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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 (29 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
239.1.b.a	$239$	$1$	239.b	239.b	$2$	$1$	$1$	$0.119$	$\Q$	$D_{3}$	$\Q(\sqrt{-239}) $	None	✓	$2$	$0$	$-1$	$2$	$-1$	$0$		$1$		$q-q^{2}+2q^{3}-q^{5}-2q^{6}+q^{8}+3q^{9}+\cdots$
239.1.b.b	$239$	$1$	239.b	239.b	$2$	$2$	$2$	$0.119$	$\Q(\sqrt{5}) $	$D_{5}$	$\Q(\sqrt{-239}) $	None	✓	$2$	$0$	$-1$	$-1$	$-1$	$0$		$1$		$q+(-1+\beta )q^{2}+(-1+\beta )q^{3}+(1-\beta )q^{4}+\cdots$
239.1.b.c	$239$	$1$	239.b	239.b	$2$	$4$	$4$	$0.119$	$\Q(\zeta_{15})^+$	$D_{15}$	$\Q(\sqrt{-239}) $	None	✓	$2$	$0$	$1$	$-2$	$1$	$0$		$1$		$q+\beta _{1}q^{2}+(-1-\beta _{3})q^{3}+(1+\beta _{2})q^{4}+\cdots$
239.2.a.a	$239$	$2$	239.a	1.a	$1$	$3$	$3$	$1.908$	$\Q(\zeta_{14})^+$	$_{}$	None	None	✓	$1$	$1$	$-1$	$-1$	$-4$	$-3$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+(-1+\beta _{1}-\beta _{2})q^{3}+\beta _{2}q^{4}+\cdots$
239.2.a.b	$239$	$2$	239.a	1.a	$1$	$17$	$17$	$1.908$	$\mathbb{Q}[x]/(x^{17} - \cdots)$	$_{}$	None	None	✓	$1$	$0$	$0$	$3$	$6$	$5$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}-\beta _{12}q^{3}+(1+\beta _{2})q^{4}-\beta _{13}q^{5}+\cdots$
239.2.c.a	$239$	$2$	239.c	239.c	$7$	$6$	$1$	$1.908$	$\Q(\zeta_{14})$	$_{}$	None	None		$2$	$0$	$-2$	$5$	$-1$	$1$		$1$	$\mathrm{SU}(2)[C_{7}]$	$q+(-1+\zeta_{14}-\zeta_{14}^{2}+\zeta_{14}^{3}+\zeta_{14}^{5})q^{2}+\cdots$
239.2.c.b	$239$	$2$	239.c	239.c	$7$	$108$	$18$	$1.908$		$_{}$	None	None		$2$	$0$	$-8$	$-10$	$-2$	$-9$			$\mathrm{SU}(2)[C_{7}]$
239.2.e.a	$239$	$2$	239.e	239.e	$17$	$304$	$19$	$1.908$		$_{}$	None	None		$2$	$0$	$-13$	$-15$	$-13$	$-11$			$\mathrm{SU}(2)[C_{17}]$
239.2.g.a	$239$	$2$	239.g	239.g	$119$	$1824$	$19$	$1.908$		$_{}$	None	None		$2$	$0$	$-92$	$-97$	$-99$	$-94$			$\mathrm{SU}(2)[C_{119}]$
239.3.b.a	$239$	$3$	239.b	239.b	$2$	$15$	$15$	$6.512$	$\mathbb{Q}[x]/(x^{15} - \cdots)$	$_{}$	$\Q(\sqrt{-239}) $	None	✓	$2$	$0$	$0$	$0$	$0$	$0$		$3$	$\mathrm{U}(1)[D_{2}]$	$q+\beta _{2}q^{2}+\beta _{12}q^{3}+(4+\beta _{8}+\beta _{9})q^{4}+\cdots$
239.3.b.b	$239$	$3$	239.b	239.b	$2$	$24$	$24$	$6.512$		$_{}$	None	None		$2$	$0$	$0$	$-2$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
239.3.d.a	$239$	$3$	239.d	239.d	$14$	$234$	$39$	$6.512$		$_{}$	None	None		$2$	$0$	$0$	$-5$	$-7$	$-28$			$\mathrm{SU}(2)[C_{14}]$
239.3.f.a	$239$	$3$	239.f	239.f	$34$	$624$	$39$	$6.512$		$_{}$	None	None		$2$	$0$	$-17$	$-15$	$-17$	$-17$			$\mathrm{SU}(2)[C_{34}]$
239.3.h.a	$239$	$3$	239.h	239.h	$238$	$3744$	$39$	$6.512$		$_{}$	None	None		$2$	$0$	$-102$	$-97$	$-95$	$-74$			$\mathrm{SU}(2)[C_{238}]$
239.4.a.a	$239$	$4$	239.a	1.a	$1$	$22$	$22$	$14.101$		$_{}$	None	None	✓	$1$	$1$	$-4$	$-13$	$-37$	$-52$	$-$		$\mathrm{SU}(2)$
239.4.a.b	$239$	$4$	239.a	1.a	$1$	$37$	$37$	$14.101$		$_{}$	None	None	✓	$1$	$0$	$4$	$11$	$43$	$60$	$+$		$\mathrm{SU}(2)$
239.4.c.a	$239$	$4$	239.c	239.c	$7$	$354$	$59$	$14.101$		$_{}$	None	None		$2$	$0$	$0$	$-5$	$-13$	$-29$			$\mathrm{SU}(2)[C_{7}]$
239.4.e.a	$239$	$4$	239.e	239.e	$17$	$944$	$59$	$14.101$		$_{}$	None	None		$2$	$0$	$-17$	$-15$	$-23$	$-25$			$\mathrm{SU}(2)[C_{17}]$
239.4.g.a	$239$	$4$	239.g	239.g	$119$	$5664$	$59$	$14.101$		$_{}$	None	None		$2$	$0$	$-102$	$-97$	$-89$	$-73$			$\mathrm{SU}(2)[C_{119}]$
239.5.b.a	$239$	$5$	239.b	239.b	$2$	$15$	$15$	$24.705$	$\mathbb{Q}[x]/(x^{15} - \cdots)$	$_{}$	$\Q(\sqrt{-239}) $	None	✓	$2$	$0$	$0$	$0$	$0$	$0$		$3$	$\mathrm{U}(1)[D_{2}]$	$q+(\beta _{8}+\beta _{9})q^{2}+(\beta _{3}-2\beta _{6})q^{3}+(2^{4}+\cdots)q^{4}+\cdots$
239.5.b.b	$239$	$5$	239.b	239.b	$2$	$64$	$64$	$24.705$		$_{}$	None	None		$2$	$0$	$-8$	$-2$	$-20$	$0$			$\mathrm{SU}(2)[C_{2}]$
239.6.a.a	$239$	$6$	239.a	1.a	$1$	$42$	$42$	$38.332$		$_{}$	None	None	✓	$1$	$1$	$-8$	$-37$	$-212$	$-383$	$+$		$\mathrm{SU}(2)$
239.6.a.b	$239$	$6$	239.a	1.a	$1$	$57$	$57$	$38.332$		$_{}$	None	None	✓	$1$	$0$	$8$	$35$	$188$	$401$	$-$		$\mathrm{SU}(2)$
239.8.a.a	$239$	$8$	239.a	1.a	$1$	$62$	$62$	$74.660$		$_{}$	None	None	✓	$1$	$1$	$-24$	$-109$	$-1002$	$-2599$	$-$		$\mathrm{SU}(2)$
239.8.a.b	$239$	$8$	239.a	1.a	$1$	$77$	$77$	$74.660$		$_{}$	None	None	✓	$1$	$0$	$8$	$107$	$998$	$2889$	$+$		$\mathrm{SU}(2)$
239.10.a.a	$239$	$10$	239.a	1.a	$1$	$82$	$82$	$123.094$		$_{}$	None	None	✓	$1$	$1$	$-16$	$-325$	$-4717$	$-23516$	$+$		$\mathrm{SU}(2)$
239.10.a.b	$239$	$10$	239.a	1.a	$1$	$97$	$97$	$123.094$		$_{}$	None	None	✓	$1$	$0$	$48$	$323$	$5283$	$14900$	$-$		$\mathrm{SU}(2)$
239.12.a.a	$239$	$12$	239.a	1.a	$1$	$101$	$101$	$183.634$		$_{}$	None	None	✓	$1$	$1$	$-64$	$-1225$	$-32362$	$-81723$	$-$		$\mathrm{SU}(2)$
239.12.a.b	$239$	$12$	239.a	1.a	$1$	$116$	$116$	$183.634$		$_{}$	None	None	✓	$1$	$0$	$64$	$719$	$17638$	$187189$	$+$		$\mathrm{SU}(2)$

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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.