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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 220 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
20.2.a.a	$20$	$2$	20.a	1.a	$1$	$1$	$1$	$0.160$	$\Q$	None	✓	$1$	$0$	$0$	$-2$	$-1$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{3}-q^{5}+2q^{7}+q^{9}+2q^{13}+\cdots$
20.2.e.a	$20$	$2$	20.e	20.e	$4$	$2$	$1$	$0.160$	$\Q(\sqrt{-1}) $	$\Q(\sqrt{-1}) $		$4$	$0$	$-2$	$0$	$-4$	$0$		$1$	$\mathrm{U}(1)[D_{4}]$	$q+(-1-i)q^{2}+2iq^{4}+(-2+i)q^{5}+\cdots$
20.3.b.a	$20$	$3$	20.b	4.b	$2$	$4$	$4$	$0.545$	$\Q(\zeta_{10})$	None		$2$	$0$	$-2$	$0$	$0$	$0$		$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	$q-\zeta_{10}^{2}q^{2}+\zeta_{10}^{3}q^{3}+(-2-\zeta_{10}+\cdots)q^{4}+\cdots$
20.3.d.a	$20$	$3$	20.d	20.d	$2$	$1$	$1$	$0.545$	$\Q$	$\Q(\sqrt{-5}) $	✓	$2$	$0$	$-2$	$4$	$-5$	$-4$		$1$	$\mathrm{U}(1)[D_{2}]$	$q-2q^{2}+4q^{3}+4q^{4}-5q^{5}-8q^{6}+\cdots$
20.3.d.b	$20$	$3$	20.d	20.d	$2$	$1$	$1$	$0.545$	$\Q$	$\Q(\sqrt{-5}) $	✓	$2$	$0$	$2$	$-4$	$-5$	$4$		$1$	$\mathrm{U}(1)[D_{2}]$	$q+2q^{2}-4q^{3}+4q^{4}-5q^{5}-8q^{6}+\cdots$
20.3.d.c	$20$	$3$	20.d	20.d	$2$	$2$	$2$	$0.545$	$\Q(\sqrt{-1}) $	$\Q(\sqrt{-1}) $		$4$	$0$	$0$	$0$	$6$	$0$		$2$	$\mathrm{U}(1)[D_{2}]$	$q+iq^{2}-4q^{4}+(3-2i)q^{5}-4iq^{8}+\cdots$
20.3.f.a	$20$	$3$	20.f	5.c	$4$	$2$	$1$	$0.545$	$\Q(\sqrt{-1}) $	None		$2$	$0$	$0$	$2$	$-6$	$-14$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+(1-i)q^{3}+(-3+4i)q^{5}+(-7-7i)q^{7}+\cdots$
20.4.a.a	$20$	$4$	20.a	1.a	$1$	$1$	$1$	$1.180$	$\Q$	None	✓	$1$	$0$	$0$	$4$	$5$	$-16$	$+$	$1$	$\mathrm{SU}(2)$	$q+4q^{3}+5q^{5}-2^{4}q^{7}-11q^{9}-60q^{11}+\cdots$
20.4.c.a	$20$	$4$	20.c	5.b	$2$	$2$	$2$	$1.180$	$\Q(\sqrt{-19}) $	None		$2$	$0$	$0$	$0$	$14$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta q^{3}+(7+\beta )q^{5}+\beta q^{7}-7^{2}q^{9}+\cdots$
20.4.e.a	$20$	$4$	20.e	20.e	$4$	$2$	$1$	$1.180$	$\Q(\sqrt{-1}) $	$\Q(\sqrt{-1}) $		$4$	$0$	$4$	$0$	$-4$	$0$		$1$	$\mathrm{U}(1)[D_{4}]$	$q+(2+2i)q^{2}+8iq^{4}+(-2-11i)q^{5}+\cdots$
20.4.e.b	$20$	$4$	20.e	20.e	$4$	$12$	$6$	$1.180$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	None		$4$	$0$	$-6$	$0$	$0$	$0$		$2^{14}$	$\mathrm{SU}(2)[C_{4}]$	$q+(\beta _{1}-\beta _{5})q^{2}-\beta _{9}q^{3}+(2\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots$
20.5.b.a	$20$	$5$	20.b	4.b	$2$	$8$	$8$	$2.067$	8.0.$\cdots$.1	None		$2$	$0$	$6$	$0$	$0$	$0$		$2^{14}\cdot 5^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+(1+\beta _{1})q^{2}+\beta _{3}q^{3}+(-2+\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots$
20.5.d.a	$20$	$5$	20.d	20.d	$2$	$1$	$1$	$2.067$	$\Q$	$\Q(\sqrt{-5}) $	✓	$2$	$0$	$-4$	$2$	$25$	$82$		$1$	$\mathrm{U}(1)[D_{2}]$	$q-4q^{2}+2q^{3}+2^{4}q^{4}+5^{2}q^{5}-8q^{6}+\cdots$
20.5.d.b	$20$	$5$	20.d	20.d	$2$	$1$	$1$	$2.067$	$\Q$	$\Q(\sqrt{-5}) $	✓	$2$	$0$	$4$	$-2$	$25$	$-82$		$1$	$\mathrm{U}(1)[D_{2}]$	$q+4q^{2}-2q^{3}+2^{4}q^{4}+5^{2}q^{5}-8q^{6}+\cdots$
20.5.d.c	$20$	$5$	20.d	20.d	$2$	$8$	$8$	$2.067$	8.0.$\cdots$.2	None		$4$	$0$	$0$	$0$	$-40$	$0$		$2^{14}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{2}-\beta _{2}q^{3}+(-6+\beta _{3})q^{4}+(-5+\cdots)q^{5}+\cdots$
20.5.f.a	$20$	$5$	20.f	5.c	$4$	$4$	$2$	$2.067$	$\Q(i, \sqrt{241})$	None		$2$	$0$	$0$	$-10$	$-6$	$110$		$2$	$\mathrm{SU}(2)[C_{4}]$	$q+(-2+2\beta _{1}+\beta _{3})q^{3}+(-6\beta _{1}-\beta _{2}+\cdots)q^{5}+\cdots$
20.6.a.a	$20$	$6$	20.a	1.a	$1$	$1$	$1$	$3.208$	$\Q$	None	✓	$1$	$0$	$0$	$22$	$-25$	$218$	$-$	$1$	$\mathrm{SU}(2)$	$q+22q^{3}-5^{2}q^{5}+218q^{7}+241q^{9}+\cdots$
20.6.c.a	$20$	$6$	20.c	5.b	$2$	$2$	$2$	$3.208$	$\Q(\sqrt{-31}) $	None		$2$	$0$	$0$	$0$	$-10$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta q^{3}+(-5-5\beta )q^{5}-11\beta q^{7}+119q^{9}+\cdots$
20.6.e.a	$20$	$6$	20.e	20.e	$4$	$2$	$1$	$3.208$	$\Q(\sqrt{-1}) $	$\Q(\sqrt{-1}) $		$4$	$0$	$8$	$0$	$76$	$0$		$1$	$\mathrm{U}(1)[D_{4}]$	$q+(4+4i)q^{2}+2^{5}iq^{4}+(38+41i)q^{5}+\cdots$
20.6.e.b	$20$	$6$	20.e	20.e	$4$	$24$	$12$	$3.208$		None		$4$	$0$	$-10$	$0$	$-80$	$0$			$\mathrm{SU}(2)[C_{4}]$
20.7.b.a	$20$	$7$	20.b	4.b	$2$	$12$	$12$	$4.601$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	None		$2$	$0$	$-10$	$0$	$0$	$0$		$2^{33}\cdot 5^{7}$	$\mathrm{SU}(2)[C_{2}]$	$q+(-1-\beta _{2})q^{2}+(-\beta _{2}-\beta _{6})q^{3}+(13+\cdots)q^{4}+\cdots$
20.7.d.a	$20$	$7$	20.d	20.d	$2$	$1$	$1$	$4.601$	$\Q$	$\Q(\sqrt{-5}) $	✓	$2$	$0$	$-8$	$-44$	$-125$	$524$		$1$	$\mathrm{U}(1)[D_{2}]$	$q-8q^{2}-44q^{3}+2^{6}q^{4}-5^{3}q^{5}+352q^{6}+\cdots$
20.7.d.b	$20$	$7$	20.d	20.d	$2$	$1$	$1$	$4.601$	$\Q$	$\Q(\sqrt{-5}) $	✓	$2$	$0$	$8$	$44$	$-125$	$-524$		$1$	$\mathrm{U}(1)[D_{2}]$	$q+8q^{2}+44q^{3}+2^{6}q^{4}-5^{3}q^{5}+352q^{6}+\cdots$
20.7.d.c	$20$	$7$	20.d	20.d	$2$	$2$	$2$	$4.601$	$\Q(\sqrt{-1}) $	$\Q(\sqrt{-1}) $		$4$	$0$	$0$	$0$	$-234$	$0$		$2^{2}$	$\mathrm{U}(1)[D_{2}]$	$q+2iq^{2}-2^{6}q^{4}+(-117+11i)q^{5}+\cdots$
20.7.d.d	$20$	$7$	20.d	20.d	$2$	$12$	$12$	$4.601$	$\mathbb{Q}[x]/(x^{12} + \cdots)$	None		$4$	$0$	$0$	$0$	$460$	$0$		$2^{32}\cdot 3^{2}\cdot 5^{2}\cdot 7^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{1}q^{2}+(\beta _{1}+\beta _{2})q^{3}+(6+\beta _{4}-\beta _{8}+\cdots)q^{4}+\cdots$
20.7.f.a	$20$	$7$	20.f	5.c	$4$	$6$	$3$	$4.601$	$\mathbb{Q}[x]/(x^{6} - \cdots)$	None		$2$	$0$	$0$	$32$	$-156$	$-264$		$2^{7}\cdot 5$	$\mathrm{SU}(2)[C_{4}]$	$q+(5+5\beta _{1}+\beta _{4})q^{3}+(-5^{2}+20\beta _{1}+\cdots)q^{5}+\cdots$
20.8.a.a	$20$	$8$	20.a	1.a	$1$	$1$	$1$	$6.248$	$\Q$	None	✓	$1$	$1$	$0$	$-6$	$-125$	$-706$	$-$	$1$	$\mathrm{SU}(2)$	$q-6q^{3}-5^{3}q^{5}-706q^{7}-2151q^{9}+\cdots$
20.8.a.b	$20$	$8$	20.a	1.a	$1$	$2$	$2$	$6.248$	$\Q(\sqrt{1129}) $	None	✓	$1$	$0$	$0$	$-20$	$250$	$1660$	$+$	$2^{2}$	$\mathrm{SU}(2)$	$q+(-10-\beta )q^{3}+5^{3}q^{5}+(830+9\beta )q^{7}+\cdots$
20.8.c.a	$20$	$8$	20.c	5.b	$2$	$4$	$4$	$6.248$	$\mathbb{Q}[x]/(x^{4} + \cdots)$	None		$2$	$0$	$0$	$0$	$-156$	$0$		$2^{7}\cdot 5$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{3}+(-39-\beta _{1}+\beta _{2})q^{5}+(-5\beta _{1}+\cdots)q^{7}+\cdots$
20.8.e.a	$20$	$8$	20.e	20.e	$4$	$2$	$1$	$6.248$	$\Q(\sqrt{-1}) $	$\Q(\sqrt{-1}) $		$4$	$0$	$-16$	$0$	$556$	$0$		$1$	$\mathrm{U}(1)[D_{4}]$	$q+(-8-8i)q^{2}+2^{7}iq^{4}+(278+29i)q^{5}+\cdots$
20.8.e.b	$20$	$8$	20.e	20.e	$4$	$36$	$18$	$6.248$		None		$4$	$0$	$14$	$0$	$-560$	$0$			$\mathrm{SU}(2)[C_{4}]$
20.9.b.a	$20$	$9$	20.b	4.b	$2$	$16$	$16$	$8.148$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	None		$2$	$0$	$6$	$0$	$0$	$0$		$2^{58}\cdot 5^{16}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{1}q^{2}+(\beta _{1}+\beta _{3})q^{3}+(-3+\beta _{2}+\cdots)q^{4}+\cdots$
20.9.d.a	$20$	$9$	20.d	20.d	$2$	$1$	$1$	$8.148$	$\Q$	$\Q(\sqrt{-5}) $	✓	$2$	$0$	$-16$	$158$	$625$	$-1922$		$1$	$\mathrm{U}(1)[D_{2}]$	$q-2^{4}q^{2}+158q^{3}+2^{8}q^{4}+5^{4}q^{5}+\cdots$
20.9.d.b	$20$	$9$	20.d	20.d	$2$	$1$	$1$	$8.148$	$\Q$	$\Q(\sqrt{-5}) $	✓	$2$	$0$	$16$	$-158$	$625$	$1922$		$1$	$\mathrm{U}(1)[D_{2}]$	$q+2^{4}q^{2}-158q^{3}+2^{8}q^{4}+5^{4}q^{5}+\cdots$
20.9.d.c	$20$	$9$	20.d	20.d	$2$	$20$	$20$	$8.148$	$\mathbb{Q}[x]/(x^{20} + \cdots)$	None		$4$	$0$	$0$	$0$	$-1420$	$0$		$2^{74}\cdot 3^{4}\cdot 5^{12}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{2}+(\beta _{1}+\beta _{6})q^{3}+(-38+\beta _{2}+\cdots)q^{4}+\cdots$
20.9.f.a	$20$	$9$	20.f	5.c	$4$	$8$	$4$	$8.148$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	None		$2$	$0$	$0$	$-70$	$894$	$-2030$		$2^{13}\cdot 5^{3}$	$\mathrm{SU}(2)[C_{4}]$	$q+(-9-9\beta _{1}+\beta _{2})q^{3}+(112-58\beta _{1}+\cdots)q^{5}+\cdots$
20.10.a.a	$20$	$10$	20.a	1.a	$1$	$1$	$1$	$10.301$	$\Q$	None	✓	$1$	$1$	$0$	$-48$	$625$	$-532$	$+$	$1$	$\mathrm{SU}(2)$	$q-48q^{3}+5^{4}q^{5}-532q^{7}-17379q^{9}+\cdots$
20.10.a.b	$20$	$10$	20.a	1.a	$1$	$2$	$2$	$10.301$	$\Q(\sqrt{79}) $	None	✓	$1$	$0$	$0$	$-260$	$-1250$	$-380$	$-$	$2^{4}$	$\mathrm{SU}(2)$	$q+(-130+\beta )q^{3}-5^{4}q^{5}+(-190+\cdots)q^{7}+\cdots$
20.10.c.a	$20$	$10$	20.c	5.b	$2$	$4$	$4$	$10.301$	$\mathbb{Q}[x]/(x^{4} - \cdots)$	None		$2$	$0$	$0$	$0$	$660$	$0$		$2^{7}\cdot 5^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{3}+(165+\beta _{1}-\beta _{3})q^{5}+(3\beta _{1}+\cdots)q^{7}+\cdots$
20.10.e.a	$20$	$10$	20.e	20.e	$4$	$2$	$1$	$10.301$	$\Q(\sqrt{-1}) $	$\Q(\sqrt{-1}) $		$4$	$0$	$-32$	$0$	$1436$	$0$		$1$	$\mathrm{U}(1)[D_{4}]$	$q+(-2^{4}-2^{4}i)q^{2}+2^{9}iq^{4}+(718+\cdots)q^{5}+\cdots$
20.10.e.b	$20$	$10$	20.e	20.e	$4$	$48$	$24$	$10.301$		None		$4$	$0$	$30$	$0$	$-1440$	$0$			$\mathrm{SU}(2)[C_{4}]$
20.11.b.a	$20$	$11$	20.b	4.b	$2$	$20$	$20$	$12.707$	$\mathbb{Q}[x]/(x^{20} - \cdots)$	None		$2$	$0$	$22$	$0$	$0$	$0$		$2^{94}\cdot 3^{4}\cdot 5^{29}$	$\mathrm{SU}(2)[C_{2}]$	$q+(1-\beta _{1})q^{2}+(-\beta _{1}+\beta _{2})q^{3}+(-2^{5}+\cdots)q^{4}+\cdots$
20.11.d.a	$20$	$11$	20.d	20.d	$2$	$1$	$1$	$12.707$	$\Q$	$\Q(\sqrt{-5}) $	✓	$2$	$0$	$-32$	$-236$	$-3125$	$-33364$		$1$	$\mathrm{U}(1)[D_{2}]$	$q-2^{5}q^{2}-236q^{3}+2^{10}q^{4}-5^{5}q^{5}+\cdots$
20.11.d.b	$20$	$11$	20.d	20.d	$2$	$1$	$1$	$12.707$	$\Q$	$\Q(\sqrt{-5}) $	✓	$2$	$0$	$32$	$236$	$-3125$	$33364$		$1$	$\mathrm{U}(1)[D_{2}]$	$q+2^{5}q^{2}+236q^{3}+2^{10}q^{4}-5^{5}q^{5}+\cdots$
20.11.d.c	$20$	$11$	20.d	20.d	$2$	$2$	$2$	$12.707$	$\Q(\sqrt{-1}) $	$\Q(\sqrt{-1}) $		$4$	$0$	$0$	$0$	$-474$	$0$		$2^{2}$	$\mathrm{U}(1)[D_{2}]$	$q+8iq^{2}-2^{10}q^{4}+(-237+779i)q^{5}+\cdots$
20.11.d.d	$20$	$11$	20.d	20.d	$2$	$24$	$24$	$12.707$		None		$4$	$0$	$0$	$0$	$8280$	$0$			$\mathrm{SU}(2)[C_{2}]$
20.11.f.a	$20$	$11$	20.f	5.c	$4$	$10$	$5$	$12.707$	$\mathbb{Q}[x]/(x^{10} + \cdots)$	None		$2$	$0$	$0$	$62$	$894$	$22286$		$2^{22}\cdot 3^{2}\cdot 5^{6}$	$\mathrm{SU}(2)[C_{4}]$	$q+(6+6\beta _{1}-\beta _{2})q^{3}+(90-174\beta _{1}+\cdots)q^{5}+\cdots$
20.12.a.a	$20$	$12$	20.a	1.a	$1$	$1$	$1$	$15.367$	$\Q$	None	✓	$1$	$1$	$0$	$306$	$-3125$	$-32074$	$-$	$1$	$\mathrm{SU}(2)$	$q+306q^{3}-5^{5}q^{5}-32074q^{7}-83511q^{9}+\cdots$
20.12.a.b	$20$	$12$	20.a	1.a	$1$	$2$	$2$	$15.367$	$\Q(\sqrt{46729}) $	None	✓	$1$	$0$	$0$	$220$	$6250$	$3340$	$+$	$2^{2}$	$\mathrm{SU}(2)$	$q+(110-\beta )q^{3}+5^{5}q^{5}+(1670-111\beta )q^{7}+\cdots$
20.12.c.a	$20$	$12$	20.c	5.b	$2$	$6$	$6$	$15.367$	$\mathbb{Q}[x]/(x^{6} + \cdots)$	None		$2$	$0$	$0$	$0$	$-4126$	$0$		$2^{19}\cdot 5^{4}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{3}+(-688+2\beta _{1}-\beta _{2})q^{5}+\cdots$

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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.