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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 (41 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				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*	$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$	Coefficient ring index	Sato-Tate	$q$-expansion
151.1.b.a	$151$	$1$	151.b	151.b	$2$	$3$	$3$	$0.075$	$\Q(\zeta_{14})^+$	$D_{7}$	$\Q(\sqrt{-151}) $	None	✓	$2$	$0$	$-1$	$0$	$-1$	$0$	$1$		$q-\beta _{1}q^{2}+(1+\beta _{2})q^{4}+(-1+\beta _{1}-\beta _{2})q^{5}+\cdots$
755.1.c.b	$755$	$1$	755.c	755.c	$2$	$1$	$1$	$0.377$	$\Q$	$D_{2}$	$\Q(\sqrt{-151}) $, $\Q(\sqrt{-755}) $	$\Q(\sqrt{5}) $	✓	$4$	$0$	$0$	$0$	$-1$	$0$	$1$		$q+q^{4}-q^{5}-q^{9}+2q^{11}+q^{16}+2q^{19}+\cdots$
755.1.c.e	$755$	$1$	755.c	755.c	$2$	$6$	$6$	$0.377$	$\Q(\zeta_{14})$	$D_{14}$	$\Q(\sqrt{-151}) $	None		$4$	$0$	$0$	$0$	$1$	$0$	$1$		$q+(\zeta_{14}^{2}+\zeta_{14}^{5})q^{2}+(-1-\zeta_{14}^{3}+\cdots)q^{4}+\cdots$
1208.1.f.a	$1208$	$1$	1208.f	1208.f	$2$	$1$	$1$	$0.603$	$\Q$	$D_{2}$	$\Q(\sqrt{-151}) $, $\Q(\sqrt{-302}) $	$\Q(\sqrt{2}) $	✓	$4$	$0$	$-1$	$0$	$0$	$0$	$1$		$q-q^{2}+q^{4}-q^{8}-q^{9}+q^{16}+2q^{17}+\cdots$
1208.1.f.e	$1208$	$1$	1208.f	1208.f	$2$	$6$	$6$	$0.603$	$\Q(\zeta_{14})$	$D_{14}$	$\Q(\sqrt{-151}) $	None		$4$	$0$	$1$	$0$	$0$	$0$	$1$		$q-\zeta_{14}^{4}q^{2}-\zeta_{14}q^{4}+(\zeta_{14}^{2}+\zeta_{14}^{5}+\cdots)q^{5}+\cdots$
1359.1.d.a	$1359$	$1$	1359.d	151.b	$2$	$1$	$1$	$0.678$	$\Q$	$D_{2}$	$\Q(\sqrt{-3}) $, $\Q(\sqrt{-151}) $	$\Q(\sqrt{453}) $	✓	$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q-q^{4}+q^{16}+2q^{19}-q^{25}+2q^{31}+\cdots$
1359.1.d.b	$1359$	$1$	1359.d	151.b	$2$	$3$	$3$	$0.678$	$\Q(\zeta_{14})^+$	$D_{7}$	$\Q(\sqrt{-151}) $	None	✓	$2$	$0$	$1$	$0$	$1$	$0$	$1$		$q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}+(1-\beta _{1}+\beta _{2})q^{5}+\cdots$
1359.1.d.c	$1359$	$1$	1359.d	151.b	$2$	$6$	$6$	$0.678$	$\Q(\zeta_{28})^+$	$D_{14}$	$\Q(\sqrt{-151}) $	None	✓	$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q-\beta _{1}q^{2}+(1+\beta _{2})q^{4}+\beta _{3}q^{5}+(-\beta _{1}+\cdots)q^{8}+\cdots$
1661.1.t.a	$1661$	$1$	1661.t	1661.t	$10$	$4$	$1$	$0.829$	$\Q(\zeta_{10})$	$D_{5}$	$\Q(\sqrt{-151}) $	None		$4$	$0$	$3$	$0$	$-2$	$0$	$1$		$q+(1+\zeta_{10}^{4})q^{2}+(1-\zeta_{10}^{3}+\zeta_{10}^{4}+\cdots)q^{4}+\cdots$
1661.1.t.b	$1661$	$1$	1661.t	1661.t	$10$	$24$	$6$	$0.829$	$\Q(\zeta_{35})$	$D_{35}$	$\Q(\sqrt{-151}) $	None		$4$	$0$	$-3$	$0$	$2$	$0$	$1$		$q+(-\zeta_{70}+\zeta_{70}^{20})q^{2}+(\zeta_{70}^{2}-\zeta_{70}^{5}+\cdots)q^{4}+\cdots$
2416.1.e.a	$2416$	$1$	2416.e	151.b	$2$	$3$	$3$	$1.206$	$\Q(\zeta_{14})^+$	$D_{7}$	$\Q(\sqrt{-151}) $	None	✓	$2$	$0$	$0$	$0$	$-1$	$0$	$1$		$q+\beta _{2}q^{5}+q^{9}+\beta _{1}q^{11}-\beta _{1}q^{17}+\cdots$
2416.1.m.a	$2416$	$1$	2416.m	2416.m	$4$	$2$	$1$	$1.206$	$\Q(\sqrt{-1}) $	$D_{4}$	$\Q(\sqrt{-151}) $	None		$4$	$0$	$0$	$0$	$-2$	$0$	$1$		$q+iq^{2}-q^{4}+(-1-i)q^{5}-iq^{8}+\cdots$
2416.1.m.b	$2416$	$1$	2416.m	2416.m	$4$	$12$	$6$	$1.206$	$\Q(\zeta_{28})$	$D_{28}$	$\Q(\sqrt{-151}) $	None		$4$	$0$	$0$	$0$	$2$	$0$	$1$		$q+\zeta_{28}^{13}q^{2}-\zeta_{28}^{12}q^{4}+(\zeta_{28}^{10}+\cdots)q^{5}+\cdots$
2567.1.d.a	$2567$	$1$	2567.d	2567.d	$2$	$1$	$1$	$1.281$	$\Q$	$D_{2}$	$\Q(\sqrt{-151}) $, $\Q(\sqrt{-2567}) $	$\Q(\sqrt{17}) $	✓	$4$	$0$	$2$	$0$	$0$	$0$	$1$		$q+2q^{2}+3q^{4}+4q^{8}-q^{9}+5q^{16}+\cdots$
2567.1.d.d	$2567$	$1$	2567.d	2567.d	$2$	$6$	$6$	$1.281$	$\Q(\zeta_{14})$	$D_{14}$	$\Q(\sqrt{-151}) $	None		$4$	$0$	$-2$	$0$	$0$	$0$	$1$		$q+(-\zeta_{14}^{3}+\zeta_{14}^{4})q^{2}+(1-\zeta_{14}+\zeta_{14}^{6}+\cdots)q^{4}+\cdots$
2567.1.f.a	$2567$	$1$	2567.f	2567.f	$4$	$2$	$1$	$1.281$	$\Q(\sqrt{-1}) $	$D_{4}$	$\Q(\sqrt{-151}) $	None		$4$	$0$	$0$	$0$	$2$	$0$	$1$		$q+q^{4}+(1+i)q^{5}+iq^{9}+(-1+i+\cdots)q^{11}+\cdots$
2567.1.f.b	$2567$	$1$	2567.f	2567.f	$4$	$12$	$6$	$1.281$	$\Q(\zeta_{28})$	$D_{28}$	$\Q(\sqrt{-151}) $	None		$4$	$0$	$0$	$0$	$-2$	$0$	$1$		$q+(-\zeta_{28}^{4}-\zeta_{28}^{10})q^{2}+(-1-\zeta_{28}^{6}+\cdots)q^{4}+\cdots$
2567.1.m.a	$2567$	$1$	2567.m	2567.m	$8$	$4$	$1$	$1.281$	$\Q(\zeta_{8})$	$D_{8}$	$\Q(\sqrt{-151}) $	None		$4$	$0$	$-4$	$0$	$4$	$0$	$1$		$q+(-1-\zeta_{8}^{2})q^{2}+\zeta_{8}^{2}q^{4}+(1-\zeta_{8}^{3}+\cdots)q^{5}+\cdots$
2567.1.m.b	$2567$	$1$	2567.m	2567.m	$8$	$24$	$6$	$1.281$	$\Q(\zeta_{56})$	$D_{56}$	$\Q(\sqrt{-151}) $	None		$4$	$0$	$4$	$0$	$-4$	$0$	$1$		$q+(\zeta_{56}^{4}-\zeta_{56}^{10})q^{2}+(\zeta_{56}^{8}-\zeta_{56}^{14}+\cdots)q^{4}+\cdots$
2869.1.n.a	$2869$	$1$	2869.n	2869.n	$6$	$2$	$1$	$1.432$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-151}) $	None		$4$	$0$	$-2$	$0$	$1$	$0$	$1$		$q-\zeta_{6}q^{2}+3\zeta_{6}^{2}q^{4}+\zeta_{6}q^{5}-2q^{8}+\cdots$
2869.1.n.d	$2869$	$1$	2869.n	2869.n	$6$	$12$	$6$	$1.432$	$\Q(\zeta_{21})$	$D_{21}$	$\Q(\sqrt{-151}) $	None		$4$	$0$	$2$	$0$	$-1$	$0$	$1$		$q+(\zeta_{42}^{8}+\zeta_{42}^{20})q^{2}+(-\zeta_{42}^{7}+\zeta_{42}^{16}+\cdots)q^{4}+\cdots$
2869.1.bj.a	$2869$	$1$	2869.bj	2869.aj	$18$	$6$	$1$	$1.432$	$\Q(\zeta_{18})$	$D_{9}$	$\Q(\sqrt{-151}) $	None		$4$	$0$	$0$	$0$	$-3$	$0$	$1$		$q-\zeta_{18}^{5}q^{2}-3\zeta_{18}q^{4}+(-\zeta_{18}^{3}+\zeta_{18}^{4}+\cdots)q^{5}+\cdots$
2869.1.bj.b	$2869$	$1$	2869.bj	2869.aj	$18$	$36$	$6$	$1.432$	$\Q(\zeta_{63})$	$D_{63}$	$\Q(\sqrt{-151}) $	None		$4$	$0$	$0$	$0$	$3$	$0$	$1$		$q+(-\zeta_{126}^{41}+\zeta_{126}^{50})q^{2}+(-\zeta_{126}^{19}+\cdots)q^{4}+\cdots$
3020.1.j.a	$3020$	$1$	3020.j	3020.j	$4$	$2$	$1$	$1.507$	$\Q(\sqrt{-1}) $	$D_{4}$	$\Q(\sqrt{-151}) $	None		$4$	$0$	$-2$	$0$	$0$	$0$	$1$		$q-q^{2}+q^{4}-iq^{5}-q^{8}+iq^{9}+iq^{10}+\cdots$
3020.1.j.b	$3020$	$1$	3020.j	3020.j	$4$	$2$	$1$	$1.507$	$\Q(\sqrt{-1}) $	$D_{4}$	$\Q(\sqrt{-151}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q-iq^{2}-q^{4}-iq^{5}+iq^{8}+iq^{9}+\cdots$
3020.1.j.c	$3020$	$1$	3020.j	3020.j	$4$	$12$	$6$	$1.507$	$\Q(\zeta_{28})$	$D_{28}$	$\Q(\sqrt{-151}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q+\zeta_{28}^{3}q^{2}+\zeta_{28}^{6}q^{4}-\zeta_{28}^{9}q^{5}+\cdots$
3020.1.j.d	$3020$	$1$	3020.j	3020.j	$4$	$12$	$6$	$1.507$	$\Q(\zeta_{28})$	$D_{28}$	$\Q(\sqrt{-151}) $	None		$4$	$0$	$2$	$0$	$0$	$0$	$1$		$q+\zeta_{28}^{6}q^{2}+\zeta_{28}^{12}q^{4}+\zeta_{28}^{3}q^{5}+\cdots$
3775.1.c.c	$3775$	$1$	3775.c	755.c	$2$	$6$	$6$	$1.884$	6.0.153664.1	$D_{7}$	$\Q(\sqrt{-151}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q-\beta _{1}q^{2}+(-1+\beta _{2})q^{4}+(\beta _{1}-\beta _{3}+\cdots)q^{8}+\cdots$
3775.1.d.a	$3775$	$1$	3775.d	151.b	$2$	$1$	$1$	$1.884$	$\Q$	$D_{2}$	$\Q(\sqrt{-151}) $, $\Q(\sqrt{-755}) $	$\Q(\sqrt{5}) $	✓	$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q-q^{4}+q^{9}+2q^{11}+q^{16}-2q^{19}+\cdots$
3775.1.d.d	$3775$	$1$	3775.d	151.b	$2$	$3$	$3$	$1.884$	$\Q(\zeta_{14})^+$	$D_{7}$	$\Q(\sqrt{-151}) $	None	✓	$2$	$0$	$1$	$0$	$0$	$0$	$1$		$q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}+(1+\beta _{2})q^{8}+\cdots$
3775.1.d.g	$3775$	$1$	3775.d	151.b	$2$	$6$	$6$	$1.884$	$\Q(\zeta_{28})^+$	$D_{14}$	$\Q(\sqrt{-151}) $	None	✓	$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q-\beta _{1}q^{2}+(1+\beta _{2})q^{4}+(-\beta _{1}-\beta _{3}+\cdots)q^{8}+\cdots$
3775.1.u.a	$3775$	$1$	3775.u	3775.u	$10$	$4$	$1$	$1.884$	$\Q(\zeta_{10})$	$D_{5}$	$\Q(\sqrt{-151}) $	None		$4$	$0$	$-2$	$0$	$-1$	$0$	$1$		$q+(-\zeta_{10}^{3}+\zeta_{10}^{4})q^{2}+(-\zeta_{10}+\zeta_{10}^{2}+\cdots)q^{4}+\cdots$
3775.1.u.d	$3775$	$1$	3775.u	3775.u	$10$	$24$	$6$	$1.884$	$\Q(\zeta_{35})$	$D_{35}$	$\Q(\sqrt{-151}) $	None		$4$	$0$	$2$	$0$	$1$	$0$	$1$		$q+(\zeta_{70}^{2}-\zeta_{70}^{19})q^{2}+(-\zeta_{70}^{3}+\zeta_{70}^{4}+\cdots)q^{4}+\cdots$
3775.1.bb.a	$3775$	$1$	3775.bb	3775.ab	$10$	$4$	$1$	$1.884$	$\Q(\zeta_{10})$	$D_{10}$	$\Q(\sqrt{-151}) $	None		$4$	$0$	$0$	$0$	$1$	$0$	$1$		$q+(\zeta_{10}+\zeta_{10}^{2})q^{2}+(\zeta_{10}^{2}+\zeta_{10}^{3}+\cdots)q^{4}+\cdots$
3775.1.bb.b	$3775$	$1$	3775.bb	3775.ab	$10$	$24$	$6$	$1.884$	$\Q(\zeta_{35})$	$D_{70}$	$\Q(\sqrt{-151}) $	None		$4$	$0$	$0$	$0$	$-1$	$0$	$1$		$q+(\zeta_{70}^{31}+\zeta_{70}^{32})q^{2}+(-\zeta_{70}^{27}+\cdots)q^{4}+\cdots$
151.3.b.a	$151$	$3$	151.b	151.b	$2$	$7$	$7$	$4.114$	7.7.$\cdots$.1	$_{}$	$\Q(\sqrt{-151}) $	None	✓	$2$	$0$	$0$	$0$	$0$	$0$	$1$	$\mathrm{U}(1)[D_{2}]$	$q+\beta _{2}q^{2}+(4+\beta _{3}+\beta _{4})q^{4}+(-2\beta _{1}+\cdots)q^{5}+\cdots$
604.2.d.a	$604$	$2$	604.d	604.d	$2$	$14$	$14$	$4.823$	$\mathbb{Q}[x]/(x^{14} - \cdots)$	$_{}$	$\Q(\sqrt{-151}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$2^{3}$	$\mathrm{U}(1)[D_{2}]$	$q-\beta _{1}q^{2}+\beta _{2}q^{4}+\beta _{6}q^{5}-\beta _{3}q^{8}+\cdots$
755.2.f.d	$755$	$2$	755.f	755.f	$4$	$28$	$14$	$6.029$		$_{}$	$\Q(\sqrt{-151}) $	None		$4$	$0$	$0$	$0$	$0$	$0$		$\mathrm{U}(1)[D_{4}]$
1359.2.b.b	$1359$	$2$	1359.b	453.b	$2$	$28$	$28$	$10.852$		$_{}$	$\Q(\sqrt{-151}) $	None		$4$	$0$	$0$	$0$	$0$	$0$		$\mathrm{U}(1)[D_{2}]$
151.5.b.a	$151$	$5$	151.b	151.b	$2$	$7$	$7$	$15.609$	7.7.$\cdots$.1	$_{}$	$\Q(\sqrt{-151}) $	None	✓	$2$	$0$	$0$	$0$	$0$	$0$	$3^{3}$	$\mathrm{U}(1)[D_{2}]$	$q+\beta _{2}q^{2}+(2^{4}+3\beta _{1}-2\beta _{6})q^{4}+(-3\beta _{3}+\cdots)q^{5}+\cdots$
151.7.b.a	$151$	$7$	151.b	151.b	$2$	$7$	$7$	$34.738$	7.7.$\cdots$.1	$_{}$	$\Q(\sqrt{-151}) $	None	✓	$2$	$0$	$0$	$0$	$0$	$0$	$1$	$\mathrm{U}(1)[D_{2}]$	$q+(5\beta _{1}+\beta _{6})q^{2}+(2^{6}+6\beta _{2}+19\beta _{5}+\cdots)q^{4}+\cdots$

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Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 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.