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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 (40 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
1767.1.g.a	$1767$	$1$	1767.g	1767.g	$2$	$1$	$1$	$0.882$	$\Q$	$D_{2}$	$\Q(\sqrt{-3}) $, $\Q(\sqrt{-1767}) $	$\Q(\sqrt{589}) $	✓	✓			1767.1.g.a	$4$	$0$	$0$	$-1$	$0$	$-2$		$1$		$q-q^{3}-q^{4}-2q^{7}+q^{9}+q^{12}-2q^{13}+\cdots$
1767.1.g.b	$1767$	$1$	1767.g	1767.g	$2$	$1$	$1$	$0.882$	$\Q$	$D_{2}$	$\Q(\sqrt{-3}) $, $\Q(\sqrt{-1767}) $	$\Q(\sqrt{589}) $	✓	✓			1767.1.g.a	$4$	$0$	$0$	$1$	$0$	$-2$		$1$		$q+q^{3}-q^{4}-2q^{7}+q^{9}-q^{12}+2q^{13}+\cdots$
1767.1.g.c	$1767$	$1$	1767.g	1767.g	$2$	$2$	$2$	$0.882$	$\Q(\sqrt{2}) $	$D_{4}$	$\Q(\sqrt{-1767}) $	None	✓	✓			1767.1.g.c	$4$	$0$	$0$	$-2$	$0$	$0$		$1$		$q-\beta q^{2}-q^{3}+q^{4}+\beta q^{6}+q^{9}+\beta q^{11}+\cdots$
1767.1.g.d	$1767$	$1$	1767.g	1767.g	$2$	$2$	$2$	$0.882$	$\Q(\sqrt{2}) $	$D_{4}$	$\Q(\sqrt{-1767}) $	None	✓	✓			1767.1.g.c	$4$	$0$	$0$	$2$	$0$	$0$		$1$		$q-\beta q^{2}+q^{3}+q^{4}-\beta q^{6}+q^{9}-\beta q^{11}+\cdots$
1767.1.g.e	$1767$	$1$	1767.g	1767.g	$2$	$4$	$4$	$0.882$	$\Q(\zeta_{16})^+$	$D_{8}$	$\Q(\sqrt{-1767}) $	None	✓	✓			1767.1.g.e	$4$	$0$	$0$	$-4$	$0$	$0$		$1$		$q-\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}+\beta _{1}q^{6}+\cdots$
1767.1.g.f	$1767$	$1$	1767.g	1767.g	$2$	$4$	$4$	$0.882$	$\Q(\zeta_{16})^+$	$D_{8}$	$\Q(\sqrt{-1767}) $	None	✓	✓			1767.1.g.e	$4$	$0$	$0$	$4$	$0$	$0$		$1$		$q-\beta _{1}q^{2}+q^{3}+(1+\beta _{2})q^{4}-\beta _{1}q^{6}+\cdots$
1767.1.y.a	$1767$	$1$	1767.y	1767.y	$6$	$2$	$1$	$0.882$	$\Q(\sqrt{-3}) $	$D_{6}$	$\Q(\sqrt{-3}) $	None		✓			1767.1.y.a	$4$	$0$	$0$	$-1$	$0$	$2$		$1$		$q-\zeta_{6}q^{3}-\zeta_{6}^{2}q^{4}+q^{7}+\zeta_{6}^{2}q^{9}+\cdots$
1767.1.y.b	$1767$	$1$	1767.y	1767.y	$6$	$2$	$1$	$0.882$	$\Q(\sqrt{-3}) $	$D_{6}$	$\Q(\sqrt{-3}) $	None		✓			1767.1.y.a	$4$	$0$	$0$	$1$	$0$	$2$		$1$		$q+\zeta_{6}q^{3}-\zeta_{6}^{2}q^{4}+q^{7}+\zeta_{6}^{2}q^{9}+\cdots$
1767.1.bb.a	$1767$	$1$	1767.bb	1767.ab	$6$	$4$	$2$	$0.882$	$\Q(\zeta_{12})$	$A_{4}$	None	None		✓	✓	✓	1767.1.bb.a	$4$	$0$	$0$	$0$	$0$	$2$		$1$		$q+\zeta_{12}^{5}q^{2}+\zeta_{12}q^{3}+\zeta_{12}^{3}q^{5}-q^{6}+\cdots$
1767.1.bh.a	$1767$	$1$	1767.bh	1767.ah	$6$	$4$	$2$	$0.882$	$\Q(\zeta_{12})$	$A_{4}$	None	None		✓	✓	✓	1767.1.bb.a	$4$	$0$	$0$	$0$	$0$	$2$		$1$		$q-\zeta_{12}q^{2}+\zeta_{12}^{3}q^{3}+\zeta_{12}^{5}q^{5}-\zeta_{12}^{4}q^{6}+\cdots$
1767.1.bs.a	$1767$	$1$	1767.bs	1767.as	$10$	$4$	$1$	$0.882$	$\Q(\zeta_{10})$	$D_{10}$	$\Q(\sqrt{-3}) $	None		✓			1767.1.bs.a	$4$	$0$	$0$	$-1$	$0$	$2$		$1$		$q+\zeta_{10}^{2}q^{3}+\zeta_{10}q^{4}+(\zeta_{10}^{3}-\zeta_{10}^{4}+\cdots)q^{7}+\cdots$
1767.1.bs.b	$1767$	$1$	1767.bs	1767.as	$10$	$4$	$1$	$0.882$	$\Q(\zeta_{10})$	$D_{10}$	$\Q(\sqrt{-3}) $	None		✓			1767.1.bs.a	$4$	$0$	$0$	$1$	$0$	$2$		$1$		$q-\zeta_{10}^{2}q^{3}+\zeta_{10}q^{4}+(\zeta_{10}^{3}-\zeta_{10}^{4}+\cdots)q^{7}+\cdots$
1767.1.ce.a	$1767$	$1$	1767.ce	1767.be	$18$	$6$	$1$	$0.882$	$\Q(\zeta_{18})$	$D_{18}$	$\Q(\sqrt{-3}) $	None		✓	✓	✓	1767.1.ce.a	$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q+\zeta_{18}^{2}q^{3}-\zeta_{18}^{4}q^{4}+(\zeta_{18}^{5}+\zeta_{18}^{7}+\cdots)q^{7}+\cdots$
1767.1.cp.a	$1767$	$1$	1767.cp	1767.bp	$18$	$6$	$1$	$0.882$	$\Q(\zeta_{18})$	$D_{9}$	$\Q(\sqrt{-3}) $	None		✓	✓	✓	1767.1.cp.a	$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{18}^{5}q^{3}-\zeta_{18}q^{4}+(\zeta_{18}^{4}+\zeta_{18}^{8}+\cdots)q^{7}+\cdots$
1767.1.ct.a	$1767$	$1$	1767.ct	1767.bt	$18$	$6$	$1$	$0.882$	$\Q(\zeta_{18})$	$D_{18}$	$\Q(\sqrt{-3}) $	None		✓	✓	✓	1767.1.ce.a	$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q+\zeta_{18}^{5}q^{3}-\zeta_{18}^{4}q^{4}+(\zeta_{18}-\zeta_{18}^{8}+\cdots)q^{7}+\cdots$
1767.1.cv.a	$1767$	$1$	1767.cv	1767.bv	$18$	$6$	$1$	$0.882$	$\Q(\zeta_{18})$	$D_{9}$	$\Q(\sqrt{-3}) $	None		✓	✓	✓	1767.1.cp.a	$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q+\zeta_{18}^{8}q^{3}-\zeta_{18}q^{4}+(\zeta_{18}^{2}-\zeta_{18}^{7}+\cdots)q^{7}+\cdots$
1767.1.di.a	$1767$	$1$	1767.di	1767.ci	$30$	$8$	$1$	$0.882$	$\Q(\zeta_{15})$	$D_{15}$	$\Q(\sqrt{-3}) $	None		✓			1767.1.di.a	$4$	$0$	$0$	$1$	$0$	$2$		$1$		$q+\zeta_{30}^{2}q^{3}-\zeta_{30}q^{4}+(\zeta_{30}^{4}+\zeta_{30}^{8}+\cdots)q^{7}+\cdots$
1767.1.di.b	$1767$	$1$	1767.di	1767.ci	$30$	$8$	$1$	$0.882$	$\Q(\zeta_{15})$	$D_{15}$	$\Q(\sqrt{-3}) $	None		✓			1767.1.di.a	$4$	$0$	$0$	$1$	$0$	$2$		$1$		$q+\zeta_{30}^{2}q^{3}-\zeta_{30}q^{4}+(-\zeta_{30}^{13}+\zeta_{30}^{14}+\cdots)q^{7}+\cdots$
1767.1.dr.a	$1767$	$1$	1767.dr	1767.cr	$30$	$8$	$1$	$0.882$	$\Q(\zeta_{15})$	$D_{30}$	$\Q(\sqrt{-3}) $	None		✓			1767.1.dr.a	$4$	$0$	$0$	$-1$	$0$	$-2$		$1$		$q+\zeta_{30}^{11}q^{3}+\zeta_{30}^{13}q^{4}+(-\zeta_{30}^{2}+\cdots)q^{7}+\cdots$
1767.1.dr.b	$1767$	$1$	1767.dr	1767.cr	$30$	$8$	$1$	$0.882$	$\Q(\zeta_{15})$	$D_{30}$	$\Q(\sqrt{-3}) $	None		✓			1767.1.dr.a	$4$	$0$	$0$	$1$	$0$	$-2$		$1$		$q-\zeta_{30}^{11}q^{3}+\zeta_{30}^{13}q^{4}+(\zeta_{30}^{7}-\zeta_{30}^{14}+\cdots)q^{7}+\cdots$
1767.1.ef.a	$1767$	$1$	1767.ef	1767.df	$90$	$24$	$1$	$0.882$	$\Q(\zeta_{45})$	$D_{45}$	$\Q(\sqrt{-3}) $	None		✓	✓	✓	1767.1.ef.a	$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{90}^{11}q^{3}-\zeta_{90}^{43}q^{4}+(\zeta_{90}^{4}+\zeta_{90}^{32}+\cdots)q^{7}+\cdots$
1767.1.eh.a	$1767$	$1$	1767.eh	1767.dh	$90$	$24$	$1$	$0.882$	$\Q(\zeta_{45})$	$D_{90}$	$\Q(\sqrt{-3}) $	None		✓	✓	✓	1767.1.eh.a	$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q+\zeta_{90}^{37}q^{3}-\zeta_{90}^{26}q^{4}+(-\zeta_{90}^{34}+\cdots)q^{7}+\cdots$
1767.1.el.a	$1767$	$1$	1767.el	1767.dl	$90$	$24$	$1$	$0.882$	$\Q(\zeta_{45})$	$D_{45}$	$\Q(\sqrt{-3}) $	None		✓	✓	✓	1767.1.ef.a	$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q+\zeta_{90}^{34}q^{3}+\zeta_{90}^{32}q^{4}+(-\zeta_{90}^{31}+\cdots)q^{7}+\cdots$
1767.1.ew.a	$1767$	$1$	1767.ew	1767.dw	$90$	$24$	$1$	$0.882$	$\Q(\zeta_{45})$	$D_{90}$	$\Q(\sqrt{-3}) $	None		✓	✓	✓	1767.1.eh.a	$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q+\zeta_{90}^{4}q^{3}+\zeta_{90}^{17}q^{4}+(\zeta_{90}+\zeta_{90}^{23}+\cdots)q^{7}+\cdots$
1767.2.a.a	$1767$	$2$	1767.a	1.a	$1$	$5$	$5$	$14.110$	5.5.36497.1	$_{}$	None	None	✓	✓	✓	✓	1767.2.a.a	$1$	$1$	$-2$	$5$	$0$	$-4$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+q^{3}+(\beta _{1}+\beta _{2})q^{4}+(\beta _{1}-\beta _{3}+\cdots)q^{5}+\cdots$
1767.2.a.b	$1767$	$2$	1767.a	1.a	$1$	$6$	$6$	$14.110$	6.6.3319769.1	$_{}$	None	None	✓	✓	✓	✓	1767.2.a.b	$1$	$1$	$-2$	$6$	$-3$	$-9$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{2}q^{2}+q^{3}+\beta _{4}q^{4}+(-1+\beta _{3}+\cdots)q^{5}+\cdots$
1767.2.a.c	$1767$	$2$	1767.a	1.a	$1$	$9$	$9$	$14.110$	$\mathbb{Q}[x]/(x^{9} - \cdots)$	$_{}$	None	None	✓	✓	✓	✓	1767.2.a.c	$1$	$1$	$-2$	$-9$	$0$	$4$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}-\beta _{4}q^{5}+\cdots$
1767.2.a.d	$1767$	$2$	1767.a	1.a	$1$	$10$	$10$	$14.110$	$\mathbb{Q}[x]/(x^{10} - \cdots)$	$_{}$	None	None	✓	✓	✓	✓	1767.2.a.d	$1$	$1$	$-2$	$-10$	$-3$	$-1$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}-\beta _{4}q^{5}+\cdots$
1767.2.a.e	$1767$	$2$	1767.a	1.a	$1$	$12$	$12$	$14.110$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	$_{}$	None	None	✓	✓	✓	✓	1767.2.a.e	$1$	$0$	$5$	$-12$	$4$	$-4$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}-q^{3}+(\beta _{1}+\beta _{2})q^{4}-\beta _{8}q^{5}+\cdots$
1767.2.a.f	$1767$	$2$	1767.a	1.a	$1$	$15$	$15$	$14.110$	$\mathbb{Q}[x]/(x^{15} - \cdots)$	$_{}$	None	None	✓	✓	✓	✓	1767.2.a.f	$1$	$0$	$5$	$-15$	$9$	$7$	$-$	$2$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}+(1+\beta _{11}+\cdots)q^{5}+\cdots$
1767.2.a.g	$1767$	$2$	1767.a	1.a	$1$	$16$	$16$	$14.110$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	$_{}$	None	None	✓	✓	✓	✓	1767.2.a.g	$1$	$0$	$5$	$16$	$4$	$4$	$-$	$2$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+q^{3}+(2+\beta _{2})q^{4}+\beta _{6}q^{5}+\cdots$
1767.2.a.h	$1767$	$2$	1767.a	1.a	$1$	$18$	$18$	$14.110$	$\mathbb{Q}[x]/(x^{18} - \cdots)$	$_{}$	None	None	✓	✓	✓	✓	1767.2.a.h	$1$	$0$	$2$	$18$	$3$	$7$	$-$	$2\cdot 43$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+q^{3}+(1+\beta _{2})q^{4}-\beta _{9}q^{5}+\cdots$
1767.4.a.a	$1767$	$4$	1767.a	1.a	$1$	$26$	$26$	$104.256$		$_{}$	None	None	✓	✓	✓	✓	1767.4.a.a	$1$	$1$	$-7$	$78$	$-21$	$-91$	$-$		$\mathrm{SU}(2)$
1767.4.a.b	$1767$	$4$	1767.a	1.a	$1$	$29$	$29$	$104.256$		$_{}$	None	None	✓	✓	✓	✓	1767.4.a.b	$1$	$1$	$-7$	$87$	$-15$	$-33$	$-$		$\mathrm{SU}(2)$
1767.4.a.c	$1767$	$4$	1767.a	1.a	$1$	$30$	$30$	$104.256$		$_{}$	None	None	✓	✓	✓	✓	1767.4.a.c	$1$	$1$	$-7$	$-90$	$-21$	$-35$	$-$		$\mathrm{SU}(2)$
1767.4.a.d	$1767$	$4$	1767.a	1.a	$1$	$33$	$33$	$104.256$		$_{}$	None	None	✓	✓	✓	✓	1767.4.a.d	$1$	$1$	$-7$	$-99$	$-15$	$23$	$-$		$\mathrm{SU}(2)$
1767.4.a.e	$1767$	$4$	1767.a	1.a	$1$	$35$	$35$	$104.256$		$_{}$	None	None	✓	✓	✓	✓	1767.4.a.e	$1$	$0$	$7$	$-105$	$39$	$21$	$+$		$\mathrm{SU}(2)$
1767.4.a.f	$1767$	$4$	1767.a	1.a	$1$	$36$	$36$	$104.256$		$_{}$	None	None	✓	✓	✓	✓	1767.4.a.f	$1$	$0$	$7$	$-108$	$5$	$-33$	$+$		$\mathrm{SU}(2)$
1767.4.a.g	$1767$	$4$	1767.a	1.a	$1$	$39$	$39$	$104.256$		$_{}$	None	None	✓	✓	✓	✓	1767.4.a.g	$1$	$0$	$7$	$117$	$39$	$77$	$+$		$\mathrm{SU}(2)$
1767.4.a.h	$1767$	$4$	1767.a	1.a	$1$	$40$	$40$	$104.256$		$_{}$	None	None	✓	✓	✓	✓	1767.4.a.h	$1$	$0$	$7$	$120$	$5$	$23$	$+$		$\mathrm{SU}(2)$

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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.