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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 (27 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
2639.1.h.a	$2639$	$1$	2639.h	2639.h	$2$	$1$	$1$	$1.317$	$\Q$	$D_{2}$	$\Q(\sqrt{-91}) $, $\Q(\sqrt{-2639}) $	$\Q(\sqrt{29}) $	✓	✓	2639.1.h.a	$4$	$0$	$0$	$0$	$-2$	$-1$		$1$		$q-q^{4}-2q^{5}-q^{7}-q^{9}-q^{13}+q^{16}+\cdots$
2639.1.h.b	$2639$	$1$	2639.h	2639.h	$2$	$1$	$1$	$1.317$	$\Q$	$D_{2}$	$\Q(\sqrt{-91}) $, $\Q(\sqrt{-2639}) $	$\Q(\sqrt{29}) $	✓	✓	2639.1.h.a	$4$	$0$	$0$	$0$	$2$	$1$		$1$		$q-q^{4}+2q^{5}+q^{7}-q^{9}+q^{13}+q^{16}+\cdots$
2639.1.h.c	$2639$	$1$	2639.h	2639.h	$2$	$2$	$2$	$1.317$	$\Q(\sqrt{2}) $	$D_{4}$	$\Q(\sqrt{-2639}) $	None	✓	✓	2639.1.h.c	$4$	$0$	$0$	$0$	$-4$	$2$		$1$		$q+\beta q^{2}-\beta q^{3}+q^{4}-2q^{5}-2q^{6}+\cdots$
2639.1.h.d	$2639$	$1$	2639.h	2639.h	$2$	$2$	$2$	$1.317$	$\Q(\sqrt{2}) $	$D_{4}$	$\Q(\sqrt{-2639}) $	None	✓	✓	2639.1.h.c	$4$	$0$	$0$	$0$	$4$	$-2$		$1$		$q-\beta q^{2}-\beta q^{3}+q^{4}+2q^{5}+2q^{6}+\cdots$
2639.1.h.e	$2639$	$1$	2639.h	2639.h	$2$	$4$	$4$	$1.317$	$\Q(\zeta_{16})^+$	$D_{8}$	$\Q(\sqrt{-2639}) $	None	✓	✓	2639.1.h.e	$4$	$0$	$0$	$0$	$0$	$-4$		$1$		$q+\beta _{3}q^{2}-\beta _{1}q^{3}+(1-\beta _{2})q^{4}-\beta _{2}q^{6}+\cdots$
2639.1.h.f	$2639$	$1$	2639.h	2639.h	$2$	$4$	$4$	$1.317$	$\Q(\zeta_{16})^+$	$D_{8}$	$\Q(\sqrt{-2639}) $	None	✓	✓	2639.1.h.e	$4$	$0$	$0$	$0$	$0$	$4$		$1$		$q-\beta _{3}q^{2}-\beta _{1}q^{3}+(1-\beta _{2})q^{4}+\beta _{2}q^{6}+\cdots$
2639.1.h.g	$2639$	$1$	2639.h	2639.h	$2$	$8$	$8$	$1.317$	$\Q(\zeta_{32})^+$	$D_{16}$	$\Q(\sqrt{-2639}) $	None	✓	✓	2639.1.h.g	$4$	$0$	$0$	$0$	$0$	$-8$		$1$		$q-\beta _{1}q^{2}+\beta _{5}q^{3}+(1+\beta _{2})q^{4}+\beta _{4}q^{5}+\cdots$
2639.1.h.h	$2639$	$1$	2639.h	2639.h	$2$	$8$	$8$	$1.317$	$\Q(\zeta_{32})^+$	$D_{16}$	$\Q(\sqrt{-2639}) $	None	✓	✓	2639.1.h.g	$4$	$0$	$0$	$0$	$0$	$8$		$1$		$q-\beta _{3}q^{2}+\beta _{1}q^{3}+(1+\beta _{6})q^{4}+\beta _{4}q^{5}+\cdots$
2639.1.y.a	$2639$	$1$	2639.y	2639.y	$6$	$2$	$1$	$1.317$	$\Q(\sqrt{-3}) $	$D_{6}$	None	$\Q(\sqrt{29}) $		✓	2639.1.y.a	$4$	$0$	$0$	$0$	$0$	$-2$		$1$		$q+q^{4}-q^{7}+\zeta_{6}q^{9}-\zeta_{6}^{2}q^{13}+q^{16}+\cdots$
2639.1.bk.a	$2639$	$1$	2639.bk	2639.ak	$6$	$2$	$1$	$1.317$	$\Q(\sqrt{-3}) $	$D_{6}$	None	$\Q(\sqrt{29}) $		✓	2639.1.bk.a	$4$	$0$	$0$	$0$	$-2$	$-1$		$1$		$q-\zeta_{6}^{2}q^{4}+\zeta_{6}^{2}q^{5}+\zeta_{6}^{2}q^{7}-q^{9}+\cdots$
2639.1.bw.a	$2639$	$1$	2639.bw	2639.aw	$6$	$2$	$1$	$1.317$	$\Q(\sqrt{-3}) $	$D_{6}$	None	$\Q(\sqrt{29}) $		✓	2639.1.y.a	$4$	$0$	$0$	$0$	$0$	$1$		$1$		$q-\zeta_{6}q^{4}+\zeta_{6}q^{7}-q^{9}+\zeta_{6}^{2}q^{13}+\cdots$
2639.1.bx.a	$2639$	$1$	2639.bx	2639.ax	$6$	$2$	$1$	$1.317$	$\Q(\sqrt{-3}) $	$D_{6}$	None	$\Q(\sqrt{29}) $		✓	2639.1.bk.a	$4$	$0$	$0$	$0$	$2$	$-2$		$1$		$q-q^{4}+\zeta_{6}q^{5}-q^{7}-\zeta_{6}^{2}q^{9}+\zeta_{6}q^{13}+\cdots$
2639.1.cu.a	$2639$	$1$	2639.cu	2639.bu	$12$	$4$	$1$	$1.317$	$\Q(\zeta_{12})$	$S_{4}$	None	None		✓	2639.1.cu.a	$4$	$0$	$0$	$0$	$0$	$-4$		$1$		$q+\zeta_{12}^{3}q^{4}-q^{7}-\zeta_{12}^{5}q^{9}+(-\zeta_{12}+\cdots)q^{11}+\cdots$
2639.1.de.a	$2639$	$1$	2639.de	2639.ce	$12$	$4$	$1$	$1.317$	$\Q(\zeta_{12})$	$S_{4}$	None	None		✓	2639.1.cu.a	$4$	$0$	$0$	$0$	$0$	$2$		$1$		$q+\zeta_{12}^{5}q^{4}+\zeta_{12}^{2}q^{7}-\zeta_{12}^{3}q^{9}+\cdots$
2639.1.dx.a	$2639$	$1$	2639.dx	2639.cx	$14$	$6$	$1$	$1.317$	$\Q(\zeta_{14})$	$D_{14}$	$\Q(\sqrt{-91}) $	None		✓	2639.1.dx.a	$4$	$0$	$0$	$0$	$-5$	$1$		$1$		$q-\zeta_{14}^{2}q^{4}+(-1-\zeta_{14}^{2})q^{5}+\zeta_{14}^{5}q^{7}+\cdots$
2639.1.dx.b	$2639$	$1$	2639.dx	2639.cx	$14$	$6$	$1$	$1.317$	$\Q(\zeta_{14})$	$D_{14}$	$\Q(\sqrt{-91}) $	None		✓	2639.1.dx.a	$4$	$0$	$0$	$0$	$5$	$-1$		$1$		$q-\zeta_{14}^{2}q^{4}+(1+\zeta_{14}^{2})q^{5}-\zeta_{14}^{5}q^{7}+\cdots$
2639.1.ec.a	$2639$	$1$	2639.ec	2639.dc	$14$	$6$	$1$	$1.317$	$\Q(\zeta_{14})$	$D_{7}$	$\Q(\sqrt{-91}) $	None		✓	2639.1.ec.a	$4$	$0$	$0$	$0$	$-5$	$1$		$1$		$q-\zeta_{14}^{3}q^{4}+(-1+\zeta_{14}^{3})q^{5}-\zeta_{14}^{4}q^{7}+\cdots$
2639.1.ec.b	$2639$	$1$	2639.ec	2639.dc	$14$	$6$	$1$	$1.317$	$\Q(\zeta_{14})$	$D_{7}$	$\Q(\sqrt{-91}) $	None		✓	2639.1.ec.a	$4$	$0$	$0$	$0$	$5$	$-1$		$1$		$q-\zeta_{14}^{3}q^{4}+(1-\zeta_{14}^{3})q^{5}+\zeta_{14}^{4}q^{7}+\cdots$
2639.2.a.a	$2639$	$2$	2639.a	1.a	$1$	$1$	$1$	$21.073$	$\Q$	$_{}$	None	None	✓	✓	2639.2.a.a	$1$	$0$	$2$	$3$	$0$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{2}+3q^{3}+2q^{4}+6q^{6}+q^{7}+\cdots$
2639.2.a.b	$2639$	$2$	2639.a	1.a	$1$	$11$	$11$	$21.073$	$\mathbb{Q}[x]/(x^{11} - \cdots)$	$_{}$	None	None	✓	✓	2639.2.a.b	$1$	$1$	$-2$	$0$	$-1$	$-11$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}-\beta _{6}q^{3}+\beta _{2}q^{4}-\beta _{3}q^{5}+\cdots$
2639.2.a.c	$2639$	$2$	2639.a	1.a	$1$	$11$	$11$	$21.073$	$\mathbb{Q}[x]/(x^{11} - \cdots)$	$_{}$	None	None	✓	✓	2639.2.a.c	$1$	$1$	$0$	$-4$	$-5$	$11$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}-\beta _{8}q^{3}+\beta _{2}q^{4}-\beta _{3}q^{5}+\cdots$
2639.2.a.d	$2639$	$2$	2639.a	1.a	$1$	$15$	$15$	$21.073$	$\mathbb{Q}[x]/(x^{15} - \cdots)$	$_{}$	None	None	✓	✓	2639.2.a.d	$1$	$1$	$-2$	$-6$	$-5$	$15$	$+$	$2$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+\beta _{13}q^{3}+(1+\beta _{2})q^{4}+\beta _{12}q^{5}+\cdots$
2639.2.a.e	$2639$	$2$	2639.a	1.a	$1$	$15$	$15$	$21.073$	$\mathbb{Q}[x]/(x^{15} - \cdots)$	$_{}$	None	None	✓	✓	2639.2.a.e	$1$	$1$	$0$	$2$	$-1$	$-15$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}-\beta _{5}q^{3}+(1+\beta _{2})q^{4}-\beta _{10}q^{5}+\cdots$
2639.2.a.f	$2639$	$2$	2639.a	1.a	$1$	$27$	$27$	$21.073$		$_{}$	None	None	✓	✓	2639.2.a.f	$1$	$0$	$0$	$6$	$7$	$27$	$-$		$\mathrm{SU}(2)$
2639.2.a.g	$2639$	$2$	2639.a	1.a	$1$	$27$	$27$	$21.073$		$_{}$	None	None	✓	✓	2639.2.a.g	$1$	$0$	$4$	$-2$	$3$	$-27$	$-$		$\mathrm{SU}(2)$
2639.2.a.h	$2639$	$2$	2639.a	1.a	$1$	$29$	$29$	$21.073$		$_{}$	None	None	✓	✓	2639.2.a.h	$1$	$0$	$-1$	$9$	$1$	$29$	$-$		$\mathrm{SU}(2)$
2639.2.a.i	$2639$	$2$	2639.a	1.a	$1$	$31$	$31$	$21.073$		$_{}$	None	None	✓	✓	2639.2.a.i	$1$	$0$	$0$	$4$	$3$	$-31$	$-$		$\mathrm{SU}(2)$

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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.