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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 12713 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
7.3.b.a	$7$	$3$	7.b	7.b	$2$	$1$	$1$	$0.191$	$\Q$	$\Q(\sqrt{-7}) $	✓	$2$	$0$	$-3$	$0$	$0$	$-7$	$1$	$\mathrm{U}(1)[D_{2}]$	$q-3q^{2}+5q^{4}-7q^{7}-3q^{8}+9q^{9}+\cdots$
8.3.d.a	$8$	$3$	8.d	8.d	$2$	$1$	$1$	$0.218$	$\Q$	$\Q(\sqrt{-2}) $	✓	$2$	$0$	$-2$	$-2$	$0$	$0$	$1$	$\mathrm{U}(1)[D_{2}]$	$q-2q^{2}-2q^{3}+4q^{4}+4q^{6}-8q^{8}+\cdots$
9.3.d.a	$9$	$3$	9.d	9.d	$6$	$2$	$1$	$0.245$	$\Q(\sqrt{-3}) $	None		$2$	$0$	$-3$	$-3$	$6$	$-2$	$1$	$\mathrm{SU}(2)[C_{6}]$	$q+(-1-\zeta_{6})q^{2}+(-3+3\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots$
10.3.c.a	$10$	$3$	10.c	5.c	$4$	$2$	$1$	$0.272$	$\Q(\sqrt{-1}) $	None		$2$	$0$	$-2$	$-4$	$0$	$4$	$1$	$\mathrm{SU}(2)[C_{4}]$	$q+(-1-i)q^{2}+(-2+2i)q^{3}+2iq^{4}+\cdots$
11.3.b.a	$11$	$3$	11.b	11.b	$2$	$1$	$1$	$0.300$	$\Q$	$\Q(\sqrt{-11}) $	✓	$2$	$0$	$0$	$-5$	$-1$	$0$	$1$	$\mathrm{U}(1)[D_{2}]$	$q-5q^{3}+4q^{4}-q^{5}+2^{4}q^{9}-11q^{11}+\cdots$
11.3.d.a	$11$	$3$	11.d	11.d	$10$	$4$	$1$	$0.300$	$\Q(\zeta_{10})$	None		$2$	$0$	$-5$	$0$	$-4$	$10$	$1$	$\mathrm{SU}(2)[C_{10}]$	$q+(-2\zeta_{10}+2\zeta_{10}^{2}-\zeta_{10}^{3})q^{2}+(-2+\cdots)q^{3}+\cdots$
12.3.c.a	$12$	$3$	12.c	3.b	$2$	$1$	$1$	$0.327$	$\Q$	$\Q(\sqrt{-3}) $	✓	$2$	$0$	$0$	$-3$	$0$	$2$	$1$	$\mathrm{U}(1)[D_{2}]$	$q-3q^{3}+2q^{7}+9q^{9}-22q^{13}+26q^{19}+\cdots$
12.3.d.a	$12$	$3$	12.d	4.b	$2$	$2$	$2$	$0.327$	$\Q(\sqrt{-3}) $	None		$2$	$0$	$-2$	$0$	$-4$	$0$	$2$	$\mathrm{SU}(2)[C_{2}]$	$q+(-1-\zeta_{6})q^{2}+\zeta_{6}q^{3}+(-2+2\zeta_{6})q^{4}+\cdots$
13.3.d.a	$13$	$3$	13.d	13.d	$4$	$4$	$2$	$0.354$	$\Q(i, \sqrt{10})$	None		$2$	$0$	$-4$	$-4$	$8$	$-12$	$1$	$\mathrm{SU}(2)[C_{4}]$	$q+(-1+\beta _{1}-\beta _{2})q^{2}+(-1-\beta _{1}+\beta _{3})q^{3}+\cdots$
13.3.f.a	$13$	$3$	13.f	13.f	$12$	$4$	$1$	$0.354$	$\Q(\zeta_{12})$	None		$2$	$0$	$-2$	$-2$	$-14$	$16$	$1$	$\mathrm{SU}(2)[C_{12}]$	$q+(-1+\zeta_{12}^{2}-\zeta_{12}^{3})q^{2}+(\zeta_{12}-\zeta_{12}^{2}+\cdots)q^{3}+\cdots$
14.3.d.a	$14$	$3$	14.d	7.d	$6$	$4$	$2$	$0.381$	$\Q(\sqrt{2}, \sqrt{-3})$	None		$2$	$0$	$0$	$-6$	$-6$	$8$	$1$	$\mathrm{SU}(2)[C_{6}]$	$q+\beta _{1}q^{2}+(-2-\beta _{1}-\beta _{2}+\beta _{3})q^{3}+\cdots$
15.3.c.a	$15$	$3$	15.c	3.b	$2$	$2$	$2$	$0.409$	$\Q(\sqrt{-5}) $	None		$2$	$0$	$0$	$-4$	$0$	$-12$	$1$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta q^{2}+(-2-\beta )q^{3}-q^{4}-\beta q^{5}+\cdots$
15.3.d.a	$15$	$3$	15.d	15.d	$2$	$1$	$1$	$0.409$	$\Q$	$\Q(\sqrt{-15}) $	✓	$2$	$0$	$-1$	$3$	$-5$	$0$	$1$	$\mathrm{U}(1)[D_{2}]$	$q-q^{2}+3q^{3}-3q^{4}-5q^{5}-3q^{6}+\cdots$
15.3.d.b	$15$	$3$	15.d	15.d	$2$	$1$	$1$	$0.409$	$\Q$	$\Q(\sqrt{-15}) $	✓	$2$	$0$	$1$	$-3$	$5$	$0$	$1$	$\mathrm{U}(1)[D_{2}]$	$q+q^{2}-3q^{3}-3q^{4}+5q^{5}-3q^{6}+\cdots$
15.3.f.a	$15$	$3$	15.f	5.c	$4$	$4$	$2$	$0.409$	$\Q(i, \sqrt{6})$	None		$2$	$0$	$-4$	$0$	$-4$	$4$	$1$	$\mathrm{SU}(2)[C_{4}]$	$q+(-1+\beta _{1}-\beta _{2})q^{2}+\beta _{3}q^{3}+(-2\beta _{1}+\cdots)q^{4}+\cdots$
16.3.c.a	$16$	$3$	16.c	4.b	$2$	$1$	$1$	$0.436$	$\Q$	$\Q(\sqrt{-1}) $	✓	$2$	$0$	$0$	$0$	$-6$	$0$	$1$	$\mathrm{U}(1)[D_{2}]$	$q-6q^{5}+9q^{9}+10q^{13}-30q^{17}+\cdots$
16.3.f.a	$16$	$3$	16.f	16.f	$4$	$6$	$3$	$0.436$	6.0.399424.1	None		$2$	$0$	$-2$	$-2$	$-2$	$-4$	$2^{3}$	$\mathrm{SU}(2)[C_{4}]$	$q+\beta _{2}q^{2}+(-1-\beta _{2}+\beta _{5})q^{3}+(-1+\cdots)q^{4}+\cdots$
17.3.e.a	$17$	$3$	17.e	17.e	$16$	$8$	$1$	$0.463$	$\Q(\zeta_{16})$	None		$2$	$0$	$-8$	$-8$	$16$	$8$	$1$	$\mathrm{SU}(2)[C_{16}]$	$q+(-1+\zeta_{16}+\zeta_{16}^{2}-\zeta_{16}^{4}-\zeta_{16}^{5}+\cdots)q^{2}+\cdots$
17.3.e.b	$17$	$3$	17.e	17.e	$16$	$8$	$1$	$0.463$	$\Q(\zeta_{16})$	None		$2$	$0$	$0$	$0$	$-24$	$-16$	$1$	$\mathrm{SU}(2)[C_{16}]$	$q+(-\zeta_{16}^{2}+\zeta_{16}^{4}+\zeta_{16}^{7})q^{2}+(2\zeta_{16}^{2}+\cdots)q^{3}+\cdots$
18.3.b.a	$18$	$3$	18.b	3.b	$2$	$2$	$2$	$0.490$	$\Q(\sqrt{-2}) $	None		$2$	$0$	$0$	$0$	$0$	$-8$	$1$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta q^{2}-2q^{4}-3\beta q^{5}-4q^{7}-2\beta q^{8}+\cdots$
18.3.d.a	$18$	$3$	18.d	9.d	$6$	$4$	$2$	$0.490$	$\Q(\sqrt{-2}, \sqrt{-3})$	None		$2$	$0$	$0$	$0$	$-18$	$2$	$1$	$\mathrm{SU}(2)[C_{6}]$	$q+\beta _{1}q^{2}+(1-2\beta _{1}-2\beta _{2}+\beta _{3})q^{3}+\cdots$
19.3.b.a	$19$	$3$	19.b	19.b	$2$	$1$	$1$	$0.518$	$\Q$	$\Q(\sqrt{-19}) $	✓	$2$	$0$	$0$	$0$	$-9$	$-5$	$1$	$\mathrm{U}(1)[D_{2}]$	$q+4q^{4}-9q^{5}-5q^{7}+9q^{9}+3q^{11}+\cdots$
19.3.b.b	$19$	$3$	19.b	19.b	$2$	$2$	$2$	$0.518$	$\Q(\sqrt{-13}) $	None		$2$	$0$	$0$	$0$	$8$	$-10$	$1$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta q^{2}-\beta q^{3}-9q^{4}+4q^{5}+13q^{6}+\cdots$
19.3.d.a	$19$	$3$	19.d	19.d	$6$	$6$	$3$	$0.518$	6.0.6967728.1	None		$2$	$0$	$-3$	$-9$	$-2$	$0$	$1$	$\mathrm{SU}(2)[C_{6}]$	$q+(-1-\beta _{5})q^{2}+(\beta _{1}+2\beta _{2}+\beta _{3}+\beta _{5})q^{3}+\cdots$
19.3.f.a	$19$	$3$	19.f	19.f	$18$	$12$	$2$	$0.518$	$\mathbb{Q}[x]/(x^{12} + \cdots)$	None		$2$	$0$	$-6$	$0$	$-6$	$6$	$1$	$\mathrm{SU}(2)[C_{18}]$	$q+\beta _{10}q^{2}+(\beta _{1}-\beta _{4}-\beta _{5}+\beta _{6}-\beta _{7}+\cdots)q^{3}+\cdots$
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		$2$	$0$	$0$	$2$	$-6$	$-14$	$1$	$\mathrm{SU}(2)[C_{4}]$	$q+(1-i)q^{3}+(-3+4i)q^{5}+(-7-7i)q^{7}+\cdots$
21.3.b.a	$21$	$3$	21.b	3.b	$2$	$4$	$4$	$0.572$	4.0.65856.1	None		$2$	$0$	$0$	$-2$	$0$	$0$	$1$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{2}+(-\beta _{1}-\beta _{2}+\beta _{3})q^{3}+(-3+\cdots)q^{4}+\cdots$
21.3.d.a	$21$	$3$	21.d	7.b	$2$	$2$	$2$	$0.572$	$\Q(\sqrt{-3}) $	None		$2$	$0$	$2$	$0$	$0$	$2$	$2$	$\mathrm{SU}(2)[C_{2}]$	$q+q^{2}+\zeta_{6}q^{3}-3q^{4}-4\zeta_{6}q^{5}+\zeta_{6}q^{6}+\cdots$
21.3.f.a	$21$	$3$	21.f	7.d	$6$	$2$	$1$	$0.572$	$\Q(\sqrt{-3}) $	None		$2$	$0$	$-3$	$-3$	$9$	$13$	$1$	$\mathrm{SU}(2)[C_{6}]$	$q-3\zeta_{6}q^{2}+(-1-\zeta_{6})q^{3}+(-5+5\zeta_{6})q^{4}+\cdots$
21.3.f.b	$21$	$3$	21.f	7.d	$6$	$2$	$1$	$0.572$	$\Q(\sqrt{-3}) $	None		$2$	$0$	$-1$	$3$	$-9$	$-7$	$1$	$\mathrm{SU}(2)[C_{6}]$	$q-\zeta_{6}q^{2}+(1+\zeta_{6})q^{3}+(3-3\zeta_{6})q^{4}+\cdots$
21.3.f.c	$21$	$3$	21.f	7.d	$6$	$2$	$1$	$0.572$	$\Q(\sqrt{-3}) $	None		$2$	$0$	$2$	$-3$	$-6$	$-7$	$1$	$\mathrm{SU}(2)[C_{6}]$	$q+2\zeta_{6}q^{2}+(-1-\zeta_{6})q^{3}+(-4+2\zeta_{6})q^{5}+\cdots$
21.3.h.a	$21$	$3$	21.h	21.h	$6$	$2$	$1$	$0.572$	$\Q(\sqrt{-3}) $	$\Q(\sqrt{-3}) $		$4$	$0$	$0$	$3$	$0$	$-13$	$1$	$\mathrm{U}(1)[D_{6}]$	$q+3\zeta_{6}q^{3}-4\zeta_{6}q^{4}+(-5-3\zeta_{6})q^{7}+\cdots$
21.3.h.b	$21$	$3$	21.h	21.h	$6$	$4$	$2$	$0.572$	$\Q(\sqrt{-3}, \sqrt{-5})$	None		$4$	$0$	$0$	$-4$	$0$	$14$	$1$	$\mathrm{SU}(2)[C_{6}]$	$q+\beta _{1}q^{2}+(-\beta _{1}-2\beta _{2}+\beta _{3})q^{3}+\beta _{2}q^{4}+\cdots$
22.3.b.a	$22$	$3$	22.b	11.b	$2$	$2$	$2$	$0.599$	$\Q(\sqrt{-2}) $	None		$2$	$0$	$0$	$2$	$-2$	$0$	$1$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta q^{2}+q^{3}-2q^{4}-q^{5}+\beta q^{6}-6\beta q^{7}+\cdots$
22.3.d.a	$22$	$3$	22.d	11.d	$10$	$8$	$2$	$0.599$	8.0.64000000.1	None		$2$	$0$	$0$	$-2$	$2$	$-30$	$1$	$\mathrm{SU}(2)[C_{10}]$	$q+\beta _{1}q^{2}+(1-\beta _{1}-2\beta _{2}+\beta _{3}+2\beta _{4}+\cdots)q^{3}+\cdots$
23.3.b.a	$23$	$3$	23.b	23.b	$2$	$3$	$3$	$0.627$	3.3.621.1	$\Q(\sqrt{-23}) $	✓	$2$	$0$	$0$	$0$	$0$	$0$	$1$	$\mathrm{U}(1)[D_{2}]$	$q+(\beta _{1}+\beta _{2})q^{2}+(-2\beta _{1}-\beta _{2})q^{3}+(4+\cdots)q^{4}+\cdots$
23.3.d.a	$23$	$3$	23.d	23.d	$22$	$30$	$3$	$0.627$		None		$2$	$0$	$-11$	$-11$	$-11$	$-11$		$\mathrm{SU}(2)[C_{22}]$
24.3.b.a	$24$	$3$	24.b	8.d	$2$	$4$	$4$	$0.654$	4.0.4752.1	None		$2$	$0$	$2$	$0$	$0$	$0$	$2$	$\mathrm{SU}(2)[C_{2}]$	$q+(\beta _{1}-\beta _{2})q^{2}+\beta _{2}q^{3}+(-2-\beta _{2}+\cdots)q^{4}+\cdots$
24.3.e.a	$24$	$3$	24.e	3.b	$2$	$2$	$2$	$0.654$	$\Q(\sqrt{-2}) $	None		$2$	$0$	$0$	$2$	$0$	$-12$	$2$	$\mathrm{SU}(2)[C_{2}]$	$q+(1+\beta )q^{3}-2\beta q^{5}-6q^{7}+(-7+2\beta )q^{9}+\cdots$
24.3.h.a	$24$	$3$	24.h	24.h	$2$	$1$	$1$	$0.654$	$\Q$	$\Q(\sqrt{-6}) $	✓	$2$	$0$	$-2$	$3$	$2$	$-10$	$1$	$\mathrm{U}(1)[D_{2}]$	$q-2q^{2}+3q^{3}+4q^{4}+2q^{5}-6q^{6}+\cdots$
24.3.h.b	$24$	$3$	24.h	24.h	$2$	$1$	$1$	$0.654$	$\Q$	$\Q(\sqrt{-6}) $	✓	$2$	$0$	$2$	$-3$	$-2$	$-10$	$1$	$\mathrm{U}(1)[D_{2}]$	$q+2q^{2}-3q^{3}+4q^{4}-2q^{5}-6q^{6}+\cdots$
24.3.h.c	$24$	$3$	24.h	24.h	$2$	$4$	$4$	$0.654$	$\Q(\sqrt{2}, \sqrt{-7})$	None		$4$	$0$	$0$	$0$	$0$	$16$	$2$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{2}+(-\beta _{2}-\beta _{3})q^{3}+(-3+\beta _{3})q^{4}+\cdots$
25.3.c.a	$25$	$3$	25.c	5.c	$4$	$4$	$2$	$0.681$	$\Q(i, \sqrt{6})$	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$	$\mathrm{SU}(2)[C_{4}]$	$q+\beta _{1}q^{2}+\beta _{3}q^{3}-\beta _{2}q^{4}-3q^{6}-4\beta _{1}q^{7}+\cdots$
25.3.f.a	$25$	$3$	25.f	25.f	$20$	$32$	$4$	$0.681$		None		$2$	$0$	$-10$	$-10$	$-10$	$-10$		$\mathrm{SU}(2)[C_{20}]$
26.3.d.a	$26$	$3$	26.d	13.d	$4$	$2$	$1$	$0.708$	$\Q(\sqrt{-1}) $	None		$2$	$0$	$2$	$0$	$-6$	$4$	$1$	$\mathrm{SU}(2)[C_{4}]$	$q+(1+i)q^{2}+2iq^{4}+(-3-3i)q^{5}+\cdots$
26.3.f.a	$26$	$3$	26.f	13.f	$12$	$4$	$1$	$0.708$	$\Q(\zeta_{12})$	None		$2$	$0$	$2$	$0$	$0$	$-22$	$1$	$\mathrm{SU}(2)[C_{12}]$	$q+(\zeta_{12}+\zeta_{12}^{2}-\zeta_{12}^{3})q^{2}+(-\zeta_{12}+\cdots)q^{3}+\cdots$

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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.