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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 (45 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
1573.1.f.a	$1573$	$1$	1573.f	13.d	$4$	$2$	$1$	$0.785$	$\Q(\sqrt{-1}) $	$S_{4}$	None	None		$2$	$0$	$-2$	$2$	$0$	$0$		$1$		$q+(-1-i)q^{2}+q^{3}+iq^{4}+(-1-i+\cdots)q^{6}+\cdots$
1573.1.f.b	$1573$	$1$	1573.f	13.d	$4$	$2$	$1$	$0.785$	$\Q(\sqrt{-1}) $	$S_{4}$	None	None		$2$	$0$	$2$	$2$	$0$	$0$		$1$		$q+(1+i)q^{2}+q^{3}+iq^{4}+(1+i)q^{6}+\cdots$
1573.1.l.a	$1573$	$1$	1573.l	143.l	$10$	$4$	$1$	$0.785$	$\Q(\zeta_{10})$	$D_{5}$	$\Q(\sqrt{-143}) $	None		$4$	$0$	$-3$	$-2$	$0$	$-3$		$1$		$q+(-1+\zeta_{10}^{3})q^{2}+(-\zeta_{10}-\zeta_{10}^{3}+\cdots)q^{3}+\cdots$
1573.1.l.b	$1573$	$1$	1573.l	143.l	$10$	$4$	$1$	$0.785$	$\Q(\zeta_{10})$	$D_{5}$	$\Q(\sqrt{-143}) $	None		$4$	$0$	$-2$	$3$	$0$	$-2$		$1$		$q+(-\zeta_{10}+\zeta_{10}^{2})q^{2}+(1+\zeta_{10}^{4})q^{3}+\cdots$
1573.1.l.c	$1573$	$1$	1573.l	143.l	$10$	$4$	$1$	$0.785$	$\Q(\zeta_{10})$	$D_{5}$	$\Q(\sqrt{-143}) $	None		$4$	$0$	$2$	$3$	$0$	$2$		$1$		$q+(\zeta_{10}-\zeta_{10}^{2})q^{2}+(1+\zeta_{10}^{4})q^{3}+\cdots$
1573.1.l.d	$1573$	$1$	1573.l	143.l	$10$	$4$	$1$	$0.785$	$\Q(\zeta_{10})$	$D_{5}$	$\Q(\sqrt{-143}) $	None		$4$	$0$	$3$	$-2$	$0$	$3$		$1$		$q+(1-\zeta_{10}^{3})q^{2}+(-\zeta_{10}-\zeta_{10}^{3})q^{3}+\cdots$
1573.1.s.a	$1573$	$1$	1573.s	143.r	$20$	$8$	$1$	$0.785$	$\Q(\zeta_{20})$	$S_{4}$	None	None		$8$	$0$	$-2$	$-2$	$0$	$0$		$1$		$q+(-\zeta_{20}^{2}-\zeta_{20}^{7})q^{2}-\zeta_{20}^{6}q^{3}+\cdots$
1573.1.s.b	$1573$	$1$	1573.s	143.r	$20$	$8$	$1$	$0.785$	$\Q(\zeta_{20})$	$S_{4}$	None	None		$8$	$0$	$2$	$-2$	$0$	$0$		$1$		$q+(\zeta_{20}^{2}+\zeta_{20}^{7})q^{2}-\zeta_{20}^{6}q^{3}+\zeta_{20}^{9}q^{4}+\cdots$
1573.2.a.a	$1573$	$2$	1573.a	1.a	$1$	$1$	$1$	$12.560$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$-1$	$-1$	$-2$	$2$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}-q^{4}-2q^{5}+q^{6}+2q^{7}+\cdots$
1573.2.a.b	$1573$	$2$	1573.a	1.a	$1$	$1$	$1$	$12.560$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$0$	$-1$	$-1$	$2$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-2q^{4}-q^{5}+2q^{7}-2q^{9}+2q^{12}+\cdots$
1573.2.a.c	$1573$	$2$	1573.a	1.a	$1$	$1$	$1$	$12.560$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$1$	$-1$	$-2$	$-2$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}-q^{4}-2q^{5}-q^{6}-2q^{7}+\cdots$
1573.2.a.d	$1573$	$2$	1573.a	1.a	$1$	$2$	$2$	$12.560$	$\Q(\sqrt{5}) $	$_{}$	None	None	✓	$1$	$1$	$0$	$-2$	$-2$	$1$	$+$	$1$	$\mathrm{SU}(2)$	$q+(1-2\beta )q^{2}+(-2+2\beta )q^{3}+3q^{4}+\cdots$
1573.2.a.e	$1573$	$2$	1573.a	1.a	$1$	$2$	$2$	$12.560$	$\Q(\sqrt{5}) $	$_{}$	None	None	✓	$1$	$1$	$0$	$-2$	$-2$	$-1$	$+$	$1$	$\mathrm{SU}(2)$	$q+(1-2\beta )q^{2}-2\beta q^{3}+3q^{4}+(-2+\cdots)q^{5}+\cdots$
1573.2.a.f	$1573$	$2$	1573.a	1.a	$1$	$4$	$4$	$12.560$	4.4.1957.1	$_{}$	None	None	✓	$1$	$1$	$-3$	$0$	$0$	$-6$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1-\beta _{1}-\beta _{2})q^{2}+(-\beta _{2}-\beta _{3})q^{3}+\cdots$
1573.2.a.g	$1573$	$2$	1573.a	1.a	$1$	$4$	$4$	$12.560$	4.4.11344.1	$_{}$	None	None	✓	$1$	$1$	$-2$	$0$	$-2$	$-6$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta _{2}q^{2}+(-1+\beta _{1}-\beta _{2})q^{3}+(1+\beta _{1}+\cdots)q^{4}+\cdots$
1573.2.a.h	$1573$	$2$	1573.a	1.a	$1$	$4$	$4$	$12.560$	4.4.11344.1	$_{}$	None	None	✓	$1$	$0$	$2$	$0$	$-2$	$6$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta _{2}q^{2}+(-1+\beta _{1}-\beta _{2})q^{3}+(1+\beta _{1}+\cdots)q^{4}+\cdots$
1573.2.a.i	$1573$	$2$	1573.a	1.a	$1$	$5$	$5$	$12.560$	5.5.535120.1	$_{}$	None	None	✓	$1$	$1$	$-3$	$-1$	$-2$	$-4$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta _{1})q^{2}-\beta _{2}q^{3}+(2-\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots$
1573.2.a.j	$1573$	$2$	1573.a	1.a	$1$	$5$	$5$	$12.560$	5.5.558733.1	$_{}$	None	None	✓	$1$	$1$	$-3$	$-1$	$1$	$-4$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta _{2})q^{2}+(-\beta _{1}+\beta _{3})q^{3}+(2+\cdots)q^{4}+\cdots$
1573.2.a.k	$1573$	$2$	1573.a	1.a	$1$	$5$	$5$	$12.560$	5.5.535120.1	$_{}$	None	None	✓	$1$	$0$	$3$	$-1$	$-2$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1-\beta _{1})q^{2}-\beta _{2}q^{3}+(2-\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots$
1573.2.a.l	$1573$	$2$	1573.a	1.a	$1$	$5$	$5$	$12.560$	5.5.558733.1	$_{}$	None	None	✓	$1$	$0$	$3$	$-1$	$1$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1-\beta _{2})q^{2}+(-\beta _{1}+\beta _{3})q^{3}+(2+\beta _{1}+\cdots)q^{4}+\cdots$
1573.2.a.m	$1573$	$2$	1573.a	1.a	$1$	$6$	$6$	$12.560$	6.6.194616205.1	$_{}$	None	None	✓	$1$	$0$	$0$	$3$	$1$	$-4$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+(1+\beta _{3})q^{3}+(1+\beta _{2})q^{4}+\cdots$
1573.2.a.n	$1573$	$2$	1573.a	1.a	$1$	$8$	$8$	$12.560$	8.8.661518125.1	$_{}$	None	None	✓	$1$	$1$	$-1$	$-5$	$-5$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{3}q^{2}+(-1+\beta _{7})q^{3}+(1-\beta _{1}-\beta _{4}+\cdots)q^{4}+\cdots$
1573.2.a.o	$1573$	$2$	1573.a	1.a	$1$	$8$	$8$	$12.560$	8.8.661518125.1	$_{}$	None	None	✓	$1$	$1$	$1$	$-5$	$-5$	$2$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta _{3}q^{2}+(-1+\beta _{7})q^{3}+(1-\beta _{1}-\beta _{4}+\cdots)q^{4}+\cdots$
1573.2.a.p	$1573$	$2$	1573.a	1.a	$1$	$10$	$10$	$12.560$	$\mathbb{Q}[x]/(x^{10} - \cdots)$	$_{}$	None	None	✓	$1$	$1$	$-6$	$-2$	$2$	$-8$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta _{1})q^{2}-\beta _{3}q^{3}+(1-\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots$
1573.2.a.q	$1573$	$2$	1573.a	1.a	$1$	$10$	$10$	$12.560$	$\mathbb{Q}[x]/(x^{10} - \cdots)$	$_{}$	None	None	✓	$1$	$0$	$6$	$-2$	$2$	$8$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1-\beta _{1})q^{2}-\beta _{3}q^{3}+(1-\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots$
1573.2.a.r	$1573$	$2$	1573.a	1.a	$1$	$14$	$14$	$12.560$	$\mathbb{Q}[x]/(x^{14} - \cdots)$	$_{}$	None	None	✓	$1$	$0$	$-1$	$9$	$9$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+(1+\beta _{9})q^{3}+(1+\beta _{2})q^{4}+\cdots$
1573.2.a.s	$1573$	$2$	1573.a	1.a	$1$	$14$	$14$	$12.560$	$\mathbb{Q}[x]/(x^{14} - \cdots)$	$_{}$	None	None	✓	$1$	$0$	$1$	$9$	$9$	$-1$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+(1+\beta _{9})q^{3}+(1+\beta _{2})q^{4}+\cdots$
1573.4.a.a	$1573$	$4$	1573.a	1.a	$1$	$1$	$1$	$92.810$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$5$	$-7$	$-7$	$13$	$-$	$1$	$\mathrm{SU}(2)$	$q+5q^{2}-7q^{3}+17q^{4}-7q^{5}-35q^{6}+\cdots$
1573.4.a.b	$1573$	$4$	1573.a	1.a	$1$	$2$	$2$	$92.810$	$\Q(\sqrt{17}) $	$_{}$	None	None	✓	$1$	$0$	$-1$	$5$	$-3$	$9$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta q^{2}+(4-3\beta )q^{3}+(-4+\beta )q^{4}+\cdots$
1573.4.a.c	$1573$	$4$	1573.a	1.a	$1$	$4$	$4$	$92.810$	4.4.297133.1	$_{}$	None	None	✓	$1$	$1$	$0$	$-4$	$-6$	$17$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+(-1-\beta _{3})q^{3}+(2+\beta _{1}+2\beta _{2}+\cdots)q^{4}+\cdots$
1573.4.a.d	$1573$	$4$	1573.a	1.a	$1$	$6$	$6$	$92.810$	$\mathbb{Q}[x]/(x^{6} - \cdots)$	$_{}$	None	None	✓	$1$	$0$	$6$	$-6$	$-8$	$53$	$+$	$1$	$\mathrm{SU}(2)$	$q+(1-\beta _{1})q^{2}+(-1-\beta _{4})q^{3}+(4-\beta _{1}+\cdots)q^{4}+\cdots$
1573.4.a.e	$1573$	$4$	1573.a	1.a	$1$	$9$	$9$	$92.810$	$\mathbb{Q}[x]/(x^{9} - \cdots)$	$_{}$	None	None	✓	$1$	$0$	$0$	$8$	$30$	$-25$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+(1-\beta _{3})q^{3}+(5-\beta _{2}-\beta _{3}+\cdots)q^{4}+\cdots$
1573.4.a.f	$1573$	$4$	1573.a	1.a	$1$	$11$	$11$	$92.810$	$\mathbb{Q}[x]/(x^{11} - \cdots)$	$_{}$	None	None	✓	$1$	$1$	$-6$	$6$	$-4$	$-45$	$-$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta _{1})q^{2}+(1-\beta _{5})q^{3}+(6-\beta _{1}+\cdots)q^{4}+\cdots$
1573.4.a.g	$1573$	$4$	1573.a	1.a	$1$	$15$	$15$	$92.810$	$\mathbb{Q}[x]/(x^{15} - \cdots)$	$_{}$	None	None	✓	$1$	$1$	$-6$	$2$	$-14$	$-28$	$-$	$2^{3}$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+\beta _{4}q^{3}+(3+\beta _{2})q^{4}+(-1+\cdots)q^{5}+\cdots$
1573.4.a.h	$1573$	$4$	1573.a	1.a	$1$	$15$	$15$	$92.810$	$\mathbb{Q}[x]/(x^{15} - \cdots)$	$_{}$	None	None	✓	$1$	$1$	$-6$	$2$	$-2$	$-28$	$-$	$2^{5}$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+\beta _{5}q^{3}+(3+\beta _{1}+\beta _{2})q^{4}+\cdots$
1573.4.a.i	$1573$	$4$	1573.a	1.a	$1$	$15$	$15$	$92.810$	$\mathbb{Q}[x]/(x^{15} - \cdots)$	$_{}$	None	None	✓	$1$	$1$	$-6$	$2$	$14$	$-28$	$-$	$2^{10}$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+\beta _{5}q^{3}+(3+\beta _{1}+\beta _{2})q^{4}+\cdots$
1573.4.a.j	$1573$	$4$	1573.a	1.a	$1$	$15$	$15$	$92.810$	$\mathbb{Q}[x]/(x^{15} - \cdots)$	$_{}$	None	None	✓	$1$	$0$	$6$	$2$	$-14$	$28$	$+$	$2^{3}$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+\beta _{4}q^{3}+(3+\beta _{2})q^{4}+(-1+\cdots)q^{5}+\cdots$
1573.4.a.k	$1573$	$4$	1573.a	1.a	$1$	$15$	$15$	$92.810$	$\mathbb{Q}[x]/(x^{15} - \cdots)$	$_{}$	None	None	✓	$1$	$0$	$6$	$2$	$-2$	$28$	$+$	$2^{5}$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+\beta _{5}q^{3}+(3+\beta _{1}+\beta _{2})q^{4}+\cdots$
1573.4.a.l	$1573$	$4$	1573.a	1.a	$1$	$15$	$15$	$92.810$	$\mathbb{Q}[x]/(x^{15} - \cdots)$	$_{}$	None	None	✓	$1$	$0$	$6$	$2$	$14$	$28$	$+$	$2^{10}$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+\beta _{5}q^{3}+(3+\beta _{1}+\beta _{2})q^{4}+\cdots$
1573.4.a.m	$1573$	$4$	1573.a	1.a	$1$	$30$	$30$	$92.810$		$_{}$	None	None	✓	$1$	$1$	$-12$	$4$	$-28$	$-56$	$-$		$\mathrm{SU}(2)$
1573.4.a.n	$1573$	$4$	1573.a	1.a	$1$	$30$	$30$	$92.810$		$_{}$	None	None	✓	$1$	$0$	$12$	$4$	$-28$	$56$	$+$		$\mathrm{SU}(2)$
1573.4.a.o	$1573$	$4$	1573.a	1.a	$1$	$34$	$34$	$92.810$		$_{}$	None	None	✓	$1$	$1$	$-3$	$-29$	$-28$	$-36$	$-$		$\mathrm{SU}(2)$
1573.4.a.p	$1573$	$4$	1573.a	1.a	$1$	$34$	$34$	$92.810$		$_{}$	None	None	✓	$1$	$1$	$3$	$-29$	$-28$	$36$	$-$		$\mathrm{SU}(2)$
1573.4.a.q	$1573$	$4$	1573.a	1.a	$1$	$38$	$38$	$92.810$		$_{}$	None	None	✓	$1$	$0$	$-3$	$19$	$52$	$-12$	$+$		$\mathrm{SU}(2)$
1573.4.a.r	$1573$	$4$	1573.a	1.a	$1$	$38$	$38$	$92.810$		$_{}$	None	None	✓	$1$	$0$	$3$	$19$	$52$	$12$	$+$		$\mathrm{SU}(2)$

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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.