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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 175 matches)

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Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	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	CM	Self-dual	Inner twists	Rank*	$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
66.2.a.a	$66$	$2$	66.a	1.a	$1$	$1$	$1$	$0.527$	$\Q$	None	✓	$1$	$0$	$-1$	$1$	$0$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}-q^{6}+2q^{7}-q^{8}+\cdots$
66.2.a.b	$66$	$2$	66.a	1.a	$1$	$1$	$1$	$0.527$	$\Q$	None	✓	$1$	$0$	$1$	$-1$	$2$	$-4$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}+2q^{5}-q^{6}-4q^{7}+\cdots$
66.2.a.c	$66$	$2$	66.a	1.a	$1$	$1$	$1$	$0.527$	$\Q$	None	✓	$1$	$0$	$1$	$1$	$-4$	$-2$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}-4q^{5}+q^{6}-2q^{7}+\cdots$
66.2.b.a	$66$	$2$	66.b	33.d	$2$	$2$	$2$	$0.527$	$\Q(\sqrt{-2}) $	None		$2$	$0$	$-2$	$-2$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q-q^{2}+(-1+\beta )q^{3}+q^{4}+\beta q^{5}+(1+\cdots)q^{6}+\cdots$
66.2.b.b	$66$	$2$	66.b	33.d	$2$	$2$	$2$	$0.527$	$\Q(\sqrt{-2}) $	None		$2$	$0$	$2$	$-2$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+q^{2}+(-1+\beta )q^{3}+q^{4}+\beta q^{5}+(-1+\cdots)q^{6}+\cdots$
66.2.e.a	$66$	$2$	66.e	11.c	$5$	$4$	$1$	$0.527$	$\Q(\zeta_{10})$	None		$2$	$0$	$-1$	$1$	$8$	$-6$		$1$	$\mathrm{SU}(2)[C_{5}]$	$q-\zeta_{10}q^{2}+\zeta_{10}^{3}q^{3}+\zeta_{10}^{2}q^{4}+(2+\cdots)q^{5}+\cdots$
66.2.e.b	$66$	$2$	66.e	11.c	$5$	$4$	$1$	$0.527$	$\Q(\zeta_{10})$	None		$2$	$0$	$1$	$-1$	$0$	$-2$		$1$	$\mathrm{SU}(2)[C_{5}]$	$q+\zeta_{10}q^{2}-\zeta_{10}^{3}q^{3}+\zeta_{10}^{2}q^{4}+(-2+\cdots)q^{5}+\cdots$
66.2.h.a	$66$	$2$	66.h	33.f	$10$	$8$	$2$	$0.527$	8.0.185640625.1	None		$2$	$0$	$-2$	$2$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{10}]$	$q-\beta _{2}q^{2}+(-\beta _{1}-\beta _{2}-\beta _{3}-\beta _{4}-\beta _{5}+\cdots)q^{3}+\cdots$
66.2.h.b	$66$	$2$	66.h	33.f	$10$	$8$	$2$	$0.527$	8.0.185640625.1	None		$2$	$0$	$2$	$2$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{10}]$	$q-\beta _{6}q^{2}-\beta _{7}q^{3}+(-1+\beta _{2}+\beta _{4}+\cdots)q^{4}+\cdots$
66.3.c.a	$66$	$3$	66.c	3.b	$2$	$8$	$8$	$1.798$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	None		$2$	$0$	$0$	$-2$	$0$	$8$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{2}q^{2}+(\beta _{2}+\beta _{3})q^{3}-2q^{4}+(\beta _{1}+\cdots)q^{5}+\cdots$
66.3.d.a	$66$	$3$	66.d	11.b	$2$	$4$	$4$	$1.798$	$\Q(\sqrt{-2}, \sqrt{3})$	None		$2$	$0$	$0$	$0$	$-8$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{1}q^{2}-\beta _{2}q^{3}-2q^{4}+(-2-4\beta _{2}+\cdots)q^{5}+\cdots$
66.3.f.a	$66$	$3$	66.f	11.d	$10$	$16$	$4$	$1.798$	16.0.$\cdots$.7	None		$2$	$0$	$0$	$0$	$8$	$60$		$2^{4}$	$\mathrm{SU}(2)[C_{10}]$	$q-\beta _{6}q^{2}-\beta _{9}q^{3}+(2-2\beta _{4}-2\beta _{8}+\cdots)q^{4}+\cdots$
66.3.g.a	$66$	$3$	66.g	33.h	$10$	$32$	$8$	$1.798$		None		$4$	$0$	$0$	$2$	$0$	$-8$			$\mathrm{SU}(2)[C_{10}]$
66.4.a.a	$66$	$4$	66.a	1.a	$1$	$1$	$1$	$3.894$	$\Q$	None	✓	$1$	$0$	$-2$	$3$	$0$	$14$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{2}+3q^{3}+4q^{4}-6q^{6}+14q^{7}+\cdots$
66.4.a.b	$66$	$4$	66.a	1.a	$1$	$1$	$1$	$3.894$	$\Q$	None	✓	$1$	$0$	$2$	$-3$	$10$	$16$	$+$	$1$	$\mathrm{SU}(2)$	$q+2q^{2}-3q^{3}+4q^{4}+10q^{5}-6q^{6}+\cdots$
66.4.a.c	$66$	$4$	66.a	1.a	$1$	$2$	$2$	$3.894$	$\Q(\sqrt{97}) $	None	✓	$1$	$0$	$4$	$6$	$10$	$-2$	$+$	$2$	$\mathrm{SU}(2)$	$q+2q^{2}+3q^{3}+4q^{4}+(5-\beta )q^{5}+6q^{6}+\cdots$
66.4.b.a	$66$	$4$	66.b	33.d	$2$	$6$	$6$	$3.894$	$\mathbb{Q}[x]/(x^{6} - \cdots)$	None		$2$	$0$	$-12$	$1$	$0$	$0$		$2^{2}\cdot 3$	$\mathrm{SU}(2)[C_{2}]$	$q-2q^{2}+\beta _{1}q^{3}+4q^{4}-\beta _{5}q^{5}-2\beta _{1}q^{6}+\cdots$
66.4.b.b	$66$	$4$	66.b	33.d	$2$	$6$	$6$	$3.894$	$\mathbb{Q}[x]/(x^{6} - \cdots)$	None		$2$	$0$	$12$	$1$	$0$	$0$		$2^{2}\cdot 3$	$\mathrm{SU}(2)[C_{2}]$	$q+2q^{2}+\beta _{1}q^{3}+4q^{4}-\beta _{5}q^{5}+2\beta _{1}q^{6}+\cdots$
66.4.e.a	$66$	$4$	66.e	11.c	$5$	$4$	$1$	$3.894$	$\Q(\zeta_{10})$	None		$2$	$0$	$-2$	$3$	$-15$	$-31$		$1$	$\mathrm{SU}(2)[C_{5}]$	$q-2\zeta_{10}q^{2}+3\zeta_{10}^{3}q^{3}+4\zeta_{10}^{2}q^{4}+\cdots$
66.4.e.b	$66$	$4$	66.e	11.c	$5$	$4$	$1$	$3.894$	$\Q(\zeta_{10})$	None		$2$	$0$	$2$	$-3$	$15$	$-19$		$1$	$\mathrm{SU}(2)[C_{5}]$	$q+2\zeta_{10}q^{2}-3\zeta_{10}^{3}q^{3}+4\zeta_{10}^{2}q^{4}+\cdots$
66.4.e.c	$66$	$4$	66.e	11.c	$5$	$8$	$2$	$3.894$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	None		$2$	$0$	$-4$	$-6$	$-5$	$-13$		$1$	$\mathrm{SU}(2)[C_{5}]$	$q-2\beta _{3}q^{2}-3\beta _{2}q^{3}+(-4+4\beta _{2}+4\beta _{3}+\cdots)q^{4}+\cdots$
66.4.e.d	$66$	$4$	66.e	11.c	$5$	$8$	$2$	$3.894$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	None		$2$	$0$	$4$	$6$	$-27$	$27$		$5$	$\mathrm{SU}(2)[C_{5}]$	$q+2\beta _{2}q^{2}+(3-3\beta _{2}+3\beta _{3}-3\beta _{4}+\cdots)q^{3}+\cdots$
66.4.h.a	$66$	$4$	66.h	33.f	$10$	$24$	$6$	$3.894$		None		$2$	$0$	$-12$	$-1$	$0$	$0$			$\mathrm{SU}(2)[C_{10}]$
66.4.h.b	$66$	$4$	66.h	33.f	$10$	$24$	$6$	$3.894$		None		$2$	$0$	$12$	$-1$	$0$	$0$			$\mathrm{SU}(2)[C_{10}]$
66.5.c.a	$66$	$5$	66.c	3.b	$2$	$12$	$12$	$6.822$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	None		$2$	$0$	$0$	$10$	$0$	$-184$		$2^{14}\cdot 3^{2}\cdot 11^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{1}q^{2}+(1-\beta _{1}-\beta _{5})q^{3}-8q^{4}+\cdots$
66.5.d.a	$66$	$5$	66.d	11.b	$2$	$8$	$8$	$6.822$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	None		$2$	$0$	$0$	$0$	$72$	$0$		$2^{9}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{3}q^{2}-\beta _{1}q^{3}-8q^{4}+(9+2\beta _{1}+\cdots)q^{5}+\cdots$
66.5.f.a	$66$	$5$	66.f	11.d	$10$	$32$	$8$	$6.822$		None		$2$	$0$	$0$	$0$	$-72$	$-300$			$\mathrm{SU}(2)[C_{10}]$
66.5.g.a	$66$	$5$	66.g	33.h	$10$	$64$	$16$	$6.822$		None		$4$	$0$	$0$	$2$	$0$	$80$			$\mathrm{SU}(2)[C_{10}]$
66.6.a.a	$66$	$6$	66.a	1.a	$1$	$1$	$1$	$10.585$	$\Q$	None	✓	$1$	$0$	$-4$	$-9$	$-14$	$-112$	$-$	$1$	$\mathrm{SU}(2)$	$q-4q^{2}-9q^{3}+2^{4}q^{4}-14q^{5}+6^{2}q^{6}+\cdots$
66.6.a.b	$66$	$6$	66.a	1.a	$1$	$1$	$1$	$10.585$	$\Q$	None	✓	$1$	$1$	$-4$	$-9$	$-14$	$130$	$+$	$1$	$\mathrm{SU}(2)$	$q-4q^{2}-9q^{3}+2^{4}q^{4}-14q^{5}+6^{2}q^{6}+\cdots$
66.6.a.c	$66$	$6$	66.a	1.a	$1$	$1$	$1$	$10.585$	$\Q$	None	✓	$1$	$1$	$-4$	$9$	$-14$	$-130$	$+$	$1$	$\mathrm{SU}(2)$	$q-4q^{2}+9q^{3}+2^{4}q^{4}-14q^{5}-6^{2}q^{6}+\cdots$
66.6.a.d	$66$	$6$	66.a	1.a	$1$	$1$	$1$	$10.585$	$\Q$	None	✓	$1$	$0$	$4$	$-9$	$50$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q+4q^{2}-9q^{3}+2^{4}q^{4}+50q^{5}-6^{2}q^{6}+\cdots$
66.6.a.e	$66$	$6$	66.a	1.a	$1$	$2$	$2$	$10.585$	$\Q(\sqrt{8761}) $	None	✓	$1$	$0$	$-8$	$18$	$-14$	$210$	$-$	$2$	$\mathrm{SU}(2)$	$q-4q^{2}+9q^{3}+2^{4}q^{4}+(-7-\beta )q^{5}+\cdots$
66.6.a.f	$66$	$6$	66.a	1.a	$1$	$2$	$2$	$10.585$	$\Q(\sqrt{2161}) $	None	✓	$1$	$0$	$8$	$18$	$50$	$96$	$-$	$2$	$\mathrm{SU}(2)$	$q+4q^{2}+9q^{3}+2^{4}q^{4}+(5^{2}-\beta )q^{5}+\cdots$
66.6.b.a	$66$	$6$	66.b	33.d	$2$	$10$	$10$	$10.585$	$\mathbb{Q}[x]/(x^{10} + \cdots)$	None		$2$	$0$	$-40$	$10$	$0$	$0$		$2^{7}\cdot 3^{7}$	$\mathrm{SU}(2)[C_{2}]$	$q-4q^{2}+(1-\beta _{3})q^{3}+2^{4}q^{4}+(-\beta _{1}+\cdots)q^{5}+\cdots$
66.6.b.b	$66$	$6$	66.b	33.d	$2$	$10$	$10$	$10.585$	$\mathbb{Q}[x]/(x^{10} + \cdots)$	None		$2$	$0$	$40$	$10$	$0$	$0$		$2^{7}\cdot 3^{7}$	$\mathrm{SU}(2)[C_{2}]$	$q+4q^{2}+(1-\beta _{3})q^{3}+2^{4}q^{4}+(-\beta _{1}+\cdots)q^{5}+\cdots$
66.6.e.a	$66$	$6$	66.e	11.c	$5$	$8$	$2$	$10.585$	$\mathbb{Q}[x]/(x^{8} + \cdots)$	None		$2$	$0$	$-8$	$-18$	$150$	$474$		$2^{4}$	$\mathrm{SU}(2)[C_{5}]$	$q-4\beta _{2}q^{2}+(-9+9\beta _{2}-9\beta _{3}+9\beta _{5}+\cdots)q^{3}+\cdots$
66.6.e.b	$66$	$6$	66.e	11.c	$5$	$8$	$2$	$10.585$	$\mathbb{Q}[x]/(x^{8} + \cdots)$	None		$2$	$0$	$8$	$18$	$118$	$2$		$2^{4}$	$\mathrm{SU}(2)[C_{5}]$	$q-4\beta _{2}q^{2}+(9+9\beta _{2}+9\beta _{3}+9\beta _{5}+\cdots)q^{3}+\cdots$
66.6.e.c	$66$	$6$	66.e	11.c	$5$	$12$	$3$	$10.585$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	None		$2$	$0$	$-12$	$27$	$-118$	$216$		$2^{4}\cdot 11$	$\mathrm{SU}(2)[C_{5}]$	$q-4\beta _{5}q^{2}+9\beta _{2}q^{3}+(-2^{4}+2^{4}\beta _{2}+\cdots)q^{4}+\cdots$
66.6.e.d	$66$	$6$	66.e	11.c	$5$	$12$	$3$	$10.585$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	None		$2$	$0$	$12$	$-27$	$-62$	$-60$		$2^{4}$	$\mathrm{SU}(2)[C_{5}]$	$q+(4+4\beta _{2}-4\beta _{3}-4\beta _{4})q^{2}-9\beta _{4}q^{3}+\cdots$
66.6.h.a	$66$	$6$	66.h	33.f	$10$	$40$	$10$	$10.585$		None		$2$	$0$	$-40$	$-10$	$0$	$0$			$\mathrm{SU}(2)[C_{10}]$
66.6.h.b	$66$	$6$	66.h	33.f	$10$	$40$	$10$	$10.585$		None		$2$	$0$	$40$	$-10$	$0$	$0$			$\mathrm{SU}(2)[C_{10}]$
66.7.c.a	$66$	$7$	66.c	3.b	$2$	$20$	$20$	$15.184$	$\mathbb{Q}[x]/(x^{20} - \cdots)$	None		$2$	$0$	$0$	$-32$	$0$	$400$		$2^{29}\cdot 3^{12}\cdot 11^{10}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{2}q^{2}+(-2-\beta _{1})q^{3}-2^{5}q^{4}+(4\beta _{2}+\cdots)q^{5}+\cdots$
66.7.d.a	$66$	$7$	66.d	11.b	$2$	$12$	$12$	$15.184$	$\mathbb{Q}[x]/(x^{12} + \cdots)$	None		$2$	$0$	$0$	$0$	$-448$	$0$		$2^{15}\cdot 3^{10}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{5}q^{2}+\beta _{1}q^{3}-2^{5}q^{4}+(-37+\beta _{2}+\cdots)q^{5}+\cdots$
66.7.f.a	$66$	$7$	66.f	11.d	$10$	$48$	$12$	$15.184$		None		$2$	$0$	$0$	$0$	$448$	$-1440$			$\mathrm{SU}(2)[C_{10}]$
66.7.g.a	$66$	$7$	66.g	33.h	$10$	$96$	$24$	$15.184$		None		$4$	$0$	$0$	$-52$	$0$	$-408$			$\mathrm{SU}(2)[C_{10}]$
66.8.a.a	$66$	$8$	66.a	1.a	$1$	$1$	$1$	$20.617$	$\Q$	None	✓	$1$	$1$	$-8$	$27$	$-70$	$-8$	$-$	$1$	$\mathrm{SU}(2)$	$q-8q^{2}+3^{3}q^{3}+2^{6}q^{4}-70q^{5}-6^{3}q^{6}+\cdots$
66.8.a.b	$66$	$8$	66.a	1.a	$1$	$1$	$1$	$20.617$	$\Q$	None	✓	$1$	$1$	$8$	$-27$	$0$	$-286$	$-$	$1$	$\mathrm{SU}(2)$	$q+8q^{2}-3^{3}q^{3}+2^{6}q^{4}-6^{3}q^{6}-286q^{7}+\cdots$
66.8.a.c	$66$	$8$	66.a	1.a	$1$	$2$	$2$	$20.617$	$\Q(\sqrt{3193}) $	None	✓	$1$	$0$	$-16$	$-54$	$-70$	$-762$	$+$	$2$	$\mathrm{SU}(2)$	$q-8q^{2}-3^{3}q^{3}+2^{6}q^{4}+(-35-7\beta )q^{5}+\cdots$
66.8.a.d	$66$	$8$	66.a	1.a	$1$	$2$	$2$	$20.617$	$\Q(\sqrt{97}) $	None	✓	$1$	$1$	$-16$	$-54$	$-70$	$-278$	$-$	$2\cdot 5$	$\mathrm{SU}(2)$	$q-8q^{2}-3^{3}q^{3}+2^{6}q^{4}+(-35-5\beta )q^{5}+\cdots$

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Elliptic curves over $\Q$
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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.