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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 62 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
469.1.k.a	$469$	$1$	469.k	469.k	$6$	$2$	$1$	$0.234$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-7}) $	None		$4$	$0$	$-2$	$0$	$0$	$-1$		$1$		$q+\zeta_{6}^{2}q^{2}-3\zeta_{6}q^{4}-\zeta_{6}q^{7}-2q^{8}+\cdots$
469.1.v.a	$469$	$1$	469.v	469.v	$22$	$10$	$1$	$0.234$	$\Q(\zeta_{22})$	$D_{11}$	$\Q(\sqrt{-7}) $	None		$4$	$0$	$-2$	$0$	$0$	$-1$		$1$		$q+(-\zeta_{22}^{9}+\zeta_{22}^{10})q^{2}+(-\zeta_{22}^{7}+\cdots)q^{4}+\cdots$
469.1.bl.a	$469$	$1$	469.bl	469.al	$66$	$20$	$1$	$0.234$	$\Q(\zeta_{33})$	$D_{33}$	$\Q(\sqrt{-7}) $	None		$4$	$0$	$2$	$0$	$0$	$1$		$1$		$q+(\zeta_{66}^{10}+\zeta_{66}^{16})q^{2}+(\zeta_{66}^{20}+\zeta_{66}^{26}+\cdots)q^{4}+\cdots$
469.2.a.a	$469$	$2$	469.a	1.a	$1$	$1$	$1$	$3.745$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$-1$	$-3$	$1$	$-1$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-3q^{3}-q^{4}+q^{5}+3q^{6}-q^{7}+\cdots$
469.2.a.b	$469$	$2$	469.a	1.a	$1$	$1$	$1$	$3.745$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$1$	$1$	$-3$	$-1$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}-q^{4}-3q^{5}+q^{6}-q^{7}+\cdots$
469.2.a.c	$469$	$2$	469.a	1.a	$1$	$2$	$2$	$3.745$	$\Q(\sqrt{17}) $	$_{}$	None	None	✓	$1$	$0$	$1$	$-1$	$-3$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{2}-\beta q^{3}+(2+\beta )q^{4}+(-2+\beta )q^{5}+\cdots$
469.2.a.d	$469$	$2$	469.a	1.a	$1$	$2$	$2$	$3.745$	$\Q(\sqrt{17}) $	$_{}$	None	None	✓	$1$	$0$	$2$	$-1$	$-1$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-\beta q^{3}-q^{4}-\beta q^{5}-\beta q^{6}+q^{7}+\cdots$
469.2.a.e	$469$	$2$	469.a	1.a	$1$	$3$	$3$	$3.745$	$\Q(\zeta_{18})^+$	$_{}$	None	None	✓	$1$	$1$	$-3$	$-3$	$3$	$3$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta _{1})q^{2}+(-1-\beta _{1})q^{3}+(1+\cdots)q^{4}+\cdots$
469.2.a.f	$469$	$2$	469.a	1.a	$1$	$3$	$3$	$3.745$	3.3.148.1	$_{}$	None	None	✓	$1$	$1$	$-1$	$-1$	$-9$	$3$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+(-\beta _{1}-\beta _{2})q^{3}+(\beta _{1}+\beta _{2})q^{4}+\cdots$
469.2.a.g	$469$	$2$	469.a	1.a	$1$	$5$	$5$	$3.745$	5.5.813209.1	$_{}$	None	None	✓	$1$	$1$	$2$	$-2$	$-4$	$-5$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}-\beta _{1}q^{3}+(1+\beta _{2})q^{4}+(-1+\cdots)q^{5}+\cdots$
469.2.a.h	$469$	$2$	469.a	1.a	$1$	$7$	$7$	$3.745$	$\mathbb{Q}[x]/(x^{7} - \cdots)$	$_{}$	None	None	✓	$1$	$0$	$1$	$6$	$6$	$7$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+(1+\beta _{3})q^{3}+(2+\beta _{2})q^{4}+\cdots$
469.2.a.i	$469$	$2$	469.a	1.a	$1$	$9$	$9$	$3.745$	$\mathbb{Q}[x]/(x^{9} - \cdots)$	$_{}$	None	None	✓	$1$	$0$	$-1$	$8$	$8$	$-9$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+(1+\beta _{2})q^{3}+(1+\beta _{2}-\beta _{3}+\cdots)q^{4}+\cdots$
469.2.c.a	$469$	$2$	469.c	469.c	$2$	$2$	$2$	$3.745$	$\Q(\sqrt{-7}) $	$_{}$	$\Q(\sqrt{-7}) $	None		$4$	$0$	$0$	$0$	$0$	$0$		$2$	$\mathrm{U}(1)[D_{2}]$	$q-\beta q^{2}-5q^{4}+\beta q^{7}+3\beta q^{8}-3q^{9}+\cdots$
469.2.c.b	$469$	$2$	469.c	469.c	$2$	$4$	$4$	$3.745$	$\Q(\sqrt{-2}, \sqrt{-5})$	$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{2}q^{2}+(2\beta _{1}-\beta _{2})q^{3}+2\beta _{3}q^{6}+\cdots$
469.2.c.c	$469$	$2$	469.c	469.c	$2$	$8$	$8$	$3.745$	$\mathbb{Q}[x]/(x^{8} + \cdots)$	$_{}$	None	None		$2$	$0$	$0$	$-2$	$-2$	$-2$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{2}-\beta _{3}q^{3}+(-1+\beta _{2}+\beta _{3}+\cdots)q^{4}+\cdots$
469.2.c.d	$469$	$2$	469.c	469.c	$2$	$8$	$8$	$3.745$	$\mathbb{Q}[x]/(x^{8} + \cdots)$	$_{}$	None	None		$2$	$0$	$0$	$2$	$2$	$2$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{2}+\beta _{3}q^{3}+(-1+\beta _{2}+\beta _{3}+\cdots)q^{4}+\cdots$
469.2.c.e	$469$	$2$	469.c	469.c	$2$	$20$	$20$	$3.745$	$\mathbb{Q}[x]/(x^{20} + \cdots)$	$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$0$		$2^{6}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{10}q^{2}-\beta _{15}q^{3}+(-1-\beta _{3})q^{4}+\cdots$
469.2.e.a	$469$	$2$	469.e	469.e	$3$	$86$	$43$	$3.745$		$_{}$	None	None		$2$	$0$	$3$	$1$	$2$	$-8$			$\mathrm{SU}(2)[C_{3}]$
469.2.f.a	$469$	$2$	469.f	7.c	$3$	$8$	$4$	$3.745$	8.0.6498455769.2	$_{}$	None	None		$2$	$0$	$-1$	$3$	$5$	$-6$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q-\beta _{1}q^{2}+(1+\beta _{2}-\beta _{5}-\beta _{7})q^{3}+(\beta _{1}+\cdots)q^{4}+\cdots$
469.2.f.b	$469$	$2$	469.f	7.c	$3$	$36$	$18$	$3.745$		$_{}$	None	None		$2$	$0$	$1$	$3$	$14$	$3$			$\mathrm{SU}(2)[C_{3}]$
469.2.f.c	$469$	$2$	469.f	7.c	$3$	$44$	$22$	$3.745$		$_{}$	None	None		$2$	$0$	$0$	$-6$	$-17$	$-3$			$\mathrm{SU}(2)[C_{3}]$
469.2.g.a	$469$	$2$	469.g	67.c	$3$	$2$	$1$	$3.745$	$\Q(\sqrt{-3}) $	$_{}$	None	None		$2$	$1$	$-1$	$-4$	$0$	$1$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-1+\zeta_{6})q^{2}-2q^{3}+\zeta_{6}q^{4}+(2+\cdots)q^{6}+\cdots$
469.2.g.b	$469$	$2$	469.g	67.c	$3$	$30$	$15$	$3.745$		$_{}$	None	None		$2$	$0$	$0$	$6$	$-2$	$15$			$\mathrm{SU}(2)[C_{3}]$
469.2.g.c	$469$	$2$	469.g	67.c	$3$	$36$	$18$	$3.745$		$_{}$	None	None		$2$	$0$	$-3$	$2$	$-2$	$-18$			$\mathrm{SU}(2)[C_{3}]$
469.2.h.a	$469$	$2$	469.h	469.h	$3$	$86$	$43$	$3.745$		$_{}$	None	None		$2$	$0$	$-6$	$1$	$2$	$1$			$\mathrm{SU}(2)[C_{3}]$
469.2.i.a	$469$	$2$	469.i	469.i	$6$	$2$	$1$	$3.745$	$\Q(\sqrt{-3}) $	$_{}$	None	None		$2$	$0$	$0$	$-1$	$-3$	$4$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q+(-1+2\zeta_{6})q^{2}+(-1+\zeta_{6})q^{3}-q^{4}+\cdots$
469.2.i.b	$469$	$2$	469.i	469.i	$6$	$84$	$42$	$3.745$		$_{}$	None	None		$2$	$0$	$0$	$2$	$3$	$-11$			$\mathrm{SU}(2)[C_{6}]$
469.2.o.a	$469$	$2$	469.o	469.o	$6$	$88$	$44$	$3.745$		$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{6}]$
469.2.p.a	$469$	$2$	469.p	469.p	$6$	$2$	$1$	$3.745$	$\Q(\sqrt{-3}) $	$_{}$	None	None		$2$	$0$	$3$	$1$	$3$	$-1$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q+(2-\zeta_{6})q^{2}+\zeta_{6}q^{3}+(1-\zeta_{6})q^{4}+\cdots$
469.2.p.b	$469$	$2$	469.p	469.p	$6$	$84$	$42$	$3.745$		$_{}$	None	None		$2$	$0$	$-6$	$-2$	$-3$	$-7$			$\mathrm{SU}(2)[C_{6}]$
469.2.s.a	$469$	$2$	469.s	469.s	$6$	$2$	$1$	$3.745$	$\Q(\sqrt{-3}) $	$_{}$	None	None		$2$	$0$	$3$	$-4$	$0$	$-5$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q+(1+\zeta_{6})q^{2}-2q^{3}+\zeta_{6}q^{4}+(-2+\cdots)q^{6}+\cdots$
469.2.s.b	$469$	$2$	469.s	469.s	$6$	$2$	$1$	$3.745$	$\Q(\sqrt{-3}) $	$_{}$	None	None		$2$	$0$	$3$	$4$	$0$	$-1$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q+(1+\zeta_{6})q^{2}+2q^{3}+\zeta_{6}q^{4}+(2+2\zeta_{6})q^{6}+\cdots$
469.2.s.c	$469$	$2$	469.s	469.s	$6$	$4$	$2$	$3.745$	$\Q(\sqrt{-3}, \sqrt{-7})$	$_{}$	$\Q(\sqrt{-7}) $	None		$4$	$0$	$0$	$0$	$0$	$0$		$2^{2}$	$\mathrm{U}(1)[D_{6}]$	$q+\beta _{1}q^{2}+5\beta _{2}q^{4}+\beta _{3}q^{7}+(3\beta _{1}-3\beta _{3})q^{8}+\cdots$
469.2.s.d	$469$	$2$	469.s	469.s	$6$	$80$	$40$	$3.745$		$_{}$	None	None		$4$	$0$	$-12$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{6}]$
469.2.u.a	$469$	$2$	469.u	67.e	$11$	$160$	$16$	$3.745$		$_{}$	None	None		$2$	$0$	$-1$	$-4$	$-2$	$16$			$\mathrm{SU}(2)[C_{11}]$
469.2.u.b	$469$	$2$	469.u	67.e	$11$	$180$	$18$	$3.745$		$_{}$	None	None		$2$	$0$	$-3$	$-4$	$-2$	$-18$			$\mathrm{SU}(2)[C_{11}]$
469.2.w.a	$469$	$2$	469.w	469.w	$22$	$20$	$2$	$3.745$	20.0.$\cdots$.2	$_{}$	$\Q(\sqrt{-7}) $	None		$4$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{U}(1)[D_{22}]$	$q+(\beta _{2}-\beta _{10}+\beta _{19})q^{2}+(-\beta _{5}-2\beta _{8}+\cdots)q^{4}+\cdots$
469.2.w.b	$469$	$2$	469.w	469.w	$22$	$400$	$40$	$3.745$		$_{}$	None	None		$4$	$0$	$-22$	$0$	$0$	$-11$			$\mathrm{SU}(2)[C_{22}]$
469.2.y.a	$469$	$2$	469.y	469.y	$33$	$860$	$43$	$3.745$		$_{}$	None	None		$2$	$0$	$-5$	$-12$	$-13$	$-23$			$\mathrm{SU}(2)[C_{33}]$
469.2.z.a	$469$	$2$	469.z	67.g	$33$	$320$	$16$	$3.745$		$_{}$	None	None		$2$	$0$	$1$	$-2$	$2$	$-16$			$\mathrm{SU}(2)[C_{33}]$
469.2.z.b	$469$	$2$	469.z	67.g	$33$	$360$	$18$	$3.745$		$_{}$	None	None		$2$	$0$	$3$	$-2$	$2$	$18$			$\mathrm{SU}(2)[C_{33}]$
469.2.ba.a	$469$	$2$	469.ba	469.aa	$33$	$880$	$44$	$3.745$		$_{}$	None	None		$4$	$0$	$-11$	$-11$	$-13$	$-16$			$\mathrm{SU}(2)[C_{33}]$
469.2.bb.a	$469$	$2$	469.bb	469.ab	$33$	$860$	$43$	$3.745$		$_{}$	None	None		$2$	$0$	$-14$	$-12$	$-13$	$-14$			$\mathrm{SU}(2)[C_{33}]$
469.2.bd.a	$469$	$2$	469.bd	469.ad	$66$	$40$	$2$	$3.745$		$_{}$	$\Q(\sqrt{-7}) $	None		$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{U}(1)[D_{66}]$
469.2.bd.b	$469$	$2$	469.bd	469.ad	$66$	$840$	$42$	$3.745$		$_{}$	None	None		$4$	$0$	$-38$	$0$	$0$	$-16$			$\mathrm{SU}(2)[C_{66}]$
469.2.bg.a	$469$	$2$	469.bg	469.ag	$66$	$860$	$43$	$3.745$		$_{}$	None	None		$2$	$0$	$-8$	$-32$	$-33$	$-14$			$\mathrm{SU}(2)[C_{66}]$
469.2.bh.a	$469$	$2$	469.bh	469.ah	$66$	$880$	$44$	$3.745$		$_{}$	None	None		$4$	$0$	$-11$	$-33$	$-33$	$-22$			$\mathrm{SU}(2)[C_{66}]$
469.2.bn.a	$469$	$2$	469.bn	469.an	$66$	$860$	$43$	$3.745$		$_{}$	None	None		$2$	$0$	$-11$	$-34$	$-33$	$-15$			$\mathrm{SU}(2)[C_{66}]$
469.3.b.a	$469$	$3$	469.b	67.b	$2$	$68$	$68$	$12.779$		$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
469.3.d.a	$469$	$3$	469.d	7.b	$2$	$88$	$88$	$12.779$		$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$2$			$\mathrm{SU}(2)[C_{2}]$

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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.