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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 (35 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
2667.1.b.a	$2667$	$1$	2667.b	2667.b	$2$	$1$	$1$	$1.331$	$\Q$	$D_{2}$	$\Q(\sqrt{-3}) $, $\Q(\sqrt{-2667}) $	$\Q(\sqrt{889}) $	✓	✓			2667.1.b.a	$4$	$0$	$0$	$-1$	$0$	$1$		$1$		$q-q^{3}+q^{4}+q^{7}+q^{9}-q^{12}+q^{16}+\cdots$
2667.1.b.b	$2667$	$1$	2667.b	2667.b	$2$	$1$	$1$	$1.331$	$\Q$	$D_{2}$	$\Q(\sqrt{-3}) $, $\Q(\sqrt{-2667}) $	$\Q(\sqrt{889}) $	✓	✓			2667.1.b.a	$4$	$0$	$0$	$1$	$0$	$-1$		$1$		$q+q^{3}+q^{4}-q^{7}+q^{9}+q^{12}+q^{16}+\cdots$
2667.1.n.a	$2667$	$1$	2667.n	2667.n	$6$	$2$	$1$	$1.331$	$\Q(\sqrt{-3}) $	$D_{6}$	$\Q(\sqrt{-3}) $	None		✓			2667.1.n.a	$4$	$0$	$0$	$-1$	$0$	$1$		$1$		$q-\zeta_{6}q^{3}+q^{4}+\zeta_{6}q^{7}+\zeta_{6}^{2}q^{9}-\zeta_{6}q^{12}+\cdots$
2667.1.n.b	$2667$	$1$	2667.n	2667.n	$6$	$2$	$1$	$1.331$	$\Q(\sqrt{-3}) $	$D_{6}$	$\Q(\sqrt{-3}) $	None		✓			2667.1.n.a	$4$	$0$	$0$	$1$	$0$	$-1$		$1$		$q+\zeta_{6}q^{3}+q^{4}-\zeta_{6}q^{7}+\zeta_{6}^{2}q^{9}+\zeta_{6}q^{12}+\cdots$
2667.1.bf.a	$2667$	$1$	2667.bf	2667.af	$6$	$4$	$2$	$1.331$	$\Q(\zeta_{12})$	$A_{4}$	None	None		✓	✓	✓	2667.1.bf.a	$4$	$0$	$0$	$-2$	$0$	$-2$		$1$		$q-\zeta_{12}q^{2}+\zeta_{12}^{4}q^{3}+\zeta_{12}q^{5}-\zeta_{12}^{5}q^{6}+\cdots$
2667.1.bi.a	$2667$	$1$	2667.bi	2667.ai	$6$	$4$	$2$	$1.331$	$\Q(\zeta_{12})$	$A_{4}$	None	None		✓	✓	✓	2667.1.bf.a	$4$	$0$	$0$	$4$	$0$	$4$		$1$		$q+\zeta_{12}^{5}q^{2}+q^{3}-\zeta_{12}^{5}q^{5}+\zeta_{12}^{5}q^{6}+\cdots$
2667.1.by.a	$2667$	$1$	2667.by	2667.ay	$14$	$6$	$1$	$1.331$	$\Q(\zeta_{14})$	$D_{14}$	$\Q(\sqrt{-3}) $	None		✓			2667.1.by.a	$4$	$0$	$0$	$-1$	$0$	$-6$		$1$		$q+\zeta_{14}^{2}q^{3}-\zeta_{14}q^{4}-q^{7}+\zeta_{14}^{4}q^{9}+\cdots$
2667.1.by.b	$2667$	$1$	2667.by	2667.ay	$14$	$6$	$1$	$1.331$	$\Q(\zeta_{14})$	$D_{14}$	$\Q(\sqrt{-3}) $	None		✓			2667.1.by.a	$4$	$0$	$0$	$1$	$0$	$-1$		$1$		$q-\zeta_{14}^{2}q^{3}-\zeta_{14}q^{4}-\zeta_{14}^{5}q^{7}+\zeta_{14}^{4}q^{9}+\cdots$
2667.1.cj.a	$2667$	$1$	2667.cj	2667.bj	$18$	$6$	$1$	$1.331$	$\Q(\zeta_{18})$	$D_{9}$	$\Q(\sqrt{-3}) $	None		✓	✓	✓	2667.1.cj.a	$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{18}^{7}q^{3}+\zeta_{18}^{6}q^{4}-\zeta_{18}q^{7}-\zeta_{18}^{5}q^{9}+\cdots$
2667.1.ck.a	$2667$	$1$	2667.ck	2667.bk	$18$	$6$	$1$	$1.331$	$\Q(\zeta_{18})$	$D_{18}$	$\Q(\sqrt{-3}) $	None		✓	✓	✓	2667.1.ck.a	$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{18}^{4}q^{3}+\zeta_{18}^{6}q^{4}-\zeta_{18}^{7}q^{7}+\cdots$
2667.1.cn.a	$2667$	$1$	2667.cn	2667.bn	$18$	$6$	$1$	$1.331$	$\Q(\zeta_{18})$	$D_{18}$	$\Q(\sqrt{-3}) $	None		✓	✓	✓	2667.1.ck.a	$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q+\zeta_{18}^{2}q^{3}+\zeta_{18}^{6}q^{4}-\zeta_{18}^{2}q^{7}+\cdots$
2667.1.co.a	$2667$	$1$	2667.co	2667.bo	$18$	$6$	$1$	$1.331$	$\Q(\zeta_{18})$	$D_{9}$	$\Q(\sqrt{-3}) $	None		✓	✓	✓	2667.1.cj.a	$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q+\zeta_{18}^{8}q^{3}+\zeta_{18}^{6}q^{4}+\zeta_{18}^{8}q^{7}+\cdots$
2667.1.dy.a	$2667$	$1$	2667.dy	2667.cy	$42$	$12$	$1$	$1.331$	$\Q(\zeta_{21})$	$D_{42}$	$\Q(\sqrt{-3}) $	None		✓			2667.1.dy.a	$4$	$0$	$0$	$-1$	$0$	$1$		$1$		$q-\zeta_{42}^{16}q^{3}-\zeta_{42}^{15}q^{4}-\zeta_{42}^{19}q^{7}+\cdots$
2667.1.dy.b	$2667$	$1$	2667.dy	2667.cy	$42$	$12$	$1$	$1.331$	$\Q(\zeta_{21})$	$D_{42}$	$\Q(\sqrt{-3}) $	None		✓			2667.1.dy.a	$4$	$0$	$0$	$1$	$0$	$6$		$1$		$q+\zeta_{42}^{16}q^{3}-\zeta_{42}^{15}q^{4}+\zeta_{42}^{7}q^{7}+\cdots$
2667.1.ei.a	$2667$	$1$	2667.ei	2667.di	$126$	$36$	$1$	$1.331$	$\Q(\zeta_{63})$	$D_{126}$	$\Q(\sqrt{-3}) $	None		✓	✓	✓	2667.1.ei.a	$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q+\zeta_{126}^{10}q^{3}+\zeta_{126}^{12}q^{4}-\zeta_{126}^{28}q^{7}+\cdots$
2667.1.ej.a	$2667$	$1$	2667.ej	2667.dj	$126$	$36$	$1$	$1.331$	$\Q(\zeta_{63})$	$D_{63}$	$\Q(\sqrt{-3}) $	None		✓	✓	✓	2667.1.ej.a	$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q+\zeta_{126}^{20}q^{3}+\zeta_{126}^{24}q^{4}+\zeta_{126}^{56}q^{7}+\cdots$
2667.1.em.a	$2667$	$1$	2667.em	2667.dm	$126$	$36$	$1$	$1.331$	$\Q(\zeta_{63})$	$D_{63}$	$\Q(\sqrt{-3}) $	None		✓	✓	✓	2667.1.ej.a	$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q+\zeta_{126}^{62}q^{3}-\zeta_{126}^{3}q^{4}+\zeta_{126}^{50}q^{7}+\cdots$
2667.1.en.a	$2667$	$1$	2667.en	2667.dn	$126$	$36$	$1$	$1.331$	$\Q(\zeta_{63})$	$D_{126}$	$\Q(\sqrt{-3}) $	None		✓	✓	✓	2667.1.ei.a	$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{126}^{58}q^{3}-\zeta_{126}^{15}q^{4}-\zeta_{126}^{61}q^{7}+\cdots$
2667.2.a.a	$2667$	$2$	2667.a	1.a	$1$	$1$	$1$	$21.296$	$\Q$	$_{}$	None	None	✓	✓			2667.2.a.a	$1$	$1$	$-2$	$1$	$0$	$-1$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{2}+q^{3}+2q^{4}-2q^{6}-q^{7}+q^{9}+\cdots$
2667.2.a.b	$2667$	$2$	2667.a	1.a	$1$	$1$	$1$	$21.296$	$\Q$	$_{}$	None	None	✓	✓			2667.2.a.b	$1$	$0$	$-1$	$-1$	$4$	$-1$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}-q^{4}+4q^{5}+q^{6}-q^{7}+\cdots$
2667.2.a.c	$2667$	$2$	2667.a	1.a	$1$	$1$	$1$	$21.296$	$\Q$	$_{}$	None	None	✓	✓			2667.2.a.c	$1$	$1$	$-1$	$1$	$0$	$1$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}-q^{4}-q^{6}+q^{7}+3q^{8}+\cdots$
2667.2.a.d	$2667$	$2$	2667.a	1.a	$1$	$1$	$1$	$21.296$	$\Q$	$_{}$	None	None	✓	✓			2667.2.a.d	$1$	$0$	$0$	$1$	$3$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-2q^{4}+3q^{5}+q^{7}+q^{9}+6q^{11}+\cdots$
2667.2.a.e	$2667$	$2$	2667.a	1.a	$1$	$1$	$1$	$21.296$	$\Q$	$_{}$	None	None	✓	✓			2667.2.a.e	$1$	$0$	$2$	$1$	$3$	$-1$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{2}+q^{3}+2q^{4}+3q^{5}+2q^{6}+\cdots$
2667.2.a.f	$2667$	$2$	2667.a	1.a	$1$	$2$	$2$	$21.296$	$\Q(\sqrt{17}) $	$_{}$	None	None	✓	✓			2667.2.a.f	$1$	$1$	$0$	$2$	$-3$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-2q^{4}+(-1-\beta )q^{5}-q^{7}+q^{9}+\cdots$
2667.2.a.g	$2667$	$2$	2667.a	1.a	$1$	$2$	$2$	$21.296$	$\Q(\sqrt{2}) $	$_{}$	None	None	✓	✓			2667.2.a.g	$1$	$1$	$0$	$2$	$0$	$2$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{2}+q^{3}-\beta q^{5}+\beta q^{6}+q^{7}-2\beta q^{8}+\cdots$
2667.2.a.h	$2667$	$2$	2667.a	1.a	$1$	$2$	$2$	$21.296$	$\Q(\sqrt{6}) $	$_{}$	None	None	✓	✓			2667.2.a.h	$1$	$0$	$0$	$2$	$0$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{2}+q^{3}+4q^{4}+\beta q^{5}+\beta q^{6}+\cdots$
2667.2.a.i	$2667$	$2$	2667.a	1.a	$1$	$2$	$2$	$21.296$	$\Q(\sqrt{17}) $	$_{}$	None	None	✓	✓			2667.2.a.i	$1$	$0$	$1$	$-2$	$3$	$-2$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{2}-q^{3}+(2+\beta )q^{4}+(1+\beta )q^{5}+\cdots$
2667.2.a.j	$2667$	$2$	2667.a	1.a	$1$	$7$	$7$	$21.296$	7.7.118870813.1	$_{}$	None	None	✓	✓	✓		2667.2.a.j	$1$	$1$	$-2$	$7$	$-8$	$7$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta _{4}q^{2}+q^{3}+(\beta _{1}+\beta _{2}+\beta _{3}-\beta _{4}+\cdots)q^{4}+\cdots$
2667.2.a.k	$2667$	$2$	2667.a	1.a	$1$	$11$	$11$	$21.296$	$\mathbb{Q}[x]/(x^{11} - \cdots)$	$_{}$	None	None	✓	✓	✓		2667.2.a.k	$1$	$1$	$-2$	$11$	$1$	$-11$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+q^{3}+(1+\beta _{2})q^{4}-\beta _{7}q^{5}+\cdots$
2667.2.a.l	$2667$	$2$	2667.a	1.a	$1$	$13$	$13$	$21.296$	$\mathbb{Q}[x]/(x^{13} - \cdots)$	$_{}$	None	None	✓	✓	✓	✓	2667.2.a.l	$1$	$0$	$4$	$-13$	$12$	$13$	$-$	$2^{2}$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}+(1-\beta _{10}+\cdots)q^{5}+\cdots$
2667.2.a.m	$2667$	$2$	2667.a	1.a	$1$	$14$	$14$	$21.296$	$\mathbb{Q}[x]/(x^{14} - \cdots)$	$_{}$	None	None	✓	✓	✓	✓	2667.2.a.m	$1$	$1$	$-5$	$-14$	$-4$	$-14$	$+$	$5$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}-\beta _{3}q^{5}+\cdots$
2667.2.a.n	$2667$	$2$	2667.a	1.a	$1$	$16$	$16$	$21.296$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	$_{}$	None	None	✓	✓	✓		2667.2.a.n	$1$	$0$	$4$	$16$	$5$	$-16$	$-$	$2^{2}$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+q^{3}+(1+\beta _{2})q^{4}+\beta _{7}q^{5}+\cdots$
2667.2.a.o	$2667$	$2$	2667.a	1.a	$1$	$16$	$16$	$21.296$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	$_{}$	None	None	✓	✓	✓		2667.2.a.o	$1$	$0$	$5$	$-16$	$-1$	$-16$	$-$	$2^{3}$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}+\beta _{13}q^{5}+\cdots$
2667.2.a.p	$2667$	$2$	2667.a	1.a	$1$	$18$	$18$	$21.296$	$\mathbb{Q}[x]/(x^{18} - \cdots)$	$_{}$	None	None	✓	✓	✓	✓	2667.2.a.p	$1$	$1$	$-6$	$-18$	$-10$	$18$	$+$	$2\cdot 5$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}+(-1+\beta _{12}+\cdots)q^{5}+\cdots$
2667.2.a.q	$2667$	$2$	2667.a	1.a	$1$	$19$	$19$	$21.296$	$\mathbb{Q}[x]/(x^{19} - \cdots)$	$_{}$	None	None	✓	✓	✓		2667.2.a.q	$1$	$0$	$4$	$19$	$5$	$19$	$-$	$2^{2}$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+q^{3}+(1+\beta _{2})q^{4}-\beta _{10}q^{5}+\cdots$

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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.