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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 (1-50 of 57 matches)

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Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Inner twists	Rank*	Traces				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*	$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$	Coefficient ring index	Sato-Tate	$q$-expansion
4020.3.c.a	$4020$	$3$	4020.c	67.b	$2$	$92$	$92$	$109.537$		None		$2$	$0$	$0$	$0$	$0$	$0$		$\mathrm{SU}(2)[C_{2}]$
4032.3.d.a	$4032$	$3$	4032.d	3.b	$2$	$4$	$4$	$109.864$	$\Q(\sqrt{-2}, \sqrt{7})$	None		$4$	$0$	$0$	$0$	$0$	$0$	$2$	$\mathrm{SU}(2)[C_{2}]$	$q+2\beta _{1}q^{5}-\beta _{3}q^{7}+3\beta _{2}q^{11}-14q^{13}+\cdots$
4032.3.d.b	$4032$	$3$	4032.d	3.b	$2$	$4$	$4$	$109.864$	$\Q(\sqrt{-2}, \sqrt{7})$	None		$2$	$0$	$0$	$0$	$0$	$0$	$2\cdot 3$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{5}+\beta _{3}q^{7}+(-2\beta _{1}+\beta _{2})q^{11}+\cdots$
4032.3.d.c	$4032$	$3$	4032.d	3.b	$2$	$4$	$4$	$109.864$	$\Q(\sqrt{-2}, \sqrt{7})$	None		$2$	$0$	$0$	$0$	$0$	$0$	$2\cdot 3$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{5}-\beta _{3}q^{7}+(2\beta _{1}-\beta _{2})q^{11}+\cdots$
4032.3.d.d	$4032$	$3$	4032.d	3.b	$2$	$4$	$4$	$109.864$	$\Q(\sqrt{-2}, \sqrt{7})$	None		$4$	$0$	$0$	$0$	$0$	$0$	$2$	$\mathrm{SU}(2)[C_{2}]$	$q-5\beta _{1}q^{5}+\beta _{3}q^{7}+4\beta _{2}q^{11}+11\beta _{1}q^{17}+\cdots$
4032.3.d.e	$4032$	$3$	4032.d	3.b	$2$	$4$	$4$	$109.864$	$\Q(\sqrt{-2}, \sqrt{7})$	None		$2$	$0$	$0$	$0$	$0$	$0$	$2\cdot 3$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{5}-\beta _{3}q^{7}+(-2\beta _{1}-\beta _{2})q^{11}+\cdots$
4032.3.d.f	$4032$	$3$	4032.d	3.b	$2$	$4$	$4$	$109.864$	$\Q(\sqrt{-2}, \sqrt{7})$	None		$2$	$0$	$0$	$0$	$0$	$0$	$2$	$\mathrm{SU}(2)[C_{2}]$	$q+(-3\beta _{1}+\beta _{2})q^{5}-\beta _{3}q^{7}+(-\beta _{1}+\cdots)q^{11}+\cdots$
4032.3.d.g	$4032$	$3$	4032.d	3.b	$2$	$4$	$4$	$109.864$	$\Q(\sqrt{-2}, \sqrt{7})$	None		$2$	$0$	$0$	$0$	$0$	$0$	$2$	$\mathrm{SU}(2)[C_{2}]$	$q+(-3\beta _{1}+\beta _{2})q^{5}+\beta _{3}q^{7}+(\beta _{1}-2\beta _{2}+\cdots)q^{11}+\cdots$
4032.3.d.h	$4032$	$3$	4032.d	3.b	$2$	$4$	$4$	$109.864$	$\Q(\sqrt{-2}, \sqrt{7})$	None		$2$	$0$	$0$	$0$	$0$	$0$	$2\cdot 3$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{5}+\beta _{3}q^{7}+(2\beta _{1}+\beta _{2})q^{11}+\cdots$
4032.3.d.i	$4032$	$3$	4032.d	3.b	$2$	$4$	$4$	$109.864$	$\Q(\sqrt{-2}, \sqrt{7})$	None		$2$	$0$	$0$	$0$	$0$	$0$	$2\cdot 3$	$\mathrm{SU}(2)[C_{2}]$	$q+(2\beta _{1}-\beta _{3})q^{5}-\beta _{2}q^{7}+(4\beta _{1}-2\beta _{3})q^{11}+\cdots$
4032.3.d.j	$4032$	$3$	4032.d	3.b	$2$	$4$	$4$	$109.864$	$\Q(\sqrt{-2}, \sqrt{7})$	None		$2$	$0$	$0$	$0$	$0$	$0$	$2\cdot 3$	$\mathrm{SU}(2)[C_{2}]$	$q+(2\beta _{1}-\beta _{3})q^{5}+\beta _{2}q^{7}+(-4\beta _{1}+2\beta _{3})q^{11}+\cdots$
4032.3.d.k	$4032$	$3$	4032.d	3.b	$2$	$4$	$4$	$109.864$	$\Q(\sqrt{-2}, \sqrt{7})$	None		$4$	$0$	$0$	$0$	$0$	$0$	$2$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{3}q^{7}+\beta _{2}q^{11}+10q^{13}+14\beta _{1}q^{17}+\cdots$
4032.3.d.l	$4032$	$3$	4032.d	3.b	$2$	$8$	$8$	$109.864$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	None		$2$	$0$	$0$	$0$	$0$	$0$	$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	$q+(\beta _{2}-\beta _{4}+\beta _{5})q^{5}-\beta _{3}q^{7}+(\beta _{2}-\beta _{4}+\cdots)q^{11}+\cdots$
4032.3.d.m	$4032$	$3$	4032.d	3.b	$2$	$8$	$8$	$109.864$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	None		$2$	$0$	$0$	$0$	$0$	$0$	$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	$q+(\beta _{2}-\beta _{4}+\beta _{5})q^{5}+\beta _{3}q^{7}+(-\beta _{2}+\cdots)q^{11}+\cdots$
4032.3.d.n	$4032$	$3$	4032.d	3.b	$2$	$12$	$12$	$109.864$	$\mathbb{Q}[x]/(x^{12} + \cdots)$	None		$2$	$0$	$0$	$0$	$0$	$0$	$2^{13}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{8}q^{5}-\beta _{4}q^{7}-\beta _{6}q^{11}+(-1-\beta _{9}+\cdots)q^{13}+\cdots$
4032.3.d.o	$4032$	$3$	4032.d	3.b	$2$	$12$	$12$	$109.864$	$\mathbb{Q}[x]/(x^{12} + \cdots)$	None		$2$	$0$	$0$	$0$	$0$	$0$	$2^{13}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{8}q^{5}+\beta _{4}q^{7}+\beta _{6}q^{11}+(-1-\beta _{9}+\cdots)q^{13}+\cdots$
4032.3.d.p	$4032$	$3$	4032.d	3.b	$2$	$12$	$12$	$109.864$	12.0.$\cdots$.4	None		$4$	$0$	$0$	$0$	$0$	$0$	$2^{13}$	$\mathrm{SU}(2)[C_{2}]$	$q+(\beta _{5}-\beta _{7})q^{5}-\beta _{1}q^{7}+(\beta _{8}-\beta _{10}+\cdots)q^{11}+\cdots$
4032.3.n.a	$4032$	$3$	4032.n	24.h	$2$	$16$	$16$	$109.864$	16.0.$\cdots$.1	None		$8$	$0$	$0$	$0$	$0$	$0$	$2^{18}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{11}q^{5}-\beta _{1}q^{7}+(-7\beta _{7}+3\beta _{12}+\cdots)q^{11}+\cdots$
4032.3.n.b	$4032$	$3$	4032.n	24.h	$2$	$16$	$16$	$109.864$	16.0.$\cdots$.1	None		$8$	$0$	$0$	$0$	$0$	$0$	$2^{18}$	$\mathrm{SU}(2)[C_{2}]$	$q+(-\beta _{2}-2\beta _{6})q^{5}+\beta _{4}q^{7}+(-5\beta _{1}+\cdots)q^{11}+\cdots$
4032.3.n.c	$4032$	$3$	4032.n	24.h	$2$	$64$	$64$	$109.864$		None		$8$	$0$	$0$	$0$	$0$	$0$		$\mathrm{SU}(2)[C_{2}]$
4068.3.d.a	$4068$	$3$	4068.d	3.b	$2$	$76$	$76$	$110.845$		None		$2$	$0$	$0$	$0$	$0$	$0$		$\mathrm{SU}(2)[C_{2}]$
4068.3.h.a	$4068$	$3$	4068.h	339.c	$2$	$76$	$76$	$110.845$		None		$4$	$0$	$0$	$0$	$0$	$0$		$\mathrm{SU}(2)[C_{2}]$
4116.3.d.a	$4116$	$3$	4116.d	7.b	$2$	$24$	$24$	$112.153$		None		$2$	$0$	$0$	$0$	$0$	$0$		$\mathrm{SU}(2)[C_{2}]$
4116.3.d.b	$4116$	$3$	4116.d	7.b	$2$	$24$	$24$	$112.153$		None		$2$	$0$	$0$	$0$	$0$	$0$		$\mathrm{SU}(2)[C_{2}]$
4116.3.d.c	$4116$	$3$	4116.d	7.b	$2$	$48$	$48$	$112.153$		None		$2$	$0$	$0$	$0$	$0$	$0$		$\mathrm{SU}(2)[C_{2}]$
4140.3.c.a	$4140$	$3$	4140.c	15.d	$2$	$88$	$88$	$112.807$		None		$4$	$0$	$0$	$0$	$0$	$0$		$\mathrm{SU}(2)[C_{2}]$
4140.3.d.a	$4140$	$3$	4140.d	23.b	$2$	$16$	$16$	$112.807$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	None		$2$	$0$	$0$	$0$	$0$	$0$	$2^{6}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{4}q^{5}-\beta _{7}q^{7}+(-2\beta _{4}+\beta _{9})q^{11}+\cdots$
4140.3.d.b	$4140$	$3$	4140.d	23.b	$2$	$32$	$32$	$112.807$		None		$4$	$0$	$0$	$0$	$0$	$0$		$\mathrm{SU}(2)[C_{2}]$
4140.3.d.c	$4140$	$3$	4140.d	23.b	$2$	$32$	$32$	$112.807$		None		$2$	$0$	$0$	$0$	$0$	$0$		$\mathrm{SU}(2)[C_{2}]$
4140.3.l.a	$4140$	$3$	4140.l	3.b	$2$	$56$	$56$	$112.807$		None		$2$	$0$	$0$	$0$	$0$	$32$		$\mathrm{SU}(2)[C_{2}]$
4212.3.d.a	$4212$	$3$	4212.d	3.b	$2$	$48$	$48$	$114.769$		None		$2$	$0$	$0$	$0$	$0$	$0$		$\mathrm{SU}(2)[C_{2}]$
4212.3.d.b	$4212$	$3$	4212.d	3.b	$2$	$48$	$48$	$114.769$		None		$2$	$0$	$0$	$0$	$0$	$0$		$\mathrm{SU}(2)[C_{2}]$
4260.3.b.a	$4260$	$3$	4260.b	71.b	$2$	$96$	$96$	$116.077$		None		$2$	$0$	$0$	$0$	$0$	$0$		$\mathrm{SU}(2)[C_{2}]$
4284.3.e.a	$4284$	$3$	4284.e	3.b	$2$	$64$	$64$	$116.731$		None		$2$	$0$	$0$	$0$	$0$	$0$		$\mathrm{SU}(2)[C_{2}]$
4284.3.p.a	$4284$	$3$	4284.p	51.c	$2$	$72$	$72$	$116.731$		None		$4$	$0$	$0$	$0$	$0$	$0$		$\mathrm{SU}(2)[C_{2}]$
4356.3.e.a	$4356$	$3$	4356.e	3.b	$2$	$2$	$2$	$118.692$	$\Q(\sqrt{-2}) $	None		$2$	$0$	$0$	$0$	$0$	$-14$	$1$	$\mathrm{SU}(2)[C_{2}]$	$q+4\beta q^{5}-7q^{7}-8\beta q^{17}+q^{19}-7\beta q^{23}+\cdots$
4356.3.e.b	$4356$	$3$	4356.e	3.b	$2$	$2$	$2$	$118.692$	$\Q(\sqrt{-2}) $	None		$2$	$0$	$0$	$0$	$0$	$14$	$1$	$\mathrm{SU}(2)[C_{2}]$	$q+4\beta q^{5}+7q^{7}+8\beta q^{17}-q^{19}-7\beta q^{23}+\cdots$
4356.3.e.c	$4356$	$3$	4356.e	3.b	$2$	$4$	$4$	$118.692$	$\Q(\sqrt{-2}, \sqrt{31})$	None		$2$	$0$	$0$	$0$	$0$	$-12$	$3$	$\mathrm{SU}(2)[C_{2}]$	$q+(\beta _{1}+\beta _{2})q^{5}+(-3-\beta _{3})q^{7}+(-3+\cdots)q^{13}+\cdots$
4356.3.e.d	$4356$	$3$	4356.e	3.b	$2$	$4$	$4$	$118.692$	$\Q(\sqrt{-2}, \sqrt{31})$	None		$2$	$0$	$0$	$0$	$0$	$12$	$3$	$\mathrm{SU}(2)[C_{2}]$	$q+(\beta _{1}+\beta _{2})q^{5}+(3+\beta _{3})q^{7}+(3-2\beta _{3})q^{13}+\cdots$
4356.3.e.e	$4356$	$3$	4356.e	3.b	$2$	$8$	$8$	$118.692$	8.0.$\cdots$.48	None		$4$	$0$	$0$	$0$	$0$	$0$	$2^{5}\cdot 3^{7}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{5}-\beta _{2}q^{7}+(\beta _{2}-\beta _{3})q^{13}-\beta _{5}q^{17}+\cdots$
4356.3.e.f	$4356$	$3$	4356.e	3.b	$2$	$8$	$8$	$118.692$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	None		$2$	$0$	$0$	$0$	$0$	$16$	$2^{7}\cdot 3^{3}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{6}q^{5}+(2+\beta _{4})q^{7}+(1+\beta _{1}-\beta _{3}+\cdots)q^{13}+\cdots$
4356.3.e.g	$4356$	$3$	4356.e	3.b	$2$	$12$	$12$	$118.692$	$\mathbb{Q}[x]/(x^{12} + \cdots)$	None		$4$	$0$	$0$	$0$	$0$	$0$	$2^{5}\cdot 3^{15}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{4}q^{5}+(-\beta _{3}+\beta _{5})q^{7}-\beta _{7}q^{13}+\cdots$
4356.3.e.h	$4356$	$3$	4356.e	3.b	$2$	$16$	$16$	$118.692$	$\mathbb{Q}[x]/(x^{16} + \cdots)$	None		$2$	$0$	$0$	$0$	$0$	$-8$	$2^{2}\cdot 3^{4}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{5}+(-\beta _{2}+\beta _{6})q^{7}+(-\beta _{3}+\beta _{6}+\cdots)q^{13}+\cdots$
4356.3.e.i	$4356$	$3$	4356.e	3.b	$2$	$16$	$16$	$118.692$	$\mathbb{Q}[x]/(x^{16} + \cdots)$	None		$2$	$0$	$0$	$0$	$0$	$8$	$2^{2}\cdot 3^{4}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{5}+(\beta _{2}-\beta _{6})q^{7}+(\beta _{3}-\beta _{6})q^{13}+\cdots$
4356.3.f.a	$4356$	$3$	4356.f	11.b	$2$	$2$	$2$	$118.692$	$\Q(\sqrt{-2}) $	None		$2$	$0$	$0$	$0$	$-16$	$0$	$1$	$\mathrm{SU}(2)[C_{2}]$	$q-8q^{5}-3\beta q^{7}-17\beta q^{13}-2^{4}\beta q^{17}+\cdots$
4356.3.f.b	$4356$	$3$	4356.f	11.b	$2$	$2$	$2$	$118.692$	$\Q(\sqrt{-2}) $	None		$2$	$0$	$0$	$0$	$-2$	$0$	$1$	$\mathrm{SU}(2)[C_{2}]$	$q-q^{5}-3\beta q^{7}-4\beta q^{13}-13\beta q^{17}+\cdots$
4356.3.f.c	$4356$	$3$	4356.f	11.b	$2$	$2$	$2$	$118.692$	$\Q(\sqrt{-2}) $	None		$2$	$0$	$0$	$0$	$16$	$0$	$1$	$\mathrm{SU}(2)[C_{2}]$	$q+8q^{5}-3\beta q^{7}-17\beta q^{13}+2^{4}\beta q^{17}+\cdots$
4356.3.f.d	$4356$	$3$	4356.f	11.b	$2$	$4$	$4$	$118.692$	$\Q(\sqrt{-2}, \sqrt{3})$	None		$2$	$0$	$0$	$0$	$-8$	$0$	$1$	$\mathrm{SU}(2)[C_{2}]$	$q+(-2+\beta _{2})q^{5}+(\beta _{1}+\beta _{3})q^{7}+(7\beta _{1}+\cdots)q^{13}+\cdots$
4356.3.f.e	$4356$	$3$	4356.f	11.b	$2$	$4$	$4$	$118.692$	$\Q(\sqrt{-2}, \sqrt{3})$	$\Q(\sqrt{-3}) $		$4$	$0$	$0$	$0$	$0$	$0$	$2^{6}$	$\mathrm{U}(1)[D_{2}]$	$q+(\beta _{1}-\beta _{2})q^{7}+(11\beta _{1}+\beta _{2})q^{13}+(13\beta _{1}+\cdots)q^{19}+\cdots$
4356.3.f.f	$4356$	$3$	4356.f	11.b	$2$	$4$	$4$	$118.692$	$\Q(\sqrt{-2}, \sqrt{3})$	$\Q(\sqrt{-3}) $		$4$	$0$	$0$	$0$	$0$	$0$	$1$	$\mathrm{U}(1)[D_{2}]$	$q+(-8\beta _{1}+5\beta _{3})q^{7}+(7\beta _{1}-15\beta _{3})q^{13}+\cdots$

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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.