+(-1+\beta _{1}+\beta _{2}+\cdots)q^{7}+\cdots$
2096.2.a.r	$2096$	$2$	2096.a	1.a	$1$	$10$	$10$	$16.737$	$\mathbb{Q}[x]/(x^{10} - \cdots)$	$_{}$	None	None	✓	$1$	$0$	$0$	$-1$	$4$	$-1$	$-$	$2^{2}$	$\mathrm{SU}(2)$	$q-\beta _{2}q^{3}+\beta _{3}q^{5}+(\beta _{1}+\beta _{3}-\beta _{5}-\beta _{6}+\cdots)q^{7}+\cdots$
2096.2.a.s	$2096$	$2$	2096.a	1.a	$1$	$11$	$11$	$16.737$	$\mathbb{Q}[x]/(x^{11} - \cdots)$	$_{}$	None	None	✓	$1$	$0$	$0$	$5$	$-6$	$10$	$-$	$2^{2}$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{3}+(-1+\beta _{9})q^{5}+(1-\beta _{1}+\beta _{4}+\cdots)q^{7}+\cdots$
2096.2.d.a	$2096$	$2$	2096.d	524.b	$2$	$4$	$4$	$16.737$	$\Q(\sqrt{2}, \sqrt{-3})$	$_{}$	None	None		$4$	$0$	$0$	$0$	$-8$	$0$		$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{2}q^{3}-2q^{5}-\beta _{2}q^{7}+2\beta _{2}q^{11}+\cdots$
2096.2.d.b	$2096$	$2$	2096.d	524.b	$2$	$4$	$4$	$16.737$	$\Q(\sqrt{-3}, \sqrt{23})$	$_{}$	None	None		$4$	$0$	$0$	$0$	$-8$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q-2q^{5}+\beta _{2}q^{7}+3q^{9}-2\beta _{2}q^{11}+\cdots$
2096.2.d.c	$2096$	$2$	2096.d	524.b	$2$	$8$	$8$	$16.737$	8.0.$\cdots$.21	$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$0$		$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{3}-\beta _{3}q^{7}+(-1+\beta _{2})q^{9}+(-2\beta _{1}+\cdots)q^{11}+\cdots$
2096.2.d.d	$2096$	$2$	2096.d	524.b	$2$	$8$	$8$	$16.737$	8.0.$\cdots$.1	$_{}$	None	None		$4$	$0$	$0$	$0$	$4$	$0$		$2^{2}\cdot 3^{4}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{4}q^{3}+(1+\beta _{2})q^{5}+(\beta _{1}-\beta _{4})q^{7}+\cdots$
2096.2.d.e	$2096$	$2$	2096.d	524.b	$2$	$10$	$10$	$16.737$	10.0.$\cdots$.1	$_{}$	$\Q(\sqrt{-131}) $	None		$4$	$0$	$0$	$0$	$0$	$0$		$2^{5}$	$\mathrm{U}(1)[D_{2}]$	$q+\beta _{1}q^{3}+\beta _{4}q^{5}+\beta _{5}q^{7}+(-3-\beta _{3}+\cdots)q^{9}+\cdots$
2096.2.d.f	$2096$	$2$	2096.d	524.b	$2$	$12$	$12$	$16.737$	$\mathbb{Q}[x]/(x^{12} + \cdots)$	$_{}$	None	None		$4$	$0$	$0$	$0$	$12$	$0$		$2^{10}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{3}+(1+\beta _{9})q^{5}+(\beta _{1}+\beta _{3})q^{7}+\cdots$
2096.2.d.g	$2096$	$2$	2096.d	524.b	$2$	$20$	$20$	$16.737$	$\mathbb{Q}[x]/(x^{20} - \cdots)$	$_{}$	$\Q(\sqrt{-131}) $	None		$4$	$0$	$0$	$0$	$0$	$0$		$2^{18}$	$\mathrm{U}(1)[D_{2}]$	$q-\beta _{9}q^{3}-\beta _{7}q^{5}-\beta _{8}q^{7}+(-3+\beta _{11}+\cdots)q^{9}+\cdots$
2096.4.a.a	$2096$	$4$	2096.a	1.a	$1$	$6$	$6$	$123.668$	$\mathbb{Q}[x]/(x^{6} - \cdots)$	$_{}$	None	None	✓	$1$	$0$	$0$	$9$	$-26$	$56$	$+$	$2^{2}$	$\mathrm{SU}(2)$	$q+(1+\beta _{2})q^{3}+(-5+2\beta _{2}-\beta _{5})q^{5}+\cdots$
2096.4.a.b	$2096$	$4$	2096.a	1.a	$1$	$8$	$8$	$123.668$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	$_{}$	None	None	✓	$1$	$0$	$0$	$-1$	$18$	$-19$	$+$	$2^{2}$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{3}+(2+\beta _{3}-\beta _{5})q^{5}+(-2+\beta _{1}+\cdots)q^{7}+\cdots$
2096.4.a.c	$2096$	$4$	2096.a	1.a	$1$	$9$	$9$	$123.668$	$\mathbb{Q}[x]/(x^{9} - \cdots)$	$_{}$	None	None	✓	$1$	$1$	$0$	$2$	$-27$	$9$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{3}+(-3+\beta _{5})q^{5}+(1-\beta _{1}+\beta _{3}+\cdots)q^{7}+\cdots$
2096.4.a.d	$2096$	$4$	2096.a	1.a	$1$	$10$	$10$	$123.668$	$\mathbb{Q}[x]/(x^{10} - \cdots)$	$_{}$	None	None	✓	$1$	$1$	$0$	$-12$	$19$	$-42$	$-$	$3\cdot 5$	$\mathrm{SU}(2)$	$q+(-1-\beta _{1})q^{3}+(2+\beta _{2})q^{5}+(-4+\cdots)q^{7}+\cdots$
2096.4.a.e	$2096$	$4$	2096.a	1.a	$1$	$11$	$11$	$123.668$	$\mathbb{Q}[x]/(x^{11} - \cdots)$	$_{}$	None	None	✓	$1$	$1$	$0$	$11$	$-27$	$32$	$-$	$2^{8}$	$\mathrm{SU}(2)$	$q+(1+\beta _{2})q^{3}+(-2+\beta _{1}+\beta _{2}+\beta _{8}+\cdots)q^{5}+\cdots$
2096.4.a.f	$2096$	$4$	2096.a	1.a	$1$	$14$	$14$	$123.668$	$\mathbb{Q}[x]/(x^{14} - \cdots)$	$_{}$	None	None	✓	$1$	$0$	$0$	$8$	$4$	$43$	$+$	$2^{4}$	$\mathrm{SU}(2)$	$q+(1-\beta _{1})q^{3}-\beta _{6}q^{5}+(3-\beta _{3})q^{7}+\cdots$
2096.4.a.g	$2096$	$4$	2096.a	1.a	$1$	$19$	$19$	$123.668$	$\mathbb{Q}[x]/(x^{19} - \cdots)$	$_{}$	None	None	✓	$1$	$1$	$0$	$-10$	$4$	$-27$	$-$	$2^{10}\cdot 3$	$\mathrm{SU}(2)$	$q+(-1+\beta _{1})q^{3}-\beta _{9}q^{5}+(-1+\beta _{7}+\cdots)q^{7}+\cdots$
2096.4.a.h	$2096$	$4$	2096.a	1.a	$1$	$20$	$20$	$123.668$	$\mathbb{Q}[x]/(x^{20} - \cdots)$	$_{}$	None	None	✓	$1$	$1$	$0$	$1$	$-22$	$17$	$-$	$2^{13}$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{3}+(-1+\beta _{3})q^{5}+(1-\beta _{6})q^{7}+\cdots$
2096.4.a.i	$2096$	$4$	2096.a	1.a	$1$	$21$	$21$	$123.668$		$_{}$	None	None	✓	$1$	$1$	$0$	$-13$	$24$	$-34$	$-$		$\mathrm{SU}(2)$
2096.4.a.j	$2096$	$4$	2096.a	1.a	$1$	$21$	$21$	$123.668$		$_{}$	None	None	✓	$1$	$0$	$0$	$-7$	$33$	$-38$	$+$		$\mathrm{SU}(2)$
2096.4.a.k	$2096$	$4$	2096.a	1.a	$1$	$27$	$27$	$123.668$		$_{}$	None	None	✓	$1$	$0$	$0$	$8$	$-21$	$64$	$+$		$\mathrm{SU}(2)$
2096.4.a.l	$2096$	$4$	2096.a	1.a	$1$	$29$	$29$	$123.668$		$_{}$	None	None	✓	$1$	$0$	$0$	$-2$	$23$	$-11$	$+$		$\mathrm{SU}(2)$

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Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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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.