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Level	Weight	Analytic conductor	Analytic rank	Dim.

Bad $p$	Char.	Primitive character	Character order	Coefficient field

Self-twists	CM/RM discriminant	Inner twist count	Is twist minimal	Is self-dual

$Nk^2$	Coefficient ring index	Coefficient ring gens.	Projective image	Projective image type

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Results (30 matches)

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Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	Image	CM	RM	Self-dual	Twist minimal	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	Minimal twist	Inner twists	Rank*	$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
3891.1.c.a	$3891$	$1$	3891.c	3891.c	$2$	$1$	$1$	$1.942$	$\Q$	$D_{3}$	$\Q(\sqrt{-3891}) $	None	✓	✓	3891.1.c.a	$2$	$0$	$0$	$1$	$-1$	$-1$		$1$		$q+q^{3}+q^{4}-q^{5}-q^{7}+q^{9}-q^{11}+\cdots$
3891.1.c.b	$3891$	$1$	3891.c	3891.c	$2$	$1$	$1$	$1.942$	$\Q$	$D_{2}$	$\Q(\sqrt{-3}) $, $\Q(\sqrt{-3891}) $	$\Q(\sqrt{1297}) $	✓	✓	3891.1.c.b	$4$	$0$	$0$	$1$	$0$	$2$		$1$		$q+q^{3}+q^{4}+2q^{7}+q^{9}+q^{12}-2q^{13}+\cdots$
3891.1.c.c	$3891$	$1$	3891.c	3891.c	$2$	$1$	$1$	$1.942$	$\Q$	$D_{3}$	$\Q(\sqrt{-3891}) $	None	✓	✓	3891.1.c.a	$2$	$0$	$0$	$1$	$1$	$-1$		$1$		$q+q^{3}+q^{4}+q^{5}-q^{7}+q^{9}+q^{11}+\cdots$
3891.1.c.d	$3891$	$1$	3891.c	3891.c	$2$	$2$	$2$	$1.942$	$\Q(\sqrt{2}) $	$D_{4}$	$\Q(\sqrt{-3891}) $	None	✓	✓	3891.1.c.d	$4$	$0$	$0$	$-2$	$0$	$-4$		$1$		$q-q^{3}+q^{4}-\beta q^{5}-2q^{7}+q^{9}-\beta q^{11}+\cdots$
3891.1.c.e	$3891$	$1$	3891.c	3891.c	$2$	$2$	$2$	$1.942$	$\Q(\sqrt{3}) $	$D_{6}$	$\Q(\sqrt{-3891}) $	None	✓	✓	3891.1.c.e	$4$	$0$	$0$	$2$	$0$	$-2$		$1$		$q+q^{3}+q^{4}-\beta q^{5}-q^{7}+q^{9}+\beta q^{11}+\cdots$
3891.1.c.f	$3891$	$1$	3891.c	3891.c	$2$	$4$	$4$	$1.942$	$\Q(\zeta_{24})^+$	$D_{12}$	$\Q(\sqrt{-3891}) $	None	✓	✓	3891.1.c.f	$4$	$0$	$0$	$-4$	$0$	$4$		$1$		$q-q^{3}+q^{4}-\beta _{1}q^{5}+q^{7}+q^{9}-\beta _{3}q^{11}+\cdots$
3891.1.c.g	$3891$	$1$	3891.c	3891.c	$2$	$10$	$10$	$1.942$	$\Q(\zeta_{22})$	$D_{22}$	None	$\Q(\sqrt{1297}) $		✓	3891.1.c.g	$4$	$0$	$0$	$-1$	$0$	$-2$		$1$		$q+(-\zeta_{22}-\zeta_{22}^{10})q^{2}-\zeta_{22}^{5}q^{3}+\cdots$
3891.1.g.a	$3891$	$1$	3891.g	3891.g	$4$	$2$	$1$	$1.942$	$\Q(\sqrt{-1}) $	$D_{4}$	$\Q(\sqrt{-3}) $	None		✓	3891.1.g.a	$4$	$0$	$0$	$2$	$0$	$0$		$1$		$q+q^{3}-q^{4}+q^{9}-q^{12}-iq^{13}+q^{16}+\cdots$
3891.1.i.a	$3891$	$1$	3891.i	3891.i	$6$	$2$	$1$	$1.942$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-3}) $	None		✓	3891.1.i.a	$4$	$0$	$0$	$-1$	$0$	$1$		$1$		$q-\zeta_{6}q^{3}-\zeta_{6}q^{4}+\zeta_{6}q^{7}+\zeta_{6}^{2}q^{9}+\cdots$
3891.1.i.b	$3891$	$1$	3891.i	3891.i	$6$	$4$	$2$	$1.942$	$\Q(\sqrt{-2}, \sqrt{-3})$	$S_{4}$	None	None		✓	3891.1.i.b	$4$	$0$	$0$	$2$	$0$	$2$		$1$		$q+\beta _{1}q^{2}+\beta _{2}q^{3}+\beta _{2}q^{4}+\beta _{3}q^{5}+\cdots$
3891.1.j.a	$3891$	$1$	3891.j	3891.j	$6$	$2$	$1$	$1.942$	$\Q(\sqrt{-3}) $	$D_{6}$	$\Q(\sqrt{-3}) $	None		✓	3891.1.j.a	$4$	$0$	$0$	$-1$	$0$	$1$		$1$		$q-\zeta_{6}q^{3}-\zeta_{6}q^{4}+\zeta_{6}q^{7}+\zeta_{6}^{2}q^{9}+\cdots$
3891.1.l.a	$3891$	$1$	3891.l	3891.l	$8$	$4$	$1$	$1.942$	$\Q(\zeta_{8})$	$D_{8}$	$\Q(\sqrt{-3}) $	None		✓	3891.1.l.a	$4$	$0$	$0$	$4$	$0$	$4$		$1$		$q+q^{3}-\zeta_{8}^{2}q^{4}+(1-\zeta_{8}^{2})q^{7}+q^{9}+\cdots$
3891.1.n.a	$3891$	$1$	3891.n	3891.n	$12$	$4$	$1$	$1.942$	$\Q(\zeta_{12})$	$D_{12}$	$\Q(\sqrt{-3}) $	None		✓	3891.1.n.a	$4$	$0$	$0$	$-2$	$0$	$6$		$1$		$q+\zeta_{12}^{4}q^{3}-\zeta_{12}^{4}q^{4}+(1+\zeta_{12}^{2}+\cdots)q^{7}+\cdots$
3891.1.s.a	$3891$	$1$	3891.s	3891.s	$18$	$6$	$1$	$1.942$	$\Q(\zeta_{18})$	$D_{9}$	$\Q(\sqrt{-3}) $	None		✓	3891.1.s.a	$4$	$0$	$0$	$0$	$0$	$-3$		$1$		$q+\zeta_{18}^{4}q^{3}-\zeta_{18}q^{4}+(\zeta_{18}^{2}-\zeta_{18}^{3}+\cdots)q^{7}+\cdots$
3891.1.t.a	$3891$	$1$	3891.t	3891.t	$18$	$6$	$1$	$1.942$	$\Q(\zeta_{18})$	$D_{18}$	$\Q(\sqrt{-3}) $	None		✓	3891.1.t.a	$4$	$0$	$0$	$0$	$0$	$-3$		$1$		$q-\zeta_{18}^{5}q^{3}+\zeta_{18}^{8}q^{4}+(\zeta_{18}^{6}-\zeta_{18}^{7}+\cdots)q^{7}+\cdots$
3891.1.v.a	$3891$	$1$	3891.v	3891.v	$24$	$8$	$1$	$1.942$	$\Q(\zeta_{24})$	$D_{24}$	$\Q(\sqrt{-3}) $	None		✓	3891.1.v.a	$4$	$0$	$0$	$-4$	$0$	$8$		$1$		$q-\zeta_{24}^{4}q^{3}+\zeta_{24}^{10}q^{4}+(1+\zeta_{24}^{2}+\cdots)q^{7}+\cdots$
3891.1.x.a	$3891$	$1$	3891.x	3891.x	$36$	$12$	$1$	$1.942$	$\Q(\zeta_{36})$	$D_{36}$	$\Q(\sqrt{-3}) $	None		✓	3891.1.x.a	$4$	$0$	$0$	$0$	$0$	$-6$		$1$		$q-\zeta_{36}^{10}q^{3}-\zeta_{36}^{16}q^{4}+(\zeta_{36}^{12}+\cdots)q^{7}+\cdots$
3891.1.bb.a	$3891$	$1$	3891.bb	3891.ab	$54$	$18$	$1$	$1.942$	$\Q(\zeta_{54})$	$D_{54}$	$\Q(\sqrt{-3}) $	None		✓	3891.1.bb.a	$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q+\zeta_{54}^{22}q^{3}+\zeta_{54}^{10}q^{4}+(\zeta_{54}^{2}-\zeta_{54}^{21}+\cdots)q^{7}+\cdots$
3891.1.bc.a	$3891$	$1$	3891.bc	3891.ac	$54$	$18$	$1$	$1.942$	$\Q(\zeta_{54})$	$D_{27}$	$\Q(\sqrt{-3}) $	None		✓	3891.1.bc.a	$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{54}^{23}q^{3}+\zeta_{54}^{8}q^{4}+(\zeta_{54}^{6}-\zeta_{54}^{7}+\cdots)q^{7}+\cdots$
3891.1.be.a	$3891$	$1$	3891.be	3891.ae	$72$	$24$	$1$	$1.942$	$\Q(\zeta_{72})$	$D_{72}$	$\Q(\sqrt{-3}) $	None		✓	3891.1.be.a	$4$	$0$	$0$	$0$	$0$	$-12$		$1$		$q+\zeta_{72}^{16}q^{3}-\zeta_{72}^{22}q^{4}+(-\zeta_{72}^{12}+\cdots)q^{7}+\cdots$
3891.1.bh.a	$3891$	$1$	3891.bh	3891.ah	$108$	$36$	$1$	$1.942$	$\Q(\zeta_{108})$	$D_{108}$	$\Q(\sqrt{-3}) $	None		✓	3891.1.bh.a	$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q+\zeta_{108}^{16}q^{3}+\zeta_{108}^{22}q^{4}+(\zeta_{108}^{26}+\cdots)q^{7}+\cdots$
3891.1.bp.a	$3891$	$1$	3891.bp	3891.ap	$216$	$72$	$1$	$1.942$	$\Q(\zeta_{216})$	$D_{216}$	$\Q(\sqrt{-3}) $	None		✓	3891.1.bp.a	$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{216}^{92}q^{3}-\zeta_{216}^{86}q^{4}+(\zeta_{216}^{24}+\cdots)q^{7}+\cdots$
3891.2.a.a	$3891$	$2$	3891.a	1.a	$1$	$1$	$1$	$31.070$	$\Q$	$_{}$	None	None	✓	✓	3891.2.a.a	$1$	$0$	$-1$	$-1$	$4$	$-4$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}-q^{4}+4q^{5}+q^{6}-4q^{7}+\cdots$
3891.2.a.b	$3891$	$2$	3891.a	1.a	$1$	$1$	$1$	$31.070$	$\Q$	$_{}$	None	None	✓	✓	3891.2.a.b	$1$	$1$	$-1$	$1$	$-2$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}-q^{4}-2q^{5}-q^{6}+3q^{8}+\cdots$
3891.2.a.c	$3891$	$2$	3891.a	1.a	$1$	$1$	$1$	$31.070$	$\Q$	$_{}$	None	None	✓	✓	3891.2.a.c	$1$	$1$	$-1$	$1$	$1$	$3$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}-q^{4}+q^{5}-q^{6}+3q^{7}+\cdots$
3891.2.a.d	$3891$	$2$	3891.a	1.a	$1$	$2$	$2$	$31.070$	$\Q(\sqrt{2}) $	$_{}$	None	None	✓	✓	3891.2.a.d	$1$	$1$	$2$	$-2$	$0$	$-4$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}-q^{4}+2\beta q^{5}-q^{6}-2q^{7}+\cdots$
3891.2.a.e	$3891$	$2$	3891.a	1.a	$1$	$38$	$38$	$31.070$		$_{}$	None	None	✓	✓	3891.2.a.e	$1$	$1$	$-1$	$38$	$-18$	$-31$	$+$		$\mathrm{SU}(2)$
3891.2.a.f	$3891$	$2$	3891.a	1.a	$1$	$43$	$43$	$31.070$		$_{}$	None	None	✓	✓	3891.2.a.f	$1$	$1$	$-6$	$-43$	$-21$	$20$	$+$		$\mathrm{SU}(2)$
3891.2.a.g	$3891$	$2$	3891.a	1.a	$1$	$62$	$62$	$31.070$		$_{}$	None	None	✓	✓	3891.2.a.g	$1$	$0$	$7$	$-62$	$21$	$-12$	$-$		$\mathrm{SU}(2)$
3891.2.a.h	$3891$	$2$	3891.a	1.a	$1$	$69$	$69$	$31.070$		$_{}$	None	None	✓	✓	3891.2.a.h	$1$	$0$	$4$	$69$	$21$	$36$	$-$		$\mathrm{SU}(2)$

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Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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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.