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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 (39 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
3724.1.e.a	$3724$	$1$	3724.e	19.b	$2$	$1$	$1$	$1.859$	$\Q$	$D_{3}$	$\Q(\sqrt{-19}) $	None	✓	$2$	$0$	$0$	$0$	$-2$	$0$		$1$		$q-2q^{5}+q^{9}-q^{11}+q^{17}-q^{19}+\cdots$
3724.1.e.b	$3724$	$1$	3724.e	19.b	$2$	$1$	$1$	$1.859$	$\Q$	$D_{3}$	$\Q(\sqrt{-19}) $	None	✓	$2$	$0$	$0$	$0$	$-1$	$0$		$1$		$q-q^{5}+q^{9}+2q^{11}-q^{17}+q^{19}+\cdots$
3724.1.e.c	$3724$	$1$	3724.e	19.b	$2$	$1$	$1$	$1.859$	$\Q$	$D_{3}$	$\Q(\sqrt{-19}) $	None	✓	$2$	$0$	$0$	$0$	$1$	$0$		$1$		$q+q^{5}+q^{9}-q^{11}+q^{17}-q^{19}+2q^{23}+\cdots$
3724.1.e.d	$3724$	$1$	3724.e	19.b	$2$	$1$	$1$	$1.859$	$\Q$	$D_{3}$	$\Q(\sqrt{-19}) $	None	✓	$2$	$0$	$0$	$0$	$1$	$0$		$1$		$q+q^{5}+q^{9}+2q^{11}+q^{17}-q^{19}+\cdots$
3724.1.e.e	$3724$	$1$	3724.e	19.b	$2$	$1$	$1$	$1.859$	$\Q$	$D_{3}$	$\Q(\sqrt{-19}) $	None	✓	$2$	$0$	$0$	$0$	$2$	$0$		$1$		$q+2q^{5}+q^{9}-q^{11}-q^{17}+q^{19}+\cdots$
3724.1.n.a	$3724$	$1$	3724.n	532.n	$6$	$4$	$2$	$1.859$	$\Q(\zeta_{12})$	$A_{4}$	None	None		$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q+\zeta_{12}q^{2}+\zeta_{12}^{3}q^{3}+\zeta_{12}^{2}q^{4}+\zeta_{12}^{4}q^{6}+\cdots$
3724.1.bb.a	$3724$	$1$	3724.bb	76.g	$6$	$4$	$2$	$1.859$	$\Q(\zeta_{12})$	$A_{4}$	None	None		$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{12}^{5}q^{2}+\zeta_{12}^{5}q^{3}-\zeta_{12}^{4}q^{4}+\cdots$
3724.1.bb.b	$3724$	$1$	3724.bb	76.g	$6$	$4$	$2$	$1.859$	$\Q(\zeta_{12})$	$A_{4}$	None	None		$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q+\zeta_{12}^{5}q^{2}+\zeta_{12}^{5}q^{3}-\zeta_{12}^{4}q^{4}+\cdots$
3724.1.bc.a	$3724$	$1$	3724.bc	133.r	$6$	$2$	$1$	$1.859$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-19}) $	None		$4$	$0$	$0$	$0$	$-1$	$0$		$1$		$q-\zeta_{6}q^{5}-\zeta_{6}q^{9}+\zeta_{6}^{2}q^{11}+\zeta_{6}^{2}q^{17}+\cdots$
3724.1.bc.b	$3724$	$1$	3724.bc	133.r	$6$	$2$	$1$	$1.859$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-19}) $	None		$4$	$0$	$0$	$0$	$-1$	$0$		$1$		$q-\zeta_{6}q^{5}-\zeta_{6}q^{9}-\zeta_{6}^{2}q^{11}+\zeta_{6}^{2}q^{17}+\cdots$
3724.1.bc.c	$3724$	$1$	3724.bc	133.r	$6$	$2$	$1$	$1.859$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-19}) $	None		$4$	$0$	$0$	$0$	$1$	$0$		$1$		$q+\zeta_{6}q^{5}-\zeta_{6}q^{9}-\zeta_{6}^{2}q^{11}-\zeta_{6}^{2}q^{17}+\cdots$
3724.1.bc.d	$3724$	$1$	3724.bc	133.r	$6$	$2$	$1$	$1.859$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-19}) $	None		$4$	$0$	$0$	$0$	$2$	$0$		$1$		$q+\zeta_{6}q^{5}-\zeta_{6}q^{9}-\zeta_{6}^{2}q^{11}+\zeta_{6}^{2}q^{17}+\cdots$
3724.1.bk.a	$3724$	$1$	3724.bk	532.ak	$6$	$4$	$2$	$1.859$	$\Q(\zeta_{12})$	$A_{4}$	None	None		$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q+\zeta_{12}^{3}q^{2}+\zeta_{12}q^{3}-q^{4}+\zeta_{12}^{4}q^{6}+\cdots$
3724.1.bv.a	$3724$	$1$	3724.bv	931.aa	$14$	$12$	$2$	$1.859$	$\Q(\zeta_{21})$	$D_{21}$	$\Q(\sqrt{-19}) $	None		$4$	$0$	$0$	$0$	$2$	$1$		$1$		$q+(-\zeta_{42}-\zeta_{42}^{5})q^{5}-\zeta_{42}^{17}q^{7}+\cdots$
3724.1.dj.a	$3724$	$1$	3724.dj	931.aq	$42$	$12$	$1$	$1.859$	$\Q(\zeta_{21})$	$D_{21}$	$\Q(\sqrt{-19}) $	None		$4$	$0$	$0$	$0$	$-1$	$-2$		$1$		$q+(-\zeta_{42}-\zeta_{42}^{3})q^{5}-\zeta_{42}^{9}q^{7}-\zeta_{42}^{11}q^{9}+\cdots$
3724.1.dj.b	$3724$	$1$	3724.dj	931.aq	$42$	$12$	$1$	$1.859$	$\Q(\zeta_{21})$	$D_{21}$	$\Q(\sqrt{-19}) $	None		$4$	$0$	$0$	$0$	$2$	$1$		$1$		$q+(\zeta_{42}^{8}-\zeta_{42}^{17})q^{5}+\zeta_{42}^{16}q^{7}+\cdots$
3724.2.a.a	$3724$	$2$	3724.a	1.a	$1$	$1$	$1$	$29.736$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$0$	$-2$	$1$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{3}+q^{5}+q^{9}+5q^{11}+4q^{13}+\cdots$
3724.2.a.b	$3724$	$2$	3724.a	1.a	$1$	$1$	$1$	$29.736$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$0$	$0$	$2$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+2q^{5}-3q^{9}+4q^{11}-4q^{13}-6q^{17}+\cdots$
3724.2.a.c	$3724$	$2$	3724.a	1.a	$1$	$2$	$2$	$29.736$	$\Q(\sqrt{3}) $	$_{}$	None	None	✓	$1$	$1$	$0$	$-2$	$0$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta )q^{3}+(1-2\beta )q^{9}+(-3+2\beta )q^{11}+\cdots$
3724.2.a.d	$3724$	$2$	3724.a	1.a	$1$	$2$	$2$	$29.736$	$\Q(\sqrt{5}) $	$_{}$	None	None	✓	$1$	$1$	$0$	$-1$	$4$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta q^{3}+(1+2\beta )q^{5}+(-2+\beta )q^{9}+\cdots$
3724.2.a.e	$3724$	$2$	3724.a	1.a	$1$	$2$	$2$	$29.736$	$\Q(\sqrt{21}) $	$_{}$	None	None	✓	$1$	$1$	$0$	$1$	$-6$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{3}-3q^{5}+(2+\beta )q^{9}+(-1-\beta )q^{11}+\cdots$
3724.2.a.f	$3724$	$2$	3724.a	1.a	$1$	$2$	$2$	$29.736$	$\Q(\sqrt{3}) $	$_{}$	None	None	✓	$1$	$1$	$0$	$2$	$0$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+(1+\beta )q^{3}+(1+2\beta )q^{9}+(-3-2\beta )q^{11}+\cdots$
3724.2.a.g	$3724$	$2$	3724.a	1.a	$1$	$2$	$2$	$29.736$	$\Q(\sqrt{5}) $	$_{}$	None	None	✓	$1$	$0$	$0$	$3$	$2$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1+\beta )q^{3}+q^{5}+(-1+3\beta )q^{9}+(-2+\cdots)q^{11}+\cdots$
3724.2.a.h	$3724$	$2$	3724.a	1.a	$1$	$3$	$3$	$29.736$	3.3.404.1	$_{}$	None	None	✓	$1$	$1$	$0$	$-2$	$-3$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta _{1})q^{3}+(-1-\beta _{1}+\beta _{2})q^{5}+\cdots$
3724.2.a.i	$3724$	$2$	3724.a	1.a	$1$	$3$	$3$	$29.736$	3.3.733.1	$_{}$	None	None	✓	$1$	$0$	$0$	$1$	$-2$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{3}+(-1+\beta _{1}+\beta _{2})q^{5}+(2+\beta _{2})q^{9}+\cdots$
3724.2.a.j	$3724$	$2$	3724.a	1.a	$1$	$3$	$3$	$29.736$	3.3.404.1	$_{}$	None	None	✓	$1$	$1$	$0$	$2$	$3$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+(1-\beta _{1})q^{3}+(1+\beta _{1}-\beta _{2})q^{5}+(1+\cdots)q^{9}+\cdots$
3724.2.a.k	$3724$	$2$	3724.a	1.a	$1$	$5$	$5$	$29.736$	5.5.11350832.1	$_{}$	None	None	✓	$1$	$1$	$0$	$-2$	$0$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{3}+\beta _{2}q^{5}+(1+\beta _{1}+\beta _{2})q^{9}+\cdots$
3724.2.a.l	$3724$	$2$	3724.a	1.a	$1$	$5$	$5$	$29.736$	5.5.11350832.1	$_{}$	None	None	✓	$1$	$0$	$0$	$2$	$0$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{3}-\beta _{2}q^{5}+(1+\beta _{1}+\beta _{2})q^{9}+\cdots$
3724.2.a.m	$3724$	$2$	3724.a	1.a	$1$	$7$	$7$	$29.736$	$\mathbb{Q}[x]/(x^{7} - \cdots)$	$_{}$	None	None	✓	$1$	$0$	$0$	$0$	$-2$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{3}-\beta _{6}q^{5}+(2-\beta _{4}+\beta _{5})q^{9}+\cdots$
3724.2.a.n	$3724$	$2$	3724.a	1.a	$1$	$7$	$7$	$29.736$	$\mathbb{Q}[x]/(x^{7} - \cdots)$	$_{}$	None	None	✓	$1$	$0$	$0$	$0$	$2$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{3}+\beta _{6}q^{5}+(2-\beta _{4}+\beta _{5})q^{9}+\cdots$
3724.2.a.o	$3724$	$2$	3724.a	1.a	$1$	$8$	$8$	$29.736$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	$_{}$	None	None	✓	$1$	$1$	$0$	$-4$	$0$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{3}-\beta _{2}q^{5}+(\beta _{1}+\beta _{2}+\beta _{3})q^{9}+\cdots$
3724.2.a.p	$3724$	$2$	3724.a	1.a	$1$	$8$	$8$	$29.736$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	$_{}$	None	None	✓	$1$	$0$	$0$	$4$	$0$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{3}+\beta _{2}q^{5}+(\beta _{1}+\beta _{2}+\beta _{3})q^{9}+\cdots$
3724.2.g.a	$3724$	$2$	3724.g	133.c	$2$	$2$	$2$	$29.736$	$\Q(\sqrt{-3}) $	$_{}$	None	None		$2$	$1$	$0$	$-4$	$0$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q-2q^{3}+q^{9}-3q^{11}-2q^{13}-3\zeta_{6}q^{17}+\cdots$
3724.2.g.b	$3724$	$2$	3724.g	133.c	$2$	$2$	$2$	$29.736$	$\Q(\sqrt{-3}) $	$_{}$	None	None		$2$	$0$	$0$	$4$	$0$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q+2q^{3}+q^{9}-3q^{11}+2q^{13}+3\zeta_{6}q^{17}+\cdots$
3724.2.g.c	$3724$	$2$	3724.g	133.c	$2$	$4$	$4$	$29.736$	$\Q(\sqrt{-3}, \sqrt{-19})$	$_{}$	$\Q(\sqrt{-19}) $	None		$4$	$0$	$0$	$0$	$0$	$0$		$2^{2}$	$\mathrm{U}(1)[D_{2}]$	$q+(-\beta _{1}-2\beta _{3})q^{5}-3q^{9}+(-2-\beta _{2}+\cdots)q^{11}+\cdots$
3724.2.g.d	$3724$	$2$	3724.g	133.c	$2$	$4$	$4$	$29.736$	$\Q(\sqrt{-3}, \sqrt{-19})$	$_{}$	$\Q(\sqrt{-19}) $	None		$4$	$0$	$0$	$0$	$0$	$0$		$2^{2}$	$\mathrm{U}(1)[D_{2}]$	$q+(-\beta _{1}-\beta _{3})q^{5}-3q^{9}+5q^{11}+(4\beta _{1}+\cdots)q^{17}+\cdots$
3724.2.g.e	$3724$	$2$	3724.g	133.c	$2$	$8$	$8$	$29.736$	8.0.3288334336.2	$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$0$		$2\cdot 7^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{4}q^{5}-3q^{9}-2q^{11}-\beta _{1}q^{13}+\cdots$
3724.2.g.f	$3724$	$2$	3724.g	133.c	$2$	$16$	$16$	$29.736$	$\mathbb{Q}[x]/(x^{16} + \cdots)$	$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$0$		$2^{12}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{6}q^{3}+\beta _{9}q^{5}+(3+\beta _{4})q^{9}+(\beta _{4}+\cdots)q^{11}+\cdots$
3724.2.g.g	$3724$	$2$	3724.g	133.c	$2$	$32$	$32$	$29.736$		$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$

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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.