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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 (42 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
3775.1.c.a	$3775$	$1$	3775.c	755.c	$2$	$4$	$4$	$1.884$	$\Q(i, \sqrt{5})$	$A_{5}$	None	None		✓			3775.1.d.e	$2$	$0$	$0$	$-4$	$0$	$2$		$1$		$q-\beta _{1}q^{2}-q^{3}+\beta _{2}q^{4}+\beta _{1}q^{6}-\beta _{2}q^{7}+\cdots$
3775.1.c.b	$3775$	$1$	3775.c	755.c	$2$	$4$	$4$	$1.884$	$\Q(i, \sqrt{5})$	$A_{5}$	None	None		✓			3775.1.d.e	$2$	$0$	$0$	$4$	$0$	$-2$		$1$		$q-\beta _{1}q^{2}+q^{3}+\beta _{2}q^{4}-\beta _{1}q^{6}+\beta _{2}q^{7}+\cdots$
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			✓		151.1.b.a	$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\beta _{1}q^{2}+(-1+\beta _{2})q^{4}+(\beta _{1}-\beta _{3}+\cdots)q^{8}+\cdots$
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}) $	✓				755.1.c.b	$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q-q^{4}+q^{9}+2q^{11}+q^{16}-2q^{19}+\cdots$
3775.1.d.b	$3775$	$1$	3775.d	151.b	$2$	$2$	$2$	$1.884$	$\Q(\sqrt{-3}) $	$D_{6}$	$\Q(\sqrt{-755}) $	None					755.1.c.d	$4$	$0$	$0$	$0$	$0$	$0$		$2$		$q+(\zeta_{6}+\zeta_{6}^{2})q^{3}-q^{4}+(-1-\zeta_{6}+\zeta_{6}^{2}+\cdots)q^{9}+\cdots$
3775.1.d.c	$3775$	$1$	3775.d	151.b	$2$	$2$	$2$	$1.884$	$\Q(\sqrt{-1}) $	$D_{3}$	$\Q(\sqrt{-755}) $	None					755.1.c.a	$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q-i q^{3}-q^{4}-2 i q^{7}-q^{11}+i q^{12}+\cdots$
3775.1.d.d	$3775$	$1$	3775.d	151.b	$2$	$3$	$3$	$1.884$	$\Q(\zeta_{14})^+$	$D_{7}$	$\Q(\sqrt{-151}) $	None	✓				151.1.b.a	$2$	$0$	$1$	$0$	$0$	$0$		$1$		$q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}+(1+\beta _{2})q^{8}+\cdots$
3775.1.d.e	$3775$	$1$	3775.d	151.b	$2$	$4$	$4$	$1.884$	$\Q(i, \sqrt{5})$	$A_{5}$	None	None		✓			3775.1.d.e	$2$	$0$	$-2$	$0$	$0$	$0$		$1$		$q+\beta _{2}q^{2}+\beta _{3}q^{3}-\beta _{2}q^{4}+\beta _{1}q^{6}+\cdots$
3775.1.d.f	$3775$	$1$	3775.d	151.b	$2$	$4$	$4$	$1.884$	$\Q(i, \sqrt{5})$	$A_{5}$	None	None		✓			3775.1.d.e	$2$	$0$	$2$	$0$	$0$	$0$		$1$		$q-\beta _{2}q^{2}+\beta _{3}q^{3}-\beta _{2}q^{4}-\beta _{1}q^{6}+\cdots$
3775.1.d.g	$3775$	$1$	3775.d	151.b	$2$	$6$	$6$	$1.884$	$\Q(\zeta_{28})^+$	$D_{14}$	$\Q(\sqrt{-151}) $	None	✓		✓		755.1.c.e	$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\beta _{1}q^{2}+(1+\beta _{2})q^{4}+(-\beta _{1}-\beta _{3}+\cdots)q^{8}+\cdots$
3775.1.n.a	$3775$	$1$	3775.n	151.e	$6$	$2$	$1$	$1.884$	$\Q(\sqrt{-3}) $	$D_{6}$	None	$\Q(\sqrt{5}) $			✓	✓	755.1.k.a	$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q+\zeta_{6}q^{4}+q^{9}-\zeta_{6}^{2}q^{11}+\zeta_{6}^{2}q^{16}+\cdots$
3775.1.u.a	$3775$	$1$	3775.u	3775.u	$10$	$4$	$1$	$1.884$	$\Q(\zeta_{10})$	$D_{5}$	$\Q(\sqrt{-151}) $	None		✓			3775.1.u.a	$4$	$0$	$-2$	$0$	$-1$	$0$		$1$		$q+(-\zeta_{10}^{3}+\zeta_{10}^{4})q^{2}+(-\zeta_{10}+\zeta_{10}^{2}+\cdots)q^{4}+\cdots$
3775.1.u.b	$3775$	$1$	3775.u	3775.u	$10$	$8$	$2$	$1.884$	$\Q(\zeta_{20})$	$A_{5}$	None	None		✓			3775.1.u.b	$4$	$0$	$-2$	$0$	$2$	$0$		$1$		$q-\zeta_{20}^{2}q^{2}+\zeta_{20}^{9}q^{3}+\zeta_{20}^{6}q^{5}+\cdots$
3775.1.u.c	$3775$	$1$	3775.u	3775.u	$10$	$8$	$2$	$1.884$	$\Q(\zeta_{20})$	$A_{5}$	None	None		✓			3775.1.u.c	$4$	$0$	$0$	$0$	$2$	$0$		$1$		$q+(\zeta_{20}-\zeta_{20}^{7})q^{3}-\zeta_{20}^{4}q^{4}-\zeta_{20}^{8}q^{5}+\cdots$
3775.1.u.d	$3775$	$1$	3775.u	3775.u	$10$	$24$	$6$	$1.884$	$\Q(\zeta_{35})$	$D_{35}$	$\Q(\sqrt{-151}) $	None		✓	✓		3775.1.u.d	$4$	$0$	$2$	$0$	$1$	$0$		$1$		$q+(\zeta_{70}^{2}-\zeta_{70}^{19})q^{2}+(-\zeta_{70}^{3}+\zeta_{70}^{4}+\cdots)q^{4}+\cdots$
3775.1.bb.a	$3775$	$1$	3775.bb	3775.ab	$10$	$4$	$1$	$1.884$	$\Q(\zeta_{10})$	$D_{10}$	$\Q(\sqrt{-151}) $	None		✓			3775.1.bb.a	$4$	$0$	$0$	$0$	$1$	$0$		$1$		$q+(\zeta_{10}+\zeta_{10}^{2})q^{2}+(\zeta_{10}^{2}+\zeta_{10}^{3}+\cdots)q^{4}+\cdots$
3775.1.bb.b	$3775$	$1$	3775.bb	3775.ab	$10$	$24$	$6$	$1.884$	$\Q(\zeta_{35})$	$D_{70}$	$\Q(\sqrt{-151}) $	None		✓	✓		3775.1.bb.b	$4$	$0$	$0$	$0$	$-1$	$0$		$1$		$q+(\zeta_{70}^{31}+\zeta_{70}^{32})q^{2}+(-\zeta_{70}^{27}+\cdots)q^{4}+\cdots$
3775.1.bi.a	$3775$	$1$	3775.bi	755.o	$12$	$4$	$1$	$1.884$	$\Q(\zeta_{12})$	$S_{4}$	None	None			✓	✓	755.1.o.a	$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{12}q^{4}-\zeta_{12}^{3}q^{9}-\zeta_{12}^{2}q^{11}+\cdots$
3775.2.a.a	$3775$	$2$	3775.a	1.a	$1$	$1$	$1$	$30.144$	$\Q$	$_{}$	None	None	✓				755.2.a.f	$1$	$1$	$-2$	$-3$	$0$	$1$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{2}-3q^{3}+2q^{4}+6q^{6}+q^{7}+\cdots$
3775.2.a.b	$3775$	$2$	3775.a	1.a	$1$	$1$	$1$	$30.144$	$\Q$	$_{}$	None	None	✓				755.2.a.e	$1$	$1$	$-2$	$-1$	$0$	$-3$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{2}-q^{3}+2q^{4}+2q^{6}-3q^{7}+\cdots$
3775.2.a.c	$3775$	$2$	3775.a	1.a	$1$	$1$	$1$	$30.144$	$\Q$	$_{}$	None	None	✓				755.2.a.d	$1$	$1$	$-2$	$3$	$0$	$1$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{2}+3q^{3}+2q^{4}-6q^{6}+q^{7}+\cdots$
3775.2.a.d	$3775$	$2$	3775.a	1.a	$1$	$1$	$1$	$30.144$	$\Q$	$_{}$	None	None	✓				755.2.a.c	$1$	$1$	$-1$	$-1$	$0$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}-q^{4}+q^{6}+3q^{8}-2q^{9}+\cdots$
3775.2.a.e	$3775$	$2$	3775.a	1.a	$1$	$1$	$1$	$30.144$	$\Q$	$_{}$	None	None	✓				755.2.a.b	$1$	$0$	$-1$	$2$	$0$	$-2$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+2q^{3}-q^{4}-2q^{6}-2q^{7}+3q^{8}+\cdots$
3775.2.a.f	$3775$	$2$	3775.a	1.a	$1$	$1$	$1$	$30.144$	$\Q$	$_{}$	None	None	✓				755.2.a.a	$1$	$1$	$0$	$0$	$0$	$-3$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{4}-3q^{7}-3q^{9}+3q^{11}+3q^{13}+\cdots$
3775.2.a.g	$3775$	$2$	3775.a	1.a	$1$	$2$	$2$	$30.144$	$\Q(\sqrt{13}) $	$_{}$	None	None	✓	✓			3775.2.a.g	$1$	$0$	$-1$	$0$	$0$	$5$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta q^{2}+(1+\beta )q^{4}+(3-\beta )q^{7}-3q^{8}+\cdots$
3775.2.a.h	$3775$	$2$	3775.a	1.a	$1$	$2$	$2$	$30.144$	$\Q(\sqrt{13}) $	$_{}$	None	None	✓	✓			3775.2.a.g	$1$	$1$	$1$	$0$	$0$	$-5$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{2}+(1+\beta )q^{4}+(-3+\beta )q^{7}+3q^{8}+\cdots$
3775.2.a.i	$3775$	$2$	3775.a	1.a	$1$	$2$	$2$	$30.144$	$\Q(\sqrt{2}) $	$_{}$	None	None	✓				755.2.a.g	$1$	$0$	$2$	$2$	$0$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+(1+\beta )q^{3}-q^{4}+(1+\beta )q^{6}+\cdots$
3775.2.a.j	$3775$	$2$	3775.a	1.a	$1$	$3$	$3$	$30.144$	3.3.257.1	$_{}$	None	None	✓				151.2.a.b	$1$	$0$	$0$	$-6$	$0$	$6$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta _{2}q^{2}-2q^{3}+(1+\beta _{1}-\beta _{2})q^{4}+\cdots$
3775.2.a.k	$3775$	$2$	3775.a	1.a	$1$	$3$	$3$	$30.144$	$\Q(\zeta_{14})^+$	$_{}$	None	None	✓				151.2.a.a	$1$	$1$	$2$	$1$	$0$	$3$	$+$	$1$	$\mathrm{SU}(2)$	$q+(1-\beta _{1})q^{2}+\beta _{1}q^{3}+(1-2\beta _{1}+\beta _{2})q^{4}+\cdots$
3775.2.a.l	$3775$	$2$	3775.a	1.a	$1$	$4$	$4$	$30.144$	$\Q(\zeta_{24})^+$	$_{}$	None	None	✓				755.2.b.a	$2$	$1$	$0$	$0$	$0$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+\beta _{3}q^{3}+\beta _{2}q^{4}-q^{6}+(3\beta _{1}+\cdots)q^{7}+\cdots$
3775.2.a.m	$3775$	$2$	3775.a	1.a	$1$	$4$	$4$	$30.144$	$\Q(\zeta_{24})^+$	$_{}$	None	None	✓				755.2.b.b	$2$	$1$	$0$	$0$	$0$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+(\beta _{1}+\beta _{3})q^{2}+(\beta _{1}+\beta _{3})q^{3}+2q^{6}+\cdots$
3775.2.a.n	$3775$	$2$	3775.a	1.a	$1$	$5$	$5$	$30.144$	5.5.220669.1	$_{}$	None	None	✓				755.2.a.i	$1$	$1$	$0$	$3$	$0$	$7$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+(1+\beta _{4})q^{3}+(1+\beta _{2})q^{4}+\cdots$
3775.2.a.o	$3775$	$2$	3775.a	1.a	$1$	$5$	$5$	$30.144$	5.5.106069.1	$_{}$	None	None	✓				755.2.a.h	$1$	$0$	$1$	$2$	$0$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta _{4}q^{2}+\beta _{1}q^{3}+(\beta _{1}-\beta _{4})q^{4}+(-1+\cdots)q^{6}+\cdots$
3775.2.a.p	$3775$	$2$	3775.a	1.a	$1$	$6$	$6$	$30.144$	6.6.4838537.1	$_{}$	None	None	✓				151.2.a.c	$1$	$0$	$-1$	$5$	$0$	$-3$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+(1+\beta _{2}-\beta _{3}+\beta _{4})q^{3}+(\beta _{1}+\cdots)q^{4}+\cdots$
3775.2.a.q	$3775$	$2$	3775.a	1.a	$1$	$15$	$15$	$30.144$	$\mathbb{Q}[x]/(x^{15} - \cdots)$	$_{}$	None	None	✓				755.2.a.j	$1$	$1$	$2$	$-5$	$0$	$-11$	$+$	$2^{3}$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}-\beta _{3}q^{3}+(1+\beta _{2})q^{4}+\beta _{4}q^{6}+\cdots$
3775.2.a.r	$3775$	$2$	3775.a	1.a	$1$	$18$	$18$	$30.144$	$\mathbb{Q}[x]/(x^{18} - \cdots)$	$_{}$	None	None	✓				755.2.a.k	$1$	$0$	$2$	$-2$	$0$	$-4$	$-$	$2$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+\beta _{10}q^{3}+(2+\beta _{2})q^{4}+(1+\cdots)q^{6}+\cdots$
3775.2.a.s	$3775$	$2$	3775.a	1.a	$1$	$22$	$22$	$30.144$		$_{}$	None	None	✓				755.2.b.c	$2$	$1$	$0$	$0$	$0$	$0$	$+$		$\mathrm{SU}(2)$
3775.2.a.t	$3775$	$2$	3775.a	1.a	$1$	$23$	$23$	$30.144$		$_{}$	None	None	✓	✓	✓		3775.2.a.t	$1$	$1$	$-6$	$-7$	$0$	$-3$	$+$		$\mathrm{SU}(2)$
3775.2.a.u	$3775$	$2$	3775.a	1.a	$1$	$23$	$23$	$30.144$		$_{}$	None	None	✓	✓			3775.2.a.t	$1$	$0$	$6$	$7$	$0$	$3$	$-$		$\mathrm{SU}(2)$
3775.2.a.v	$3775$	$2$	3775.a	1.a	$1$	$25$	$25$	$30.144$		$_{}$	None	None	✓	✓	✓		3775.2.a.v	$1$	$1$	$-7$	$-5$	$0$	$-8$	$+$		$\mathrm{SU}(2)$
3775.2.a.w	$3775$	$2$	3775.a	1.a	$1$	$25$	$25$	$30.144$		$_{}$	None	None	✓	✓	✓		3775.2.a.v	$1$	$0$	$7$	$5$	$0$	$8$	$-$		$\mathrm{SU}(2)$
3775.2.a.x	$3775$	$2$	3775.a	1.a	$1$	$44$	$44$	$30.144$		$_{}$	None	None	✓		✓		755.2.b.d	$2$	$0$	$0$	$0$	$0$	$0$	$-$		$\mathrm{SU}(2)$

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Hilbert	Bianchi

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.