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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

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Results (1-50 of 1211 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
4.5.b.a	$4$	$5$	4.b	4.b	$2$	$1$	$1$	$0.413$	$\Q$	$\Q(\sqrt{-1}) $	✓	$2$	$0$	$-4$	$0$	$-14$	$0$		$1$	$\mathrm{U}(1)[D_{2}]$	$q-4q^{2}+2^{4}q^{4}-14q^{5}-2^{6}q^{8}+3^{4}q^{9}+\cdots$
3.7.b.a	$3$	$7$	3.b	3.b	$2$	$1$	$1$	$0.690$	$\Q$	$\Q(\sqrt{-3}) $	✓	$2$	$0$	$0$	$-27$	$0$	$-286$		$1$	$\mathrm{U}(1)[D_{2}]$	$q-3^{3}q^{3}+2^{6}q^{4}-286q^{7}+3^{6}q^{9}+\cdots$
7.5.b.a	$7$	$5$	7.b	7.b	$2$	$1$	$1$	$0.724$	$\Q$	$\Q(\sqrt{-7}) $	✓	$2$	$0$	$1$	$0$	$0$	$49$		$1$	$\mathrm{U}(1)[D_{2}]$	$q+q^{2}-15q^{4}+7^{2}q^{7}-31q^{8}+3^{4}q^{9}+\cdots$
8.5.d.a	$8$	$5$	8.d	8.d	$2$	$1$	$1$	$0.827$	$\Q$	$\Q(\sqrt{-2}) $	✓	$2$	$0$	$4$	$-14$	$0$	$0$		$1$	$\mathrm{U}(1)[D_{2}]$	$q+4q^{2}-14q^{3}+2^{4}q^{4}-56q^{6}+2^{6}q^{8}+\cdots$
11.5.b.a	$11$	$5$	11.b	11.b	$2$	$1$	$1$	$1.137$	$\Q$	$\Q(\sqrt{-11}) $	✓	$2$	$0$	$0$	$7$	$-49$	$0$		$1$	$\mathrm{U}(1)[D_{2}]$	$q+7q^{3}+2^{4}q^{4}-7^{2}q^{5}-2^{5}q^{9}+11^{2}q^{11}+\cdots$
12.5.c.a	$12$	$5$	12.c	3.b	$2$	$1$	$1$	$1.240$	$\Q$	$\Q(\sqrt{-3}) $	✓	$2$	$0$	$0$	$9$	$0$	$-94$		$1$	$\mathrm{U}(1)[D_{2}]$	$q+9q^{3}-94q^{7}+3^{4}q^{9}+146q^{13}+\cdots$
15.5.d.a	$15$	$5$	15.d	15.d	$2$	$1$	$1$	$1.551$	$\Q$	$\Q(\sqrt{-15}) $	✓	$2$	$0$	$-7$	$9$	$25$	$0$		$1$	$\mathrm{U}(1)[D_{2}]$	$q-7q^{2}+9q^{3}+33q^{4}+5^{2}q^{5}-63q^{6}+\cdots$
15.5.d.b	$15$	$5$	15.d	15.d	$2$	$1$	$1$	$1.551$	$\Q$	$\Q(\sqrt{-15}) $	✓	$2$	$0$	$7$	$-9$	$-25$	$0$		$1$	$\mathrm{U}(1)[D_{2}]$	$q+7q^{2}-9q^{3}+33q^{4}-5^{2}q^{5}-63q^{6}+\cdots$
7.7.b.a	$7$	$7$	7.b	7.b	$2$	$1$	$1$	$1.610$	$\Q$	$\Q(\sqrt{-7}) $	✓	$2$	$0$	$9$	$0$	$0$	$-343$		$1$	$\mathrm{U}(1)[D_{2}]$	$q+9q^{2}+17q^{4}-7^{3}q^{7}-423q^{8}+\cdots$
8.7.d.a	$8$	$7$	8.d	8.d	$2$	$1$	$1$	$1.840$	$\Q$	$\Q(\sqrt{-2}) $	✓	$2$	$0$	$-8$	$46$	$0$	$0$		$1$	$\mathrm{U}(1)[D_{2}]$	$q-8q^{2}+46q^{3}+2^{6}q^{4}-368q^{6}+\cdots$
19.5.b.a	$19$	$5$	19.b	19.b	$2$	$1$	$1$	$1.964$	$\Q$	$\Q(\sqrt{-19}) $	✓	$2$	$0$	$0$	$0$	$31$	$-73$		$1$	$\mathrm{U}(1)[D_{2}]$	$q+2^{4}q^{4}+31q^{5}-73q^{7}+3^{4}q^{9}+\cdots$
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}) $	✓	$2$	$0$	$4$	$-2$	$25$	$-82$		$1$	$\mathrm{U}(1)[D_{2}]$	$q+4q^{2}-2q^{3}+2^{4}q^{4}+5^{2}q^{5}-8q^{6}+\cdots$
21.5.h.a	$21$	$5$	21.h	21.h	$6$	$2$	$1$	$2.171$	$\Q(\sqrt{-3}) $	$\Q(\sqrt{-3}) $		$4$	$0$	$0$	$-9$	$0$	$71$		$1$	$\mathrm{U}(1)[D_{6}]$	$q-9\zeta_{6}q^{3}-2^{4}\zeta_{6}q^{4}+(55-39\zeta_{6})q^{7}+\cdots$
23.5.b.a	$23$	$5$	23.b	23.b	$2$	$3$	$3$	$2.378$	3.3.621.1	$\Q(\sqrt{-23}) $	✓	$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{U}(1)[D_{2}]$	$q+(\beta _{1}-2\beta _{2})q^{2}+(6\beta _{1}-\beta _{2})q^{3}+(2^{4}+\cdots)q^{4}+\cdots$
24.5.h.a	$24$	$5$	24.h	24.h	$2$	$1$	$1$	$2.481$	$\Q$	$\Q(\sqrt{-6}) $	✓	$2$	$0$	$-4$	$-9$	$46$	$2$		$1$	$\mathrm{U}(1)[D_{2}]$	$q-4q^{2}-9q^{3}+2^{4}q^{4}+46q^{5}+6^{2}q^{6}+\cdots$
24.5.h.b	$24$	$5$	24.h	24.h	$2$	$1$	$1$	$2.481$	$\Q$	$\Q(\sqrt{-6}) $	✓	$2$	$0$	$4$	$9$	$-46$	$2$		$1$	$\mathrm{U}(1)[D_{2}]$	$q+4q^{2}+9q^{3}+2^{4}q^{4}-46q^{5}+6^{2}q^{6}+\cdots$
11.7.b.a	$11$	$7$	11.b	11.b	$2$	$1$	$1$	$2.531$	$\Q$	$\Q(\sqrt{-11}) $	✓	$2$	$0$	$0$	$10$	$74$	$0$		$1$	$\mathrm{U}(1)[D_{2}]$	$q+10q^{3}+2^{6}q^{4}+74q^{5}-629q^{9}+\cdots$
27.5.b.a	$27$	$5$	27.b	3.b	$2$	$1$	$1$	$2.791$	$\Q$	$\Q(\sqrt{-3}) $	✓	$2$	$0$	$0$	$0$	$0$	$71$		$1$	$\mathrm{U}(1)[D_{2}]$	$q+2^{4}q^{4}+71q^{7}-337q^{13}+2^{8}q^{16}+\cdots$
31.5.b.a	$31$	$5$	31.b	31.b	$2$	$3$	$3$	$3.204$	3.3.837.1	$\Q(\sqrt{-31}) $	✓	$2$	$0$	$0$	$0$	$0$	$0$		$3$	$\mathrm{U}(1)[D_{2}]$	$q+(-\beta _{1}+\beta _{2})q^{2}+(2^{4}-6\beta _{1}+\beta _{2})q^{4}+\cdots$
20.6.e.a	$20$	$6$	20.e	20.e	$4$	$2$	$1$	$3.208$	$\Q(\sqrt{-1}) $	$\Q(\sqrt{-1}) $		$4$	$0$	$8$	$0$	$76$	$0$		$1$	$\mathrm{U}(1)[D_{4}]$	$q+(4+4i)q^{2}+2^{5}iq^{4}+(38+41i)q^{5}+\cdots$
32.5.d.a	$32$	$5$	32.d	8.d	$2$	$1$	$1$	$3.308$	$\Q$	$\Q(\sqrt{-2}) $	✓	$2$	$0$	$0$	$14$	$0$	$0$		$1$	$\mathrm{U}(1)[D_{2}]$	$q+14q^{3}+115q^{9}+46q^{11}-574q^{17}+\cdots$
21.6.g.a	$21$	$6$	21.g	21.g	$6$	$2$	$1$	$3.368$	$\Q(\sqrt{-3}) $	$\Q(\sqrt{-3}) $		$4$	$0$	$0$	$27$	$0$	$211$		$1$	$\mathrm{U}(1)[D_{6}]$	$q+(9+9\zeta_{6})q^{3}+(-2^{5}+2^{5}\zeta_{6})q^{4}+\cdots$
15.7.d.a	$15$	$7$	15.d	15.d	$2$	$1$	$1$	$3.451$	$\Q$	$\Q(\sqrt{-15}) $	✓	$2$	$0$	$-11$	$-27$	$125$	$0$		$1$	$\mathrm{U}(1)[D_{2}]$	$q-11q^{2}-3^{3}q^{3}+57q^{4}+5^{3}q^{5}+\cdots$
15.7.d.b	$15$	$7$	15.d	15.d	$2$	$1$	$1$	$3.451$	$\Q$	$\Q(\sqrt{-15}) $	✓	$2$	$0$	$11$	$27$	$-125$	$0$		$1$	$\mathrm{U}(1)[D_{2}]$	$q+11q^{2}+3^{3}q^{3}+57q^{4}-5^{3}q^{5}+\cdots$
35.5.c.a	$35$	$5$	35.c	35.c	$2$	$1$	$1$	$3.618$	$\Q$	$\Q(\sqrt{-35}) $	✓	$2$	$0$	$0$	$-17$	$25$	$49$		$1$	$\mathrm{U}(1)[D_{2}]$	$q-17q^{3}+2^{4}q^{4}+5^{2}q^{5}+7^{2}q^{7}+\cdots$
35.5.c.b	$35$	$5$	35.c	35.c	$2$	$1$	$1$	$3.618$	$\Q$	$\Q(\sqrt{-35}) $	✓	$2$	$0$	$0$	$17$	$-25$	$-49$		$1$	$\mathrm{U}(1)[D_{2}]$	$q+17q^{3}+2^{4}q^{4}-5^{2}q^{5}-7^{2}q^{7}+\cdots$
16.7.c.a	$16$	$7$	16.c	4.b	$2$	$1$	$1$	$3.681$	$\Q$	$\Q(\sqrt{-1}) $	✓	$2$	$0$	$0$	$0$	$234$	$0$		$1$	$\mathrm{U}(1)[D_{2}]$	$q+234q^{5}+3^{6}q^{9}-4070q^{13}-990q^{17}+\cdots$
36.5.d.a	$36$	$5$	36.d	4.b	$2$	$1$	$1$	$3.721$	$\Q$	$\Q(\sqrt{-1}) $	✓	$2$	$0$	$4$	$0$	$14$	$0$		$1$	$\mathrm{U}(1)[D_{2}]$	$q+4q^{2}+2^{4}q^{4}+14q^{5}+2^{6}q^{8}+56q^{10}+\cdots$
24.6.f.a	$24$	$6$	24.f	24.f	$2$	$2$	$2$	$3.849$	$\Q(\sqrt{-2}) $	$\Q(\sqrt{-2}) $		$4$	$0$	$0$	$-2$	$0$	$0$		$1$	$\mathrm{U}(1)[D_{2}]$	$q+4\beta q^{2}+(-1+11\beta )q^{3}-2^{5}q^{4}+\cdots$
39.5.d.a	$39$	$5$	39.d	39.d	$2$	$1$	$1$	$4.031$	$\Q$	$\Q(\sqrt{-39}) $	✓	$2$	$0$	$-5$	$9$	$-2$	$0$		$1$	$\mathrm{U}(1)[D_{2}]$	$q-5q^{2}+9q^{3}+9q^{4}-2q^{5}-45q^{6}+\cdots$
39.5.d.b	$39$	$5$	39.d	39.d	$2$	$1$	$1$	$4.031$	$\Q$	$\Q(\sqrt{-39}) $	✓	$2$	$0$	$5$	$9$	$2$	$0$		$1$	$\mathrm{U}(1)[D_{2}]$	$q+5q^{2}+9q^{3}+9q^{4}+2q^{5}+45q^{6}+\cdots$
39.5.d.c	$39$	$5$	39.d	39.d	$2$	$2$	$2$	$4.031$	$\Q(\sqrt{39}) $	$\Q(\sqrt{-39}) $	✓	$4$	$0$	$0$	$-18$	$0$	$0$		$1$	$\mathrm{U}(1)[D_{2}]$	$q+\beta q^{2}-9q^{3}+23q^{4}+8\beta q^{5}-9\beta q^{6}+\cdots$
39.5.h.a	$39$	$5$	39.h	39.h	$6$	$2$	$1$	$4.031$	$\Q(\sqrt{-3}) $	$\Q(\sqrt{-3}) $		$4$	$0$	$0$	$9$	$0$	$117$		$1$	$\mathrm{U}(1)[D_{6}]$	$q+(9-9\zeta_{6})q^{3}+2^{4}\zeta_{6}q^{4}+(78-39\zeta_{6})q^{7}+\cdots$
39.5.i.a	$39$	$5$	39.i	39.i	$6$	$2$	$1$	$4.031$	$\Q(\sqrt{-3}) $	$\Q(\sqrt{-3}) $		$4$	$0$	$0$	$-9$	$0$	$-71$		$1$	$\mathrm{U}(1)[D_{6}]$	$q-9\zeta_{6}q^{3}+(-2^{4}+2^{4}\zeta_{6})q^{4}+(-71+\cdots)q^{7}+\cdots$
40.5.e.a	$40$	$5$	40.e	40.e	$2$	$1$	$1$	$4.135$	$\Q$	$\Q(\sqrt{-10}) $	✓	$2$	$0$	$-4$	$0$	$-25$	$62$		$1$	$\mathrm{U}(1)[D_{2}]$	$q-4q^{2}+2^{4}q^{4}-5^{2}q^{5}+62q^{7}-2^{6}q^{8}+\cdots$
40.5.e.b	$40$	$5$	40.e	40.e	$2$	$1$	$1$	$4.135$	$\Q$	$\Q(\sqrt{-10}) $	✓	$2$	$0$	$4$	$0$	$25$	$-62$		$1$	$\mathrm{U}(1)[D_{2}]$	$q+4q^{2}+2^{4}q^{4}+5^{2}q^{5}-62q^{7}+2^{6}q^{8}+\cdots$
27.6.a.a	$27$	$6$	27.a	1.a	$1$	$1$	$1$	$4.330$	$\Q$	$\Q(\sqrt{-3}) $	✓	$2$	$1$	$0$	$0$	$0$	$-211$	$+$	$1$	$N(\mathrm{U}(1))$	$q-2^{5}q^{4}-211q^{7}-775q^{13}+2^{10}q^{16}+\cdots$
19.7.b.a	$19$	$7$	19.b	19.b	$2$	$1$	$1$	$4.371$	$\Q$	$\Q(\sqrt{-19}) $	✓	$2$	$0$	$0$	$0$	$-54$	$610$		$1$	$\mathrm{U}(1)[D_{2}]$	$q+2^{6}q^{4}-54q^{5}+610q^{7}+3^{6}q^{9}+\cdots$
43.5.b.a	$43$	$5$	43.b	43.b	$2$	$1$	$1$	$4.445$	$\Q$	$\Q(\sqrt{-43}) $	✓	$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{U}(1)[D_{2}]$	$q+2^{4}q^{4}+3^{4}q^{9}+199q^{11}-7^{2}q^{13}+\cdots$
28.6.d.a	$28$	$6$	28.d	28.d	$2$	$2$	$2$	$4.491$	$\Q(\sqrt{-7}) $	$\Q(\sqrt{-7}) $		$4$	$0$	$-11$	$0$	$0$	$0$		$1$	$\mathrm{U}(1)[D_{2}]$	$q+(-5-\beta )q^{2}+(23+11\beta )q^{4}+(7^{2}+\cdots)q^{7}+\cdots$
44.5.d.a	$44$	$5$	44.d	11.b	$2$	$2$	$2$	$4.548$	$\Q(\sqrt{33}) $	$\Q(\sqrt{-11}) $	✓	$2$	$0$	$0$	$-7$	$49$	$0$		$1$	$\mathrm{U}(1)[D_{2}]$	$q+(-1-5\beta )q^{3}+(23+3\beta )q^{5}+(120+\cdots)q^{9}+\cdots$
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}) $		$4$	$0$	$0$	$0$	$-234$	$0$		$2^{2}$	$\mathrm{U}(1)[D_{2}]$	$q+2iq^{2}-2^{6}q^{4}+(-117+11i)q^{5}+\cdots$
47.5.b.a	$47$	$5$	47.b	47.b	$2$	$5$	$5$	$4.858$	5.5.6903125.1	$\Q(\sqrt{-47}) $	✓	$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{U}(1)[D_{2}]$	$q+(2\beta _{1}+\beta _{4})q^{2}+(-2\beta _{2}+5\beta _{3})q^{3}+\cdots$
48.5.e.a	$48$	$5$	48.e	3.b	$2$	$1$	$1$	$4.962$	$\Q$	$\Q(\sqrt{-3}) $	✓	$2$	$0$	$0$	$-9$	$0$	$94$		$1$	$\mathrm{U}(1)[D_{2}]$	$q-9q^{3}+94q^{7}+3^{4}q^{9}+146q^{13}+\cdots$
49.5.d.a	$49$	$5$	49.d	7.d	$6$	$2$	$1$	$5.065$	$\Q(\sqrt{-3}) $	$\Q(\sqrt{-7}) $		$4$	$0$	$-1$	$0$	$0$	$0$		$1$	$\mathrm{U}(1)[D_{6}]$	$q-\zeta_{6}q^{2}+(15-15\zeta_{6})q^{4}-31q^{8}+\cdots$
32.6.a.b	$32$	$6$	32.a	1.a	$1$	$1$	$1$	$5.132$	$\Q$	$\Q(\sqrt{-1}) $	✓	$2$	$1$	$0$	$0$	$-82$	$0$	$+$	$1$	$N(\mathrm{U}(1))$	$q-82q^{5}-3^{5}q^{9}-1194q^{13}+2242q^{17}+\cdots$
51.5.c.a	$51$	$5$	51.c	51.c	$2$	$1$	$1$	$5.272$	$\Q$	$\Q(\sqrt{-51}) $	✓	$2$	$0$	$0$	$-9$	$1$	$0$		$1$	$\mathrm{U}(1)[D_{2}]$	$q-9q^{3}+2^{4}q^{4}+q^{5}+3^{4}q^{9}+217q^{11}+\cdots$

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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.