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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 (21 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
1503.1.d.a	$1503$	$1$	1503.d	167.b	$2$	$5$	$5$	$0.750$	$\Q(\zeta_{22})^+$	$D_{11}$	$\Q(\sqrt{-167}) $	None	✓	$2$	$0$	$1$	$0$	$0$	$-1$		$1$		$q+(1-\beta _{1}+\beta _{2}-\beta _{3}+\beta _{4})q^{2}+(1-\beta _{1}+\cdots)q^{4}+\cdots$
1503.1.f.a	$1503$	$1$	1503.f	1503.f	$6$	$2$	$1$	$0.750$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-167}) $	None		$4$	$0$	$1$	$-1$	$0$	$1$		$1$		$q+\zeta_{6}q^{2}-\zeta_{6}q^{3}-\zeta_{6}^{2}q^{6}+\zeta_{6}q^{7}+\cdots$
1503.1.f.b	$1503$	$1$	1503.f	1503.f	$6$	$20$	$10$	$0.750$	$\Q(\zeta_{33})$	$D_{33}$	$\Q(\sqrt{-167}) $	None		$4$	$0$	$-1$	$1$	$0$	$-1$		$1$		$q+(-\zeta_{66}^{9}-\zeta_{66}^{13})q^{2}+\zeta_{66}^{14}q^{3}+\cdots$
1503.2.a.a	$1503$	$2$	1503.a	1.a	$1$	$1$	$1$	$12.002$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$-1$	$0$	$4$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{4}+4q^{5}+4q^{7}+3q^{8}-4q^{10}+\cdots$
1503.2.a.b	$1503$	$2$	1503.a	1.a	$1$	$2$	$2$	$12.002$	$\Q(\sqrt{5}) $	$_{}$	None	None	✓	$1$	$1$	$1$	$0$	$2$	$-5$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{2}+(-1+\beta )q^{4}+q^{5}+(-2-\beta )q^{7}+\cdots$
1503.2.a.c	$1503$	$2$	1503.a	1.a	$1$	$5$	$5$	$12.002$	5.5.38569.1	$_{}$	None	None	✓	$1$	$1$	$0$	$0$	$1$	$-4$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+(\beta _{2}+\beta _{3})q^{4}+(-\beta _{1}-\beta _{4})q^{5}+\cdots$
1503.2.a.d	$1503$	$2$	1503.a	1.a	$1$	$5$	$5$	$12.002$	5.5.36497.1	$_{}$	None	None	✓	$1$	$0$	$4$	$0$	$9$	$-4$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1-\beta _{3})q^{2}+(1+\beta _{1}-2\beta _{3}+\beta _{4})q^{4}+\cdots$
1503.2.a.e	$1503$	$2$	1503.a	1.a	$1$	$8$	$8$	$12.002$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	$_{}$	None	None	✓	$1$	$1$	$-3$	$0$	$-7$	$-4$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+(1+\beta _{3}+\beta _{5}+\beta _{7})q^{4}+(-1+\cdots)q^{5}+\cdots$
1503.2.a.f	$1503$	$2$	1503.a	1.a	$1$	$8$	$8$	$12.002$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	$_{}$	None	None	✓	$1$	$0$	$3$	$0$	$-1$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{3}q^{2}+(1-\beta _{2}+\beta _{5}+\beta _{6}+\beta _{7})q^{4}+\cdots$
1503.2.a.g	$1503$	$2$	1503.a	1.a	$1$	$12$	$12$	$12.002$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	$_{}$	None	None	✓	$1$	$0$	$-2$	$0$	$-4$	$11$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+(1+\beta _{4}+\beta _{6}+\beta _{7})q^{4}+(-1+\cdots)q^{5}+\cdots$
1503.2.a.h	$1503$	$2$	1503.a	1.a	$1$	$14$	$14$	$12.002$	$\mathbb{Q}[x]/(x^{14} - \cdots)$	$_{}$	None	None	✓	$1$	$1$	$-6$	$0$	$-12$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+(1+\beta _{1}+\beta _{2})q^{4}+(-1-\beta _{11}+\cdots)q^{5}+\cdots$
1503.2.a.i	$1503$	$2$	1503.a	1.a	$1$	$14$	$14$	$12.002$	$\mathbb{Q}[x]/(x^{14} - \cdots)$	$_{}$	None	None	✓	$1$	$0$	$6$	$0$	$12$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+(1+\beta _{1}+\beta _{2})q^{4}+(1+\beta _{11}+\cdots)q^{5}+\cdots$
1503.2.c.a	$1503$	$2$	1503.c	501.c	$2$	$56$	$56$	$12.002$		$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
1503.4.a.a	$1503$	$4$	1503.a	1.a	$1$	$15$	$15$	$88.680$	$\mathbb{Q}[x]/(x^{15} - \cdots)$	$_{}$	None	None	✓	$1$	$1$	$7$	$0$	$26$	$-85$	$-$	$2^{3}$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+(2+\beta _{1}+\beta _{2})q^{4}+(2+\beta _{11}+\cdots)q^{5}+\cdots$
1503.4.a.b	$1503$	$4$	1503.a	1.a	$1$	$19$	$19$	$88.680$	$\mathbb{Q}[x]/(x^{19} - \cdots)$	$_{}$	None	None	✓	$1$	$1$	$-1$	$0$	$-12$	$-28$	$-$	$2^{2}$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+(3+\beta _{2})q^{4}+(-1-\beta _{13}+\cdots)q^{5}+\cdots$
1503.4.a.c	$1503$	$4$	1503.a	1.a	$1$	$19$	$19$	$88.680$	$\mathbb{Q}[x]/(x^{19} - \cdots)$	$_{}$	None	None	✓	$1$	$0$	$9$	$0$	$62$	$-28$	$+$	$2^{3}$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+(2+\beta _{1}+\beta _{2})q^{4}+(4-\beta _{1}+\cdots)q^{5}+\cdots$
1503.4.a.d	$1503$	$4$	1503.a	1.a	$1$	$23$	$23$	$88.680$		$_{}$	None	None	✓	$1$	$1$	$-11$	$0$	$-48$	$28$	$-$		$\mathrm{SU}(2)$
1503.4.a.e	$1503$	$4$	1503.a	1.a	$1$	$23$	$23$	$88.680$		$_{}$	None	None	✓	$1$	$0$	$3$	$0$	$-2$	$28$	$+$		$\mathrm{SU}(2)$
1503.4.a.f	$1503$	$4$	1503.a	1.a	$1$	$26$	$26$	$88.680$		$_{}$	None	None	✓	$1$	$0$	$-5$	$0$	$-34$	$83$	$+$		$\mathrm{SU}(2)$
1503.4.a.g	$1503$	$4$	1503.a	1.a	$1$	$41$	$41$	$88.680$		$_{}$	None	None	✓	$1$	$1$	$-12$	$0$	$-60$	$-20$	$-$		$\mathrm{SU}(2)$
1503.4.a.h	$1503$	$4$	1503.a	1.a	$1$	$41$	$41$	$88.680$		$_{}$	None	None	✓	$1$	$0$	$12$	$0$	$60$	$-20$	$+$		$\mathrm{SU}(2)$

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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.