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Level	Weight	Analytic conductor	Analytic rank	Dim.

Bad $p$	Char.	Primitive character	Character order	Is maximal/largest

Coefficient field	Self-twists	CM/RM discriminant	Inner twist count	Is self-dual

Coefficient ring index	Coefficient ring gens.	Is twist minimal	Projective image

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Results (1-50 of 68 matches)

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Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	Image	CM	RM	Self-dual	Twist minimal	Largest	Maximal	Minimal twist	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	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
161.1.l.a	$161$	$1$	161.l	161.l	$22$	$10$	$1$	$0.080$	$\Q(\zeta_{22})$	$D_{11}$	$\Q(\sqrt{-7}) $	None		✓	✓	✓	161.1.l.a	$4$	$0$	$-2$	$0$	$0$	$-1$		$1$		$q+(-\zeta_{22}+\zeta_{22}^{8})q^{2}+(\zeta_{22}^{2}-\zeta_{22}^{5}+\cdots)q^{4}+\cdots$
161.2.a.a	$161$	$2$	161.a	1.a	$1$	$1$	$1$	$1.286$	$\Q$	$_{}$	None	None	✓	✓			161.2.a.a	$1$	$0$	$-1$	$0$	$2$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{4}+2q^{5}+q^{7}+3q^{8}-3q^{9}+\cdots$
161.2.a.b	$161$	$2$	161.a	1.a	$1$	$2$	$2$	$1.286$	$\Q(\sqrt{5}) $	$_{}$	None	None	✓	✓	✓	✓	161.2.a.b	$1$	$1$	$-1$	$-2$	$-2$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta q^{2}-q^{3}+(-1+\beta )q^{4}+(-2+2\beta )q^{5}+\cdots$
161.2.a.c	$161$	$2$	161.a	1.a	$1$	$3$	$3$	$1.286$	3.3.148.1	$_{}$	None	None	✓	✓	✓	✓	161.2.a.c	$1$	$0$	$-1$	$2$	$2$	$-3$	$-$	$1$	$\mathrm{SU}(2)$	$q+(-\beta _{1}-\beta _{2})q^{2}+(1-\beta _{1})q^{3}+(1+2\beta _{1}+\cdots)q^{4}+\cdots$
161.2.a.d	$161$	$2$	161.a	1.a	$1$	$5$	$5$	$1.286$	5.5.2147108.1	$_{}$	None	None	✓	✓	✓		161.2.a.d	$1$	$0$	$2$	$0$	$-4$	$5$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+\beta _{3}q^{3}+(2+\beta _{2})q^{4}+(-1+\cdots)q^{5}+\cdots$
161.2.c.a	$161$	$2$	161.c	161.c	$2$	$2$	$2$	$1.286$	$\Q(\sqrt{-7}) $	$_{}$	$\Q(\sqrt{-7}) $	None		✓			161.2.c.a	$4$	$0$	$-2$	$0$	$0$	$0$		$2$	$\mathrm{U}(1)[D_{2}]$	$q-q^{2}-q^{4}-\beta q^{7}+3q^{8}+3q^{9}-2\beta q^{11}+\cdots$
161.2.c.b	$161$	$2$	161.c	161.c	$2$	$12$	$12$	$1.286$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	$_{}$	None	None		✓	✓		161.2.c.b	$4$	$0$	$0$	$0$	$0$	$0$		$2^{6}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{4}q^{2}-\beta _{6}q^{3}+(1-\beta _{3})q^{4}-\beta _{2}q^{5}+\cdots$
161.2.e.a	$161$	$2$	161.e	7.c	$3$	$14$	$7$	$1.286$	$\mathbb{Q}[x]/(x^{14} + \cdots)$	$_{}$	None	None		✓			161.2.e.a	$2$	$0$	$0$	$-5$	$-4$	$-2$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q-\beta _{2}q^{2}+(-1-\beta _{6}-\beta _{10}-\beta _{11}+\cdots)q^{3}+\cdots$
161.2.e.b	$161$	$2$	161.e	7.c	$3$	$14$	$7$	$1.286$	$\mathbb{Q}[x]/(x^{14} + \cdots)$	$_{}$	None	None		✓			161.2.e.b	$2$	$0$	$0$	$3$	$4$	$0$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q-\beta _{1}q^{2}+(-\beta _{5}-\beta _{12})q^{3}+(-1+\beta _{2}+\cdots)q^{4}+\cdots$
161.2.g.a	$161$	$2$	161.g	161.g	$6$	$28$	$14$	$1.286$		$_{}$	None	None		✓	✓	✓	161.2.g.a	$4$	$0$	$-4$	$-6$	$0$	$0$			$\mathrm{SU}(2)[C_{6}]$
161.2.i.a	$161$	$2$	161.i	23.c	$11$	$50$	$5$	$1.286$		$_{}$	None	None		✓			161.2.i.a	$2$	$0$	$2$	$0$	$-11$	$5$			$\mathrm{SU}(2)[C_{11}]$
161.2.i.b	$161$	$2$	161.i	23.c	$11$	$70$	$7$	$1.286$		$_{}$	None	None		✓	✓		161.2.i.b	$2$	$0$	$-4$	$-4$	$7$	$-7$			$\mathrm{SU}(2)[C_{11}]$
161.2.k.a	$161$	$2$	161.k	161.k	$22$	$20$	$2$	$1.286$	20.0.$\cdots$.2	$_{}$	$\Q(\sqrt{-7}) $	None		✓			161.2.k.a	$4$	$0$	$2$	$0$	$0$	$0$		$1$	$\mathrm{U}(1)[D_{22}]$	$q+(\beta _{4}+\beta _{6}-\beta _{14})q^{2}+(-\beta _{2}+\beta _{13}+\cdots)q^{4}+\cdots$
161.2.k.b	$161$	$2$	161.k	161.k	$22$	$120$	$12$	$1.286$		$_{}$	None	None		✓	✓		161.2.k.b	$4$	$0$	$-22$	$0$	$0$	$-11$			$\mathrm{SU}(2)[C_{22}]$
161.2.m.a	$161$	$2$	161.m	161.m	$33$	$280$	$14$	$1.286$		$_{}$	None	None		✓	✓	✓	161.2.m.a	$4$	$0$	$-11$	$-9$	$-11$	$-20$			$\mathrm{SU}(2)[C_{33}]$
161.2.o.a	$161$	$2$	161.o	161.o	$66$	$280$	$14$	$1.286$		$_{}$	None	None		✓	✓	✓	161.2.o.a	$4$	$0$	$-7$	$-27$	$-33$	$-22$			$\mathrm{SU}(2)[C_{66}]$
161.3.b.a	$161$	$3$	161.b	7.b	$2$	$28$	$28$	$4.387$		$_{}$	None	None		✓	✓	✓	161.3.b.a	$2$	$0$	$0$	$0$	$0$	$18$			$\mathrm{SU}(2)[C_{2}]$
161.3.d.a	$161$	$3$	161.d	23.b	$2$	$24$	$24$	$4.387$		$_{}$	None	None		✓	✓	✓	161.3.d.a	$2$	$0$	$-2$	$-4$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
161.3.f.a	$161$	$3$	161.f	161.f	$6$	$60$	$30$	$4.387$		$_{}$	None	None		✓	✓	✓	161.3.f.a	$4$	$0$	$-4$	$-2$	$0$	$0$			$\mathrm{SU}(2)[C_{6}]$
161.3.h.a	$161$	$3$	161.h	7.d	$6$	$60$	$30$	$4.387$		$_{}$	None	None		✓	✓	✓	161.3.h.a	$2$	$0$	$0$	$-6$	$0$	$-10$			$\mathrm{SU}(2)[C_{6}]$
161.3.j.a	$161$	$3$	161.j	23.d	$22$	$240$	$24$	$4.387$		$_{}$	None	None		✓	✓	✓	161.3.j.a	$2$	$0$	$2$	$4$	$0$	$0$			$\mathrm{SU}(2)[C_{22}]$
161.3.l.a	$161$	$3$	161.l	161.l	$22$	$20$	$2$	$4.387$	20.0.$\cdots$.2	$_{}$	$\Q(\sqrt{-7}) $	None		✓			161.3.l.a	$4$	$0$	$6$	$0$	$0$	$14$		$1$	$\mathrm{U}(1)[D_{22}]$	$q+(\beta _{4}-\beta _{5}+2\beta _{6}-\beta _{14})q^{2}+(-3\beta _{2}+\cdots)q^{4}+\cdots$
161.3.l.b	$161$	$3$	161.l	161.l	$22$	$280$	$28$	$4.387$		$_{}$	None	None		✓	✓		161.3.l.b	$4$	$0$	$-22$	$0$	$0$	$-29$			$\mathrm{SU}(2)[C_{22}]$
161.3.n.a	$161$	$3$	161.n	161.n	$66$	$600$	$30$	$4.387$		$_{}$	None	None		✓	✓	✓	161.3.n.a	$4$	$0$	$-11$	$-27$	$-33$	$-12$			$\mathrm{SU}(2)[C_{66}]$
161.3.p.a	$161$	$3$	161.p	161.p	$66$	$600$	$30$	$4.387$		$_{}$	None	None		✓	✓	✓	161.3.p.a	$4$	$0$	$-7$	$-9$	$-11$	$-22$			$\mathrm{SU}(2)[C_{66}]$
161.4.a.a	$161$	$4$	161.a	1.a	$1$	$5$	$5$	$9.499$	$\mathbb{Q}[x]/(x^{5} - \cdots)$	$_{}$	None	None	✓	✓	✓	✓	161.4.a.a	$1$	$1$	$-4$	$-11$	$-4$	$35$	$-$	$2$	$\mathrm{SU}(2)$	$q+(-1+\beta _{1})q^{2}+(-2-\beta _{4})q^{3}+\beta _{2}q^{4}+\cdots$
161.4.a.b	$161$	$4$	161.a	1.a	$1$	$8$	$8$	$9.499$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	$_{}$	None	None	✓	✓	✓	✓	161.4.a.b	$1$	$1$	$0$	$-3$	$-24$	$-56$	$-$	$2^{2}$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+\beta _{4}q^{3}+(3+\beta _{1}+\beta _{3}-\beta _{4}+\cdots)q^{4}+\cdots$
161.4.a.c	$161$	$4$	161.a	1.a	$1$	$9$	$9$	$9.499$	$\mathbb{Q}[x]/(x^{9} - \cdots)$	$_{}$	None	None	✓	✓	✓	✓	161.4.a.c	$1$	$0$	$0$	$9$	$-4$	$-63$	$+$	$2^{2}$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+(1-\beta _{4})q^{3}+(5+\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots$
161.4.a.d	$161$	$4$	161.a	1.a	$1$	$12$	$12$	$9.499$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	$_{}$	None	None	✓	✓	✓	✓	161.4.a.d	$1$	$0$	$4$	$1$	$16$	$84$	$+$	$2^{4}$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}-\beta _{4}q^{3}+(6+\beta _{2})q^{4}+(1+\beta _{1}+\cdots)q^{5}+\cdots$
161.4.c.a	$161$	$4$	161.c	161.c	$2$	$2$	$2$	$9.499$	$\Q(\sqrt{-7}) $	$_{}$	$\Q(\sqrt{-7}) $	None		✓			161.4.c.a	$4$	$0$	$10$	$0$	$0$	$0$		$2$	$\mathrm{U}(1)[D_{2}]$	$q+5q^{2}+17q^{4}+7\beta q^{7}+45q^{8}+3^{3}q^{9}+\cdots$
161.4.c.b	$161$	$4$	161.c	161.c	$2$	$8$	$8$	$9.499$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	$_{}$	None	None		✓			161.4.c.b	$4$	$0$	$-8$	$0$	$0$	$0$		$2^{4}\cdot 7$	$\mathrm{SU}(2)[C_{2}]$	$q-q^{2}-\beta _{2}q^{3}-7q^{4}+(-\beta _{1}-\beta _{3}+\cdots)q^{5}+\cdots$
161.4.c.c	$161$	$4$	161.c	161.c	$2$	$36$	$36$	$9.499$		$_{}$	None	None		✓	✓		161.4.c.c	$4$	$0$	$-8$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
161.4.e.a	$161$	$4$	161.e	7.c	$3$	$44$	$22$	$9.499$		$_{}$	None	None		✓			161.4.e.a	$2$	$0$	$0$	$-6$	$-20$	$-12$			$\mathrm{SU}(2)[C_{3}]$
161.4.e.b	$161$	$4$	161.e	7.c	$3$	$44$	$22$	$9.499$		$_{}$	None	None		✓			161.4.e.b	$2$	$0$	$0$	$18$	$20$	$-44$			$\mathrm{SU}(2)[C_{3}]$
161.4.g.a	$161$	$4$	161.g	161.g	$6$	$92$	$46$	$9.499$		$_{}$	None	None		✓	✓	✓	161.4.g.a	$4$	$0$	$0$	$-6$	$0$	$0$			$\mathrm{SU}(2)[C_{6}]$
161.4.i.a	$161$	$4$	161.i	23.c	$11$	$170$	$17$	$9.499$		$_{}$	None	None		✓			161.4.i.a	$2$	$0$	$0$	$10$	$10$	$-119$			$\mathrm{SU}(2)[C_{11}]$
161.4.i.b	$161$	$4$	161.i	23.c	$11$	$190$	$19$	$9.499$		$_{}$	None	None		✓	✓		161.4.i.b	$2$	$0$	$2$	$-2$	$-26$	$133$			$\mathrm{SU}(2)[C_{11}]$
161.4.k.a	$161$	$4$	161.k	161.k	$22$	$20$	$2$	$9.499$	20.0.$\cdots$.2	$_{}$	$\Q(\sqrt{-7}) $	None		✓			161.4.k.a	$4$	$0$	$-10$	$0$	$0$	$0$		$1$	$\mathrm{U}(1)[D_{22}]$	$q+(-3-\beta _{2}-3\beta _{3}-3\beta _{5}+3\beta _{6}-3\beta _{8}+\cdots)q^{2}+\cdots$
161.4.k.b	$161$	$4$	161.k	161.k	$22$	$440$	$44$	$9.499$		$_{}$	None	None		✓	✓		161.4.k.b	$4$	$0$	$-6$	$0$	$0$	$-11$			$\mathrm{SU}(2)[C_{22}]$
161.4.m.a	$161$	$4$	161.m	161.m	$33$	$920$	$46$	$9.499$		$_{}$	None	None		✓	✓	✓	161.4.m.a	$4$	$0$	$-7$	$-9$	$3$	$-22$			$\mathrm{SU}(2)[C_{33}]$
161.4.o.a	$161$	$4$	161.o	161.o	$66$	$920$	$46$	$9.499$		$_{}$	None	None		✓	✓	✓	161.4.o.a	$4$	$0$	$-11$	$-27$	$-33$	$-22$			$\mathrm{SU}(2)[C_{66}]$
161.5.b.a	$161$	$5$	161.b	7.b	$2$	$60$	$60$	$16.643$		$_{}$	None	None		✓	✓	✓	161.5.b.a	$2$	$0$	$0$	$0$	$0$	$-130$			$\mathrm{SU}(2)[C_{2}]$
161.5.d.a	$161$	$5$	161.d	23.b	$2$	$48$	$48$	$16.643$		$_{}$	None	None		✓	✓	✓	161.5.d.a	$2$	$0$	$6$	$20$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
161.6.a.a	$161$	$6$	161.a	1.a	$1$	$10$	$10$	$25.822$	$\mathbb{Q}[x]/(x^{10} - \cdots)$	$_{}$	None	None	✓	✓	✓	✓	161.6.a.a	$1$	$1$	$-8$	$-2$	$-92$	$490$	$+$	$2^{6}$	$\mathrm{SU}(2)$	$q+(-1+\beta _{1})q^{2}-\beta _{3}q^{3}+(7-\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots$
161.6.a.b	$161$	$6$	161.a	1.a	$1$	$13$	$13$	$25.822$	$\mathbb{Q}[x]/(x^{13} - \cdots)$	$_{}$	None	None	✓	✓	✓	✓	161.6.a.b	$1$	$1$	$0$	$-12$	$8$	$-637$	$+$	$2^{7}\cdot 3^{3}$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+(-1+\beta _{4})q^{3}+(12+\beta _{1}+\cdots)q^{4}+\cdots$
161.6.a.c	$161$	$6$	161.a	1.a	$1$	$14$	$14$	$25.822$	$\mathbb{Q}[x]/(x^{14} - \cdots)$	$_{}$	None	None	✓	✓	✓	✓	161.6.a.c	$1$	$0$	$0$	$24$	$108$	$-686$	$-$	$2^{10}$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+(2+\beta _{1}-\beta _{2})q^{3}+(19+\beta _{1}+\cdots)q^{4}+\cdots$
161.6.a.d	$161$	$6$	161.a	1.a	$1$	$17$	$17$	$25.822$	$\mathbb{Q}[x]/(x^{17} - \cdots)$	$_{}$	None	None	✓	✓	✓	✓	161.6.a.d	$1$	$0$	$8$	$34$	$8$	$833$	$-$	$2^{11}$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+(2+\beta _{1}-\beta _{3})q^{3}+(20+\beta _{1}+\cdots)q^{4}+\cdots$
161.6.c.a	$161$	$6$	161.c	161.c	$2$	$2$	$2$	$25.822$	$\Q(\sqrt{-7}) $	$_{}$	$\Q(\sqrt{-7}) $	None		✓			161.6.c.a	$4$	$0$	$-22$	$0$	$0$	$0$		$2$	$\mathrm{U}(1)[D_{2}]$	$q-11q^{2}+89q^{4}+7^{2}\beta q^{7}-627q^{8}+\cdots$
161.6.c.b	$161$	$6$	161.c	161.c	$2$	$76$	$76$	$25.822$		$_{}$	None	None		✓	✓		161.6.c.b	$4$	$0$	$16$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
161.7.b.a	$161$	$7$	161.b	7.b	$2$	$88$	$88$	$37.039$		$_{}$	None	None		✓	✓	✓	161.7.b.a	$2$	$0$	$0$	$0$	$0$	$8$			$\mathrm{SU}(2)[C_{2}]$

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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.