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Level	Weight	Analytic conductor	$Nk^2$	Dim.

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

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

Coefficient ring index	Coefficient ring gens.		Projective image	Projective image type
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Results (45 matches)

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Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	Image	CM	RM	Self-dual	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	Inner twists	Rank*	$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
3179.1.b.a	$3179$	$1$	3179.b	187.b	$2$	$2$	$2$	$1.587$	$\Q(\sqrt{-1}) $	$D_{3}$	$\Q(\sqrt{-11}) $	None		$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q-iq^{3}+q^{4}-iq^{5}-iq^{11}-iq^{12}+\cdots$
3179.1.b.b	$3179$	$1$	3179.b	187.b	$2$	$6$	$6$	$1.587$	6.0.419904.1	$D_{9}$	$\Q(\sqrt{-11}) $	None		$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\beta _{1}q^{3}+q^{4}-\beta _{5}q^{5}+(-1+\beta _{2}+\cdots)q^{9}+\cdots$
3179.1.c.a	$3179$	$1$	3179.c	11.b	$2$	$1$	$1$	$1.587$	$\Q$	$D_{3}$	$\Q(\sqrt{-11}) $	None	✓	$2$	$0$	$0$	$-1$	$-1$	$0$		$1$		$q-q^{3}+q^{4}-q^{5}+q^{11}-q^{12}+q^{15}+\cdots$
3179.1.c.b	$3179$	$1$	3179.c	11.b	$2$	$1$	$1$	$1.587$	$\Q$	$D_{3}$	$\Q(\sqrt{-11}) $	None	✓	$2$	$0$	$0$	$1$	$1$	$0$		$1$		$q+q^{3}+q^{4}+q^{5}-q^{11}+q^{12}+q^{15}+\cdots$
3179.1.c.c	$3179$	$1$	3179.c	11.b	$2$	$3$	$3$	$1.587$	$\Q(\zeta_{18})^+$	$D_{9}$	$\Q(\sqrt{-11}) $	None	✓	$2$	$0$	$0$	$0$	$0$	$0$		$1$		$q+\beta _{1}q^{3}+q^{4}+(-\beta _{1}+\beta _{2})q^{5}+(1+\cdots)q^{9}+\cdots$
3179.1.c.d	$3179$	$1$	3179.c	11.b	$2$	$3$	$3$	$1.587$	$\Q(\zeta_{18})^+$	$D_{9}$	$\Q(\sqrt{-11}) $	None	✓	$2$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\beta _{1}q^{3}+q^{4}+(\beta _{1}-\beta _{2})q^{5}+(1+\beta _{2})q^{9}+\cdots$
3179.1.f.a	$3179$	$1$	3179.f	187.f	$4$	$4$	$2$	$1.587$	$\Q(\zeta_{8})$	$D_{3}$	$\Q(\sqrt{-11}) $	None		$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{8}q^{3}-q^{4}+\zeta_{8}q^{5}-\zeta_{8}^{3}q^{11}+\cdots$
3179.1.f.b	$3179$	$1$	3179.f	187.f	$4$	$12$	$6$	$1.587$	12.0.$\cdots$.1	$D_{9}$	$\Q(\sqrt{-11}) $	None		$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\beta _{8}q^{3}-q^{4}+(-\beta _{8}+\beta _{11})q^{5}+(\beta _{7}+\cdots)q^{9}+\cdots$
3179.1.i.a	$3179$	$1$	3179.i	187.i	$8$	$8$	$2$	$1.587$	$\Q(\zeta_{16})$	$D_{3}$	$\Q(\sqrt{-11}) $	None		$16$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{16}^{7}q^{3}+\zeta_{16}^{4}q^{4}-\zeta_{16}^{3}q^{5}+\cdots$
3179.1.i.b	$3179$	$1$	3179.i	187.i	$8$	$24$	$6$	$1.587$	24.0.$\cdots$.1	$D_{9}$	$\Q(\sqrt{-11}) $	None		$16$	$0$	$0$	$0$	$0$	$0$		$1$		$q+(-\beta _{20}-\beta _{23})q^{3}-\beta _{13}q^{4}+\beta _{12}q^{5}+\cdots$
3179.2.a.a	$3179$	$2$	3179.a	1.a	$1$	$1$	$1$	$25.384$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$-2$	$1$	$-1$	$2$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{2}+q^{3}+2q^{4}-q^{5}-2q^{6}+2q^{7}+\cdots$
3179.2.a.b	$3179$	$2$	3179.a	1.a	$1$	$1$	$1$	$25.384$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$0$	$-1$	$-3$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-2q^{4}-3q^{5}-2q^{7}-2q^{9}+\cdots$
3179.2.a.c	$3179$	$2$	3179.a	1.a	$1$	$1$	$1$	$25.384$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$2$	$-3$	$-2$	$-2$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{2}-3q^{3}+2q^{4}-2q^{5}-6q^{6}+\cdots$
3179.2.a.d	$3179$	$2$	3179.a	1.a	$1$	$1$	$1$	$25.384$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$2$	$0$	$-4$	$5$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{2}+2q^{4}-4q^{5}+5q^{7}-3q^{9}+\cdots$
3179.2.a.e	$3179$	$2$	3179.a	1.a	$1$	$1$	$1$	$25.384$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$2$	$0$	$-1$	$2$	$+$	$1$	$\mathrm{SU}(2)$	$q+2q^{2}+2q^{4}-q^{5}+2q^{7}-3q^{9}+\cdots$
3179.2.a.f	$3179$	$2$	3179.a	1.a	$1$	$1$	$1$	$25.384$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$2$	$0$	$1$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q+2q^{2}+2q^{4}+q^{5}-2q^{7}-3q^{9}+\cdots$
3179.2.a.g	$3179$	$2$	3179.a	1.a	$1$	$1$	$1$	$25.384$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$2$	$3$	$2$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{2}+3q^{3}+2q^{4}+2q^{5}+6q^{6}+\cdots$
3179.2.a.h	$3179$	$2$	3179.a	1.a	$1$	$2$	$2$	$25.384$	$\Q(\sqrt{2}) $	$_{}$	None	None	✓	$1$	$1$	$-4$	$-4$	$0$	$2$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{2}+(-2-\beta )q^{3}+2q^{4}-2\beta q^{5}+\cdots$
3179.2.a.i	$3179$	$2$	3179.a	1.a	$1$	$2$	$2$	$25.384$	$\Q(\sqrt{2}) $	$_{}$	None	None	✓	$1$	$0$	$-4$	$4$	$0$	$-2$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{2}+(2-\beta )q^{3}+2q^{4}-2\beta q^{5}+\cdots$
3179.2.a.j	$3179$	$2$	3179.a	1.a	$1$	$2$	$2$	$25.384$	$\Q(\sqrt{2}) $	$_{}$	None	None	✓	$1$	$0$	$-2$	$-2$	$2$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta )q^{2}+(-1-\beta )q^{3}+(1-2\beta )q^{4}+\cdots$
3179.2.a.k	$3179$	$2$	3179.a	1.a	$1$	$2$	$2$	$25.384$	$\Q(\sqrt{3}) $	$_{}$	None	None	✓	$1$	$1$	$-2$	$0$	$4$	$4$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta )q^{2}+\beta q^{3}+(2-2\beta )q^{4}+\cdots$
3179.2.a.l	$3179$	$2$	3179.a	1.a	$1$	$2$	$2$	$25.384$	$\Q(\sqrt{2}) $	$_{}$	None	None	✓	$1$	$0$	$-2$	$2$	$-2$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta )q^{2}+(1+\beta )q^{3}+(1-2\beta )q^{4}+\cdots$
3179.2.a.m	$3179$	$2$	3179.a	1.a	$1$	$2$	$2$	$25.384$	$\Q(\sqrt{2}) $	$_{}$	None	None	✓	$1$	$0$	$0$	$-4$	$2$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{2}-2q^{3}+(1+2\beta )q^{5}-2\beta q^{6}+\cdots$
3179.2.a.n	$3179$	$2$	3179.a	1.a	$1$	$2$	$2$	$25.384$	$\Q(\sqrt{2}) $	$_{}$	None	None	✓	$1$	$0$	$0$	$4$	$-2$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{2}+2q^{3}+(-1-2\beta )q^{5}+2\beta q^{6}+\cdots$
3179.2.a.o	$3179$	$2$	3179.a	1.a	$1$	$2$	$2$	$25.384$	$\Q(\sqrt{17}) $	$_{}$	None	None	✓	$1$	$1$	$4$	$1$	$-1$	$-3$	$+$	$1$	$\mathrm{SU}(2)$	$q+2q^{2}+(1-\beta )q^{3}+2q^{4}+(-1+\beta )q^{5}+\cdots$
3179.2.a.p	$3179$	$2$	3179.a	1.a	$1$	$3$	$3$	$25.384$	3.3.788.1	$_{}$	None	None	✓	$1$	$1$	$-3$	$-1$	$-1$	$4$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-\beta _{1}q^{3}-q^{4}-\beta _{2}q^{5}+\beta _{1}q^{6}+\cdots$
3179.2.a.q	$3179$	$2$	3179.a	1.a	$1$	$3$	$3$	$25.384$	$\Q(\zeta_{18})^+$	$_{}$	None	None	✓	$1$	$1$	$-3$	$0$	$-3$	$-6$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta _{1})q^{2}+\beta _{1}q^{3}+(1-2\beta _{1}+\cdots)q^{4}+\cdots$
3179.2.a.r	$3179$	$2$	3179.a	1.a	$1$	$3$	$3$	$25.384$	$\Q(\zeta_{18})^+$	$_{}$	None	None	✓	$1$	$1$	$-3$	$0$	$3$	$6$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta _{1})q^{2}-\beta _{1}q^{3}+(1-2\beta _{1}+\cdots)q^{4}+\cdots$
3179.2.a.s	$3179$	$2$	3179.a	1.a	$1$	$3$	$3$	$25.384$	3.3.788.1	$_{}$	None	None	✓	$1$	$1$	$-3$	$1$	$1$	$-4$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+\beta _{1}q^{3}-q^{4}+\beta _{2}q^{5}-\beta _{1}q^{6}+\cdots$
3179.2.a.t	$3179$	$2$	3179.a	1.a	$1$	$3$	$3$	$25.384$	3.3.148.1	$_{}$	None	None	✓	$1$	$0$	$-2$	$3$	$7$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta _{1})q^{2}+(1+\beta _{2})q^{3}+(1-\beta _{1}+\cdots)q^{4}+\cdots$
3179.2.a.u	$3179$	$2$	3179.a	1.a	$1$	$3$	$3$	$25.384$	3.3.148.1	$_{}$	None	None	✓	$1$	$0$	$1$	$-3$	$1$	$-6$	$-$	$1$	$\mathrm{SU}(2)$	$q+(\beta _{1}+\beta _{2})q^{2}+(-1+\beta _{2})q^{3}+(1+2\beta _{1}+\cdots)q^{4}+\cdots$
3179.2.a.v	$3179$	$2$	3179.a	1.a	$1$	$3$	$3$	$25.384$	3.3.148.1	$_{}$	None	None	✓	$1$	$0$	$1$	$3$	$-1$	$6$	$-$	$1$	$\mathrm{SU}(2)$	$q+(\beta _{1}+\beta _{2})q^{2}+(1-\beta _{2})q^{3}+(1+2\beta _{1}+\cdots)q^{4}+\cdots$
3179.2.a.w	$3179$	$2$	3179.a	1.a	$1$	$4$	$4$	$25.384$	4.4.33844.1	$_{}$	None	None	✓	$1$	$0$	$1$	$-1$	$-3$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+\beta _{3}q^{3}+(1+\beta _{1}+\beta _{2})q^{4}+\cdots$
3179.2.a.x	$3179$	$2$	3179.a	1.a	$1$	$6$	$6$	$25.384$	6.6.1397493.1	$_{}$	None	None	✓	$1$	$1$	$0$	$-3$	$3$	$-3$	$+$	$1$	$\mathrm{SU}(2)$	$q+(\beta _{2}+\beta _{3}+\beta _{5})q^{2}+(-\beta _{1}-\beta _{5})q^{3}+\cdots$
3179.2.a.y	$3179$	$2$	3179.a	1.a	$1$	$6$	$6$	$25.384$	6.6.22313961.1	$_{}$	None	None	✓	$1$	$1$	$0$	$0$	$-6$	$6$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{5}q^{2}+(-\beta _{1}-\beta _{5})q^{3}+(\beta _{2}+\beta _{5})q^{4}+\cdots$
3179.2.a.z	$3179$	$2$	3179.a	1.a	$1$	$6$	$6$	$25.384$	6.6.22313961.1	$_{}$	None	None	✓	$1$	$1$	$0$	$0$	$6$	$-6$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{5}q^{2}-\beta _{1}q^{3}+(\beta _{2}+\beta _{5})q^{4}+(1+\cdots)q^{5}+\cdots$
3179.2.a.ba	$3179$	$2$	3179.a	1.a	$1$	$6$	$6$	$25.384$	6.6.1397493.1	$_{}$	None	None	✓	$1$	$1$	$0$	$3$	$-3$	$3$	$+$	$1$	$\mathrm{SU}(2)$	$q+(\beta _{2}+\beta _{3}+\beta _{5})q^{2}+(\beta _{1}+\beta _{5})q^{3}+\cdots$
3179.2.a.bb	$3179$	$2$	3179.a	1.a	$1$	$8$	$8$	$25.384$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	$_{}$	None	None	✓	$1$	$1$	$1$	$-2$	$-4$	$-5$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+\beta _{4}q^{3}+(1+\beta _{2})q^{4}+\beta _{5}q^{5}+\cdots$
3179.2.a.bc	$3179$	$2$	3179.a	1.a	$1$	$8$	$8$	$25.384$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	$_{}$	None	None	✓	$1$	$0$	$1$	$2$	$4$	$5$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}-\beta _{4}q^{3}+(1+\beta _{2})q^{4}-\beta _{5}q^{5}+\cdots$
3179.2.a.bd	$3179$	$2$	3179.a	1.a	$1$	$14$	$14$	$25.384$	$\mathbb{Q}[x]/(x^{14} - \cdots)$	$_{}$	None	None	✓	$1$	$1$	$2$	$0$	$-8$	$-12$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+\beta _{9}q^{3}+(1+\beta _{2})q^{4}+(-1+\cdots)q^{5}+\cdots$
3179.2.a.be	$3179$	$2$	3179.a	1.a	$1$	$14$	$14$	$25.384$	$\mathbb{Q}[x]/(x^{14} - \cdots)$	$_{}$	None	None	✓	$1$	$0$	$2$	$0$	$8$	$12$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}-\beta _{9}q^{3}+(1+\beta _{2})q^{4}+(1+\beta _{3}+\cdots)q^{5}+\cdots$
3179.2.a.bf	$3179$	$2$	3179.a	1.a	$1$	$27$	$27$	$25.384$		$_{}$	None	None	✓	$1$	$0$	$3$	$-3$	$-6$	$3$	$-$		$\mathrm{SU}(2)$
3179.2.a.bg	$3179$	$2$	3179.a	1.a	$1$	$27$	$27$	$25.384$		$_{}$	None	None	✓	$1$	$0$	$3$	$3$	$6$	$-3$	$-$		$\mathrm{SU}(2)$
3179.2.a.bh	$3179$	$2$	3179.a	1.a	$1$	$28$	$28$	$25.384$		$_{}$	None	None	✓	$1$	$1$	$0$	$-8$	$-16$	$-12$	$+$		$\mathrm{SU}(2)$
3179.2.a.bi	$3179$	$2$	3179.a	1.a	$1$	$28$	$28$	$25.384$		$_{}$	None	None	✓	$1$	$0$	$0$	$8$	$16$	$12$	$-$		$\mathrm{SU}(2)$

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Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
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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.