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Level	Weight	Analytic conductor	Analytic rank	Dim.

Bad $p$	Char.	Primitive character	Character order	Coefficient field

Self-twists	CM/RM discriminant	Inner twist count	Is twist minimal	Is self-dual

$Nk^2$	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	Twist minimal	Minimal twist	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	Twist minimal	Minimal twist	Inner twists	Rank*	$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
1675.1.b.a	$1675$	$1$	1675.b	67.b	$2$	$1$	$1$	$0.836$	$\Q$	$D_{3}$	$\Q(\sqrt{-67}) $	None	✓	✓	1675.1.b.a	$2$	$0$	$0$	$0$	$0$	$0$		$1$		$q+q^{4}+q^{9}+q^{16}-q^{17}-q^{19}+2q^{23}+\cdots$
1675.1.b.b	$1675$	$1$	1675.b	67.b	$2$	$1$	$1$	$0.836$	$\Q$	$D_{3}$	$\Q(\sqrt{-67}) $	None	✓	✓	1675.1.b.a	$2$	$0$	$0$	$0$	$0$	$0$		$1$		$q+q^{4}+q^{9}+q^{16}+q^{17}-q^{19}-2q^{23}+\cdots$
1675.1.b.c	$1675$	$1$	1675.b	67.b	$2$	$2$	$2$	$0.836$	$\Q(\sqrt{-1}) $	$D_{3}$	$\Q(\sqrt{-335}) $	None			335.1.d.a	$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q-iq^{2}+iq^{3}+q^{6}-iq^{7}-iq^{8}+\cdots$
1675.1.b.d	$1675$	$1$	1675.b	67.b	$2$	$6$	$6$	$0.836$	6.0.419904.1	$D_{9}$	$\Q(\sqrt{-335}) $	None			335.1.d.c	$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\beta _{1}q^{2}+\beta _{5}q^{3}+(-1+\beta _{2})q^{4}+(-1+\cdots)q^{6}+\cdots$
1675.1.d.a	$1675$	$1$	1675.d	335.d	$2$	$2$	$2$	$0.836$	$\Q(\sqrt{-1}) $	$D_{3}$	$\Q(\sqrt{-67}) $	None		✓	1675.1.b.a	$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q-q^{4}-q^{9}+q^{16}-iq^{17}+q^{19}+\cdots$
1675.1.p.a	$1675$	$1$	1675.p	335.l	$12$	$8$	$2$	$0.836$	$\Q(\zeta_{24})$	$A_{4}$	None	None		✓	1675.1.p.a	$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{24}^{5}q^{2}+\zeta_{24}q^{7}-\zeta_{24}^{3}q^{8}-\zeta_{24}^{6}q^{9}+\cdots$
1675.2.a.a	$1675$	$2$	1675.a	1.a	$1$	$1$	$1$	$13.375$	$\Q$	$_{}$	None	None	✓		67.2.a.a	$1$	$1$	$-2$	$2$	$0$	$2$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{2}+2q^{3}+2q^{4}-4q^{6}+2q^{7}+\cdots$
1675.2.a.b	$1675$	$2$	1675.a	1.a	$1$	$1$	$1$	$13.375$	$\Q$	$_{}$	None	None	✓	✓	1675.2.a.b	$1$	$1$	$0$	$-2$	$0$	$2$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{3}-2q^{4}+2q^{7}+q^{9}+4q^{12}+\cdots$
1675.2.a.c	$1675$	$2$	1675.a	1.a	$1$	$1$	$1$	$13.375$	$\Q$	$_{}$	None	None	✓		335.2.a.a	$1$	$1$	$0$	$0$	$0$	$2$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{4}+2q^{7}-3q^{9}-2q^{11}+2q^{13}+\cdots$
1675.2.a.d	$1675$	$2$	1675.a	1.a	$1$	$1$	$1$	$13.375$	$\Q$	$_{}$	None	None	✓	✓	1675.2.a.b	$1$	$1$	$0$	$2$	$0$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q+2q^{3}-2q^{4}-2q^{7}+q^{9}-4q^{12}+\cdots$
1675.2.a.e	$1675$	$2$	1675.a	1.a	$1$	$2$	$2$	$13.375$	$\Q(\sqrt{5}) $	$_{}$	None	None	✓		335.2.a.c	$1$	$1$	$-1$	$0$	$0$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta q^{2}+(1-2\beta )q^{3}+(-1+\beta )q^{4}+\cdots$
1675.2.a.f	$1675$	$2$	1675.a	1.a	$1$	$2$	$2$	$13.375$	$\Q(\sqrt{2}) $	$_{}$	None	None	✓		335.2.a.b	$1$	$0$	$0$	$0$	$0$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{2}-\beta q^{3}-2q^{6}+2q^{7}-2\beta q^{8}+\cdots$
1675.2.a.g	$1675$	$2$	1675.a	1.a	$1$	$2$	$2$	$13.375$	$\Q(\sqrt{5}) $	$_{}$	None	None	✓		67.2.a.c	$1$	$1$	$1$	$-1$	$0$	$-1$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{2}+(-1+\beta )q^{3}+(-1+\beta )q^{4}+\cdots$
1675.2.a.h	$1675$	$2$	1675.a	1.a	$1$	$2$	$2$	$13.375$	$\Q(\sqrt{5}) $	$_{}$	None	None	✓		67.2.a.b	$1$	$0$	$3$	$3$	$0$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1+\beta )q^{2}+(2-\beta )q^{3}+3\beta q^{4}+q^{6}+\cdots$
1675.2.a.i	$1675$	$2$	1675.a	1.a	$1$	$7$	$7$	$13.375$	$\mathbb{Q}[x]/(x^{7} - \cdots)$	$_{}$	None	None	✓		335.2.a.d	$1$	$1$	$-2$	$-4$	$0$	$-10$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-\beta _{2}-\beta _{5})q^{2}+(-1+\beta _{4})q^{3}+(1+\cdots)q^{4}+\cdots$
1675.2.a.j	$1675$	$2$	1675.a	1.a	$1$	$8$	$8$	$13.375$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	$_{}$	None	None	✓	✓	1675.2.a.j	$1$	$1$	$0$	$-2$	$0$	$2$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+\beta _{4}q^{3}+(1+\beta _{2})q^{4}+(-1+\cdots)q^{6}+\cdots$
1675.2.a.k	$1675$	$2$	1675.a	1.a	$1$	$8$	$8$	$13.375$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	$_{}$	None	None	✓	✓	1675.2.a.j	$1$	$1$	$0$	$2$	$0$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}-\beta _{4}q^{3}+(1+\beta _{2})q^{4}+(-1+\cdots)q^{6}+\cdots$
1675.2.a.l	$1675$	$2$	1675.a	1.a	$1$	$11$	$11$	$13.375$	$\mathbb{Q}[x]/(x^{11} - \cdots)$	$_{}$	None	None	✓		335.2.a.e	$1$	$0$	$0$	$0$	$0$	$-4$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}-\beta _{3}q^{3}+(1+\beta _{2})q^{4}+(\beta _{2}+\cdots)q^{6}+\cdots$
1675.2.a.m	$1675$	$2$	1675.a	1.a	$1$	$13$	$13$	$13.375$	$\mathbb{Q}[x]/(x^{13} - \cdots)$	$_{}$	None	None	✓	✓	1675.2.a.m	$1$	$0$	$0$	$0$	$0$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}-\beta _{5}q^{3}+(1+\beta _{2})q^{4}+(1+\beta _{6}+\cdots)q^{6}+\cdots$
1675.2.a.n	$1675$	$2$	1675.a	1.a	$1$	$13$	$13$	$13.375$	$\mathbb{Q}[x]/(x^{13} - \cdots)$	$_{}$	None	None	✓	✓	1675.2.a.m	$1$	$0$	$0$	$0$	$0$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+\beta _{5}q^{3}+(1+\beta _{2})q^{4}+(1+\beta _{6}+\cdots)q^{6}+\cdots$
1675.2.a.o	$1675$	$2$	1675.a	1.a	$1$	$16$	$16$	$13.375$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	$_{}$	None	None	✓		335.2.c.a	$1$	$1$	$-7$	$-6$	$0$	$-8$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}-\beta _{12}q^{3}+(1+\beta _{1}+\beta _{2})q^{4}+\cdots$
1675.2.a.p	$1675$	$2$	1675.a	1.a	$1$	$16$	$16$	$13.375$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	$_{}$	None	None	✓		335.2.c.a	$1$	$0$	$7$	$6$	$0$	$8$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+\beta _{12}q^{3}+(1+\beta _{1}+\beta _{2})q^{4}+\cdots$
1675.2.c.a	$1675$	$2$	1675.c	5.b	$2$	$2$	$2$	$13.375$	$\Q(\sqrt{-1}) $	$_{}$	None	None			67.2.a.a	$2$	$1$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+2iq^{2}+2iq^{3}-2q^{4}-4q^{6}-2iq^{7}+\cdots$
1675.2.c.b	$1675$	$2$	1675.c	5.b	$2$	$2$	$2$	$13.375$	$\Q(\sqrt{-1}) $	$_{}$	None	None		✓	1675.2.a.b	$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+2iq^{3}+2q^{4}+2iq^{7}-q^{9}+4iq^{12}+\cdots$
1675.2.c.c	$1675$	$2$	1675.c	5.b	$2$	$2$	$2$	$13.375$	$\Q(\sqrt{-1}) $	$_{}$	None	None			335.2.a.a	$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+2q^{4}-2iq^{7}+3q^{9}-2q^{11}+2iq^{13}+\cdots$
1675.2.c.d	$1675$	$2$	1675.c	5.b	$2$	$4$	$4$	$13.375$	$\Q(i, \sqrt{5})$	$_{}$	None	None			67.2.a.b	$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+(\beta _{1}-\beta _{3})q^{2}+(\beta _{1}+2\beta _{3})q^{3}+3\beta _{2}q^{4}+\cdots$
1675.2.c.e	$1675$	$2$	1675.c	5.b	$2$	$4$	$4$	$13.375$	$\Q(\zeta_{8})$	$_{}$	None	None			335.2.a.b	$2$	$0$	$0$	$0$	$0$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q+\zeta_{8}^{2}q^{2}+\zeta_{8}^{2}q^{3}-2q^{6}+2\zeta_{8}q^{7}+\cdots$
1675.2.c.f	$1675$	$2$	1675.c	5.b	$2$	$4$	$4$	$13.375$	$\Q(i, \sqrt{5})$	$_{}$	None	None			67.2.a.c	$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{2}+(-\beta _{1}-\beta _{3})q^{3}+(1+\beta _{2}+\cdots)q^{4}+\cdots$
1675.2.c.g	$1675$	$2$	1675.c	5.b	$2$	$4$	$4$	$13.375$	$\Q(i, \sqrt{5})$	$_{}$	None	None			335.2.a.c	$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{2}+(-2\beta _{1}-\beta _{3})q^{3}+(1+\beta _{2}+\cdots)q^{4}+\cdots$
1675.2.c.h	$1675$	$2$	1675.c	5.b	$2$	$14$	$14$	$13.375$	$\mathbb{Q}[x]/(x^{14} + \cdots)$	$_{}$	None	None			335.2.a.d	$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+(\beta _{10}-\beta _{13})q^{2}+(-\beta _{5}+\beta _{11})q^{3}+\cdots$
1675.2.c.i	$1675$	$2$	1675.c	5.b	$2$	$16$	$16$	$13.375$	$\mathbb{Q}[x]/(x^{16} + \cdots)$	$_{}$	None	None		✓	1675.2.a.j	$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{2}+\beta _{4}q^{3}+(-1+\beta _{2})q^{4}+(-1+\cdots)q^{6}+\cdots$
1675.2.c.j	$1675$	$2$	1675.c	5.b	$2$	$22$	$22$	$13.375$		$_{}$	None	None			335.2.a.e	$2$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
1675.2.c.k	$1675$	$2$	1675.c	5.b	$2$	$26$	$26$	$13.375$		$_{}$	None	None		✓	1675.2.a.m	$2$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
1675.4.a.a	$1675$	$4$	1675.a	1.a	$1$	$7$	$7$	$98.828$	$\mathbb{Q}[x]/(x^{7} - \cdots)$	$_{}$	None	None	✓		67.4.a.a	$1$	$0$	$6$	$9$	$0$	$32$	$+$	$1$	$\mathrm{SU}(2)$	$q+(1-\beta _{1})q^{2}+(1+\beta _{1}-\beta _{4})q^{3}+(3+\cdots)q^{4}+\cdots$
1675.4.a.b	$1675$	$4$	1675.a	1.a	$1$	$9$	$9$	$98.828$	$\mathbb{Q}[x]/(x^{9} - \cdots)$	$_{}$	None	None	✓		67.4.a.b	$1$	$1$	$-8$	$-9$	$0$	$-24$	$-$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta _{1})q^{2}+(-1-\beta _{7})q^{3}+(4+\cdots)q^{4}+\cdots$
1675.4.a.c	$1675$	$4$	1675.a	1.a	$1$	$11$	$11$	$98.828$	$\mathbb{Q}[x]/(x^{11} - \cdots)$	$_{}$	None	None	✓		335.4.a.a	$1$	$1$	$5$	$5$	$0$	$48$	$-$	$2^{3}$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}-\beta _{3}q^{3}+(1+\beta _{1}+\beta _{2})q^{4}+\cdots$
1675.4.a.d	$1675$	$4$	1675.a	1.a	$1$	$13$	$13$	$98.828$	$\mathbb{Q}[x]/(x^{13} - \cdots)$	$_{}$	None	None	✓		335.4.a.b	$1$	$0$	$1$	$7$	$0$	$50$	$+$	$2^{3}$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+(1+\beta _{6})q^{3}+(3+\beta _{2})q^{4}+\cdots$
1675.4.a.e	$1675$	$4$	1675.a	1.a	$1$	$20$	$20$	$98.828$	$\mathbb{Q}[x]/(x^{20} - \cdots)$	$_{}$	None	None	✓		335.4.a.c	$1$	$1$	$-5$	$-5$	$0$	$-48$	$-$	$2^{3}$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}-\beta _{5}q^{3}+(5+\beta _{2})q^{4}+(\beta _{5}+\cdots)q^{6}+\cdots$
1675.4.a.f	$1675$	$4$	1675.a	1.a	$1$	$22$	$22$	$98.828$		$_{}$	None	None	✓		335.4.a.d	$1$	$0$	$-1$	$-7$	$0$	$-50$	$+$		$\mathrm{SU}(2)$
1675.4.a.g	$1675$	$4$	1675.a	1.a	$1$	$31$	$31$	$98.828$		$_{}$	None	None	✓	✓	1675.4.a.g	$1$	$1$	$0$	$0$	$0$	$0$	$-$		$\mathrm{SU}(2)$
1675.4.a.h	$1675$	$4$	1675.a	1.a	$1$	$31$	$31$	$98.828$		$_{}$	None	None	✓	✓	1675.4.a.g	$1$	$1$	$0$	$0$	$0$	$0$	$-$		$\mathrm{SU}(2)$
1675.4.a.i	$1675$	$4$	1675.a	1.a	$1$	$35$	$35$	$98.828$		$_{}$	None	None	✓	✓	1675.4.a.i	$1$	$0$	$0$	$0$	$0$	$0$	$+$		$\mathrm{SU}(2)$
1675.4.a.j	$1675$	$4$	1675.a	1.a	$1$	$35$	$35$	$98.828$		$_{}$	None	None	✓	✓	1675.4.a.i	$1$	$0$	$0$	$0$	$0$	$0$	$+$		$\mathrm{SU}(2)$
1675.4.a.k	$1675$	$4$	1675.a	1.a	$1$	$50$	$50$	$98.828$		$_{}$	None	None	✓		335.4.c.a	$1$	$1$	$-14$	$-18$	$0$	$-56$	$-$		$\mathrm{SU}(2)$
1675.4.a.l	$1675$	$4$	1675.a	1.a	$1$	$50$	$50$	$98.828$		$_{}$	None	None	✓		335.4.c.a	$1$	$0$	$14$	$18$	$0$	$56$	$+$		$\mathrm{SU}(2)$

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Hilbert	Bianchi

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.