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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 (41 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
2075.1.c.a	$2075$	$1$	2075.c	83.b	$2$	$1$	$1$	$1.036$	$\Q$	$D_{3}$	$\Q(\sqrt{-83}) $	None	✓	$2$	$0$	$0$	$-2$	$0$	$1$		$1$		$q-2q^{3}+q^{4}+q^{7}+3q^{9}-q^{11}-2q^{12}+\cdots$
2075.1.c.b	$2075$	$1$	2075.c	83.b	$2$	$1$	$1$	$1.036$	$\Q$	$D_{3}$	$\Q(\sqrt{-83}) $	None	✓	$2$	$0$	$0$	$-1$	$0$	$-1$		$1$		$q-q^{3}+q^{4}-q^{7}-q^{11}-q^{12}+q^{16}+\cdots$
2075.1.c.c	$2075$	$1$	2075.c	83.b	$2$	$1$	$1$	$1.036$	$\Q$	$D_{3}$	$\Q(\sqrt{-83}) $	None	✓	$2$	$0$	$0$	$-1$	$0$	$2$		$1$		$q-q^{3}+q^{4}+2q^{7}+2q^{11}-q^{12}+\cdots$
2075.1.c.d	$2075$	$1$	2075.c	83.b	$2$	$1$	$1$	$1.036$	$\Q$	$D_{3}$	$\Q(\sqrt{-83}) $	None	✓	$2$	$0$	$0$	$1$	$0$	$-2$		$1$		$q+q^{3}+q^{4}-2q^{7}+2q^{11}+q^{12}+\cdots$
2075.1.c.e	$2075$	$1$	2075.c	83.b	$2$	$1$	$1$	$1.036$	$\Q$	$D_{3}$	$\Q(\sqrt{-83}) $	None	✓	$2$	$0$	$0$	$1$	$0$	$1$		$1$		$q+q^{3}+q^{4}+q^{7}-q^{11}+q^{12}+q^{16}+\cdots$
2075.1.c.f	$2075$	$1$	2075.c	83.b	$2$	$1$	$1$	$1.036$	$\Q$	$D_{3}$	$\Q(\sqrt{-83}) $	None	✓	$2$	$0$	$0$	$1$	$0$	$1$		$1$		$q+q^{3}+q^{4}+q^{7}-q^{11}+q^{12}+q^{16}+\cdots$
2075.1.c.g	$2075$	$1$	2075.c	83.b	$2$	$1$	$1$	$1.036$	$\Q$	$D_{3}$	$\Q(\sqrt{-83}) $	None	✓	$2$	$0$	$0$	$2$	$0$	$-1$		$1$		$q+2q^{3}+q^{4}-q^{7}+3q^{9}-q^{11}+2q^{12}+\cdots$
2075.1.c.h	$2075$	$1$	2075.c	83.b	$2$	$4$	$4$	$1.036$	$\Q(i, \sqrt{5})$	$D_{5}$	$\Q(\sqrt{-415}) $	None		$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\beta _{1}q^{2}+\beta _{2}q^{4}-\beta _{3}q^{8}-q^{9}+\beta _{2}q^{11}+\cdots$
2075.1.d.a	$2075$	$1$	2075.d	415.d	$2$	$2$	$2$	$1.036$	$\Q(\sqrt{-1}) $	$D_{3}$	$\Q(\sqrt{-83}) $	None		$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q-iq^{3}-q^{4}-iq^{7}-3q^{9}-q^{11}+\cdots$
2075.1.d.b	$2075$	$1$	2075.d	415.d	$2$	$2$	$2$	$1.036$	$\Q(\sqrt{-1}) $	$D_{3}$	$\Q(\sqrt{-83}) $	None		$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q-iq^{3}-q^{4}+iq^{7}-q^{11}+iq^{12}+\cdots$
2075.1.d.c	$2075$	$1$	2075.d	415.d	$2$	$2$	$2$	$1.036$	$\Q(\sqrt{-1}) $	$D_{3}$	$\Q(\sqrt{-83}) $	None		$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q+iq^{3}-q^{4}-iq^{7}-q^{11}-iq^{12}+\cdots$
2075.1.d.d	$2075$	$1$	2075.d	415.d	$2$	$2$	$2$	$1.036$	$\Q(\sqrt{-1}) $	$D_{3}$	$\Q(\sqrt{-83}) $	None		$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q-iq^{3}-q^{4}-iq^{7}+q^{11}+iq^{12}+\cdots$
2075.2.a.a	$2075$	$2$	2075.a	1.a	$1$	$1$	$1$	$16.569$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$-1$	$-3$	$0$	$-1$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-3q^{3}-q^{4}+3q^{6}-q^{7}+3q^{8}+\cdots$
2075.2.a.b	$2075$	$2$	2075.a	1.a	$1$	$1$	$1$	$16.569$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$-1$	$0$	$0$	$-1$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{4}-q^{7}+3q^{8}-3q^{9}+3q^{11}+\cdots$
2075.2.a.c	$2075$	$2$	2075.a	1.a	$1$	$1$	$1$	$16.569$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$1$	$0$	$0$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{4}+q^{7}-3q^{8}-3q^{9}+3q^{11}+\cdots$
2075.2.a.d	$2075$	$2$	2075.a	1.a	$1$	$1$	$1$	$16.569$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$1$	$1$	$0$	$3$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}-q^{4}+q^{6}+3q^{7}-3q^{8}+\cdots$
2075.2.a.e	$2075$	$2$	2075.a	1.a	$1$	$2$	$2$	$16.569$	$\Q(\sqrt{5}) $	$_{}$	None	None	✓	$1$	$1$	$1$	$1$	$0$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{2}+(1-\beta )q^{3}+(-1+\beta )q^{4}-q^{6}+\cdots$
2075.2.a.f	$2075$	$2$	2075.a	1.a	$1$	$6$	$6$	$16.569$	6.6.7783241.1	$_{}$	None	None	✓	$1$	$1$	$-2$	$-3$	$0$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+(-\beta _{2}+\beta _{4})q^{3}+\beta _{2}q^{4}+\cdots$
2075.2.a.g	$2075$	$2$	2075.a	1.a	$1$	$6$	$6$	$16.569$	6.6.9059636.1	$_{}$	None	None	✓	$1$	$1$	$-1$	$-1$	$0$	$-3$	$+$	$1$	$\mathrm{SU}(2)$	$q+(\beta _{1}+\beta _{2})q^{2}+\beta _{3}q^{3}+(1-\beta _{5})q^{4}+\cdots$
2075.2.a.h	$2075$	$2$	2075.a	1.a	$1$	$7$	$7$	$16.569$	7.7.179711353.1	$_{}$	None	None	✓	$1$	$0$	$3$	$5$	$0$	$6$	$-$	$2$	$\mathrm{SU}(2)$	$q+\beta _{6}q^{2}+(1-\beta _{1})q^{3}+(1-\beta _{5}+\beta _{6})q^{4}+\cdots$
2075.2.a.i	$2075$	$2$	2075.a	1.a	$1$	$8$	$8$	$16.569$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	$_{}$	None	None	✓	$1$	$1$	$-1$	$1$	$0$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}-\beta _{5}q^{3}+\beta _{2}q^{4}+(-\beta _{1}+\beta _{5}+\cdots)q^{6}+\cdots$
2075.2.a.j	$2075$	$2$	2075.a	1.a	$1$	$8$	$8$	$16.569$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	$_{}$	None	None	✓	$1$	$1$	$1$	$-1$	$0$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+\beta _{5}q^{3}+\beta _{2}q^{4}+(-\beta _{1}+\beta _{5}+\cdots)q^{6}+\cdots$
2075.2.a.k	$2075$	$2$	2075.a	1.a	$1$	$11$	$11$	$16.569$	$\mathbb{Q}[x]/(x^{11} - \cdots)$	$_{}$	None	None	✓	$1$	$0$	$0$	$0$	$0$	$3$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}-\beta _{7}q^{3}+(2+\beta _{2})q^{4}+(-1+\cdots)q^{6}+\cdots$
2075.2.a.l	$2075$	$2$	2075.a	1.a	$1$	$19$	$19$	$16.569$	$\mathbb{Q}[x]/(x^{19} - \cdots)$	$_{}$	None	None	✓	$1$	$0$	$0$	$-1$	$0$	$-1$	$-$	$2$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+\beta _{9}q^{3}+(2+\beta _{2})q^{4}+\beta _{7}q^{6}+\cdots$
2075.2.a.m	$2075$	$2$	2075.a	1.a	$1$	$19$	$19$	$16.569$	$\mathbb{Q}[x]/(x^{19} - \cdots)$	$_{}$	None	None	✓	$1$	$0$	$0$	$1$	$0$	$1$	$-$	$2$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}-\beta _{9}q^{3}+(2+\beta _{2})q^{4}+\beta _{7}q^{6}+\cdots$
2075.2.a.n	$2075$	$2$	2075.a	1.a	$1$	$20$	$20$	$16.569$	$\mathbb{Q}[x]/(x^{20} - \cdots)$	$_{}$	None	None	✓	$1$	$1$	$-5$	$-6$	$0$	$-14$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+\beta _{15}q^{3}+(1+\beta _{2})q^{4}+(-1+\cdots)q^{6}+\cdots$
2075.2.a.o	$2075$	$2$	2075.a	1.a	$1$	$20$	$20$	$16.569$	$\mathbb{Q}[x]/(x^{20} - \cdots)$	$_{}$	None	None	✓	$1$	$0$	$5$	$6$	$0$	$14$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}-\beta _{15}q^{3}+(1+\beta _{2})q^{4}+(-1+\cdots)q^{6}+\cdots$
2075.4.a.a	$2075$	$4$	2075.a	1.a	$1$	$1$	$1$	$122.429$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$-4$	$-7$	$0$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q-4q^{2}-7q^{3}+8q^{4}+28q^{6}+22q^{9}+\cdots$
2075.4.a.b	$2075$	$4$	2075.a	1.a	$1$	$1$	$1$	$122.429$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$4$	$7$	$0$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+4q^{2}+7q^{3}+8q^{4}+28q^{6}+22q^{9}+\cdots$
2075.4.a.c	$2075$	$4$	2075.a	1.a	$1$	$7$	$7$	$122.429$	$\mathbb{Q}[x]/(x^{7} - \cdots)$	$_{}$	None	None	✓	$1$	$0$	$5$	$11$	$0$	$46$	$+$	$2$	$\mathrm{SU}(2)$	$q+(1+\beta _{4})q^{2}+(1-\beta _{1}-\beta _{4})q^{3}+(2+\cdots)q^{4}+\cdots$
2075.4.a.d	$2075$	$4$	2075.a	1.a	$1$	$13$	$13$	$122.429$	$\mathbb{Q}[x]/(x^{13} - \cdots)$	$_{}$	None	None	✓	$1$	$1$	$-5$	$-7$	$0$	$-52$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+(-1-\beta _{8})q^{3}+(6+\beta _{2})q^{4}+\cdots$
2075.4.a.e	$2075$	$4$	2075.a	1.a	$1$	$15$	$15$	$122.429$	$\mathbb{Q}[x]/(x^{15} - \cdots)$	$_{}$	None	None	✓	$1$	$1$	$3$	$12$	$0$	$37$	$-$	$2^{3}$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+(1-\beta _{5})q^{3}+(2+\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots$
2075.4.a.f	$2075$	$4$	2075.a	1.a	$1$	$20$	$20$	$122.429$	$\mathbb{Q}[x]/(x^{20} - \cdots)$	$_{}$	None	None	✓	$1$	$1$	$-5$	$-12$	$0$	$-31$	$-$	$2^{3}$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+(-1-\beta _{5})q^{3}+(3+\beta _{2})q^{4}+\cdots$
2075.4.a.g	$2075$	$4$	2075.a	1.a	$1$	$21$	$21$	$122.429$		$_{}$	None	None	✓	$1$	$0$	$5$	$12$	$0$	$11$	$+$		$\mathrm{SU}(2)$
2075.4.a.h	$2075$	$4$	2075.a	1.a	$1$	$26$	$26$	$122.429$		$_{}$	None	None	✓	$1$	$0$	$-7$	$-12$	$0$	$-5$	$+$		$\mathrm{SU}(2)$
2075.4.a.i	$2075$	$4$	2075.a	1.a	$1$	$34$	$34$	$122.429$		$_{}$	None	None	✓	$1$	$1$	$-3$	$-13$	$0$	$-6$	$-$		$\mathrm{SU}(2)$
2075.4.a.j	$2075$	$4$	2075.a	1.a	$1$	$34$	$34$	$122.429$		$_{}$	None	None	✓	$1$	$1$	$3$	$13$	$0$	$6$	$-$		$\mathrm{SU}(2)$
2075.4.a.k	$2075$	$4$	2075.a	1.a	$1$	$47$	$47$	$122.429$		$_{}$	None	None	✓	$1$	$0$	$-1$	$6$	$0$	$6$	$+$		$\mathrm{SU}(2)$
2075.4.a.l	$2075$	$4$	2075.a	1.a	$1$	$47$	$47$	$122.429$		$_{}$	None	None	✓	$1$	$0$	$1$	$-6$	$0$	$-6$	$+$		$\mathrm{SU}(2)$
2075.4.a.m	$2075$	$4$	2075.a	1.a	$1$	$62$	$62$	$122.429$		$_{}$	None	None	✓	$1$	$1$	$-10$	$-18$	$0$	$-98$	$-$		$\mathrm{SU}(2)$
2075.4.a.n	$2075$	$4$	2075.a	1.a	$1$	$62$	$62$	$122.429$		$_{}$	None	None	✓	$1$	$0$	$10$	$18$	$0$	$98$	$+$		$\mathrm{SU}(2)$

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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.