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Level	Weight	Analytic conductor	Analytic rank	Dim.

Bad $p$	Char.	Primitive character	Character order	Is maximal/largest

Coefficient field	Self-twists	CM/RM discriminant	Inner twist count	Is self-dual

Coefficient ring index	Coefficient ring gens.	Is twist minimal	Projective image

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Results (31 matches)

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Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	Image	CM	RM	Self-dual	Twist minimal	Largest	Maximal	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	Largest	Maximal	Minimal twist	Inner twists	Rank*	$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
1055.1.d.a	$1055$	$1$	1055.d	1055.d	$2$	$1$	$1$	$0.527$	$\Q$	$D_{3}$	$\Q(\sqrt{-1055}) $	None	✓	✓			1055.1.d.a	$2$	$0$	$-2$	$1$	$1$	$1$		$1$		$q-2q^{2}+q^{3}+3q^{4}+q^{5}-2q^{6}+q^{7}+\cdots$
1055.1.d.b	$1055$	$1$	1055.d	1055.d	$2$	$1$	$1$	$0.527$	$\Q$	$D_{2}$	$\Q(\sqrt{-211}) $, $\Q(\sqrt{-1055}) $	$\Q(\sqrt{5}) $	✓	✓			1055.1.d.b	$4$	$0$	$0$	$0$	$-1$	$0$		$1$		$q-q^{4}-q^{5}-q^{9}+2q^{11}+q^{16}+2q^{19}+\cdots$
1055.1.d.c	$1055$	$1$	1055.d	1055.d	$2$	$1$	$1$	$0.527$	$\Q$	$D_{3}$	$\Q(\sqrt{-1055}) $	None	✓	✓			1055.1.d.a	$2$	$0$	$2$	$-1$	$1$	$-1$		$1$		$q+2q^{2}-q^{3}+3q^{4}+q^{5}-2q^{6}-q^{7}+\cdots$
1055.1.d.d	$1055$	$1$	1055.d	1055.d	$2$	$2$	$2$	$0.527$	$\Q(\sqrt{3}) $	$D_{6}$	$\Q(\sqrt{-1055}) $	None	✓	✓			1055.1.d.d	$4$	$0$	$0$	$0$	$-2$	$0$		$1$		$q-\beta q^{3}-q^{4}-q^{5}-\beta q^{7}+2q^{9}-q^{11}+\cdots$
1055.1.d.e	$1055$	$1$	1055.d	1055.d	$2$	$2$	$2$	$0.527$	$\Q(\sqrt{-3}) $	$D_{6}$	$\Q(\sqrt{-211}) $	None		✓			1055.1.d.e	$4$	$0$	$0$	$0$	$1$	$0$		$1$		$q-q^{4}-\zeta_{6}^{2}q^{5}-q^{9}-q^{11}+(-\zeta_{6}+\cdots)q^{13}+\cdots$
1055.1.d.f	$1055$	$1$	1055.d	1055.d	$2$	$3$	$3$	$0.527$	$\Q(\zeta_{18})^+$	$D_{9}$	$\Q(\sqrt{-1055}) $	None	✓	✓			1055.1.d.f	$2$	$0$	$-3$	$0$	$3$	$0$		$1$		$q-q^{2}-\beta _{1}q^{3}+q^{5}+\beta _{1}q^{6}+\beta _{2}q^{7}+\cdots$
1055.1.d.g	$1055$	$1$	1055.d	1055.d	$2$	$3$	$3$	$0.527$	$\Q(\zeta_{18})^+$	$D_{9}$	$\Q(\sqrt{-1055}) $	None	✓	✓			1055.1.d.f	$2$	$0$	$3$	$0$	$3$	$0$		$1$		$q+q^{2}+\beta _{1}q^{3}+q^{5}+\beta _{1}q^{6}-\beta _{2}q^{7}+\cdots$
1055.1.d.h	$1055$	$1$	1055.d	1055.d	$2$	$6$	$6$	$0.527$	$\Q(\zeta_{36})^+$	$D_{18}$	$\Q(\sqrt{-1055}) $	None	✓	✓	✓		1055.1.d.h	$4$	$0$	$0$	$0$	$-6$	$0$		$1$		$q+\beta _{3}q^{2}-\beta _{1}q^{3}+2q^{4}-q^{5}+(-2\beta _{2}+\cdots)q^{6}+\cdots$
1055.1.m.a	$1055$	$1$	1055.m	1055.m	$10$	$4$	$1$	$0.527$	$\Q(\zeta_{10})$	$D_{10}$	None	$\Q(\sqrt{5}) $		✓	✓	✓	1055.1.m.a	$4$	$0$	$0$	$0$	$1$	$0$		$1$		$q+\zeta_{10}q^{4}+\zeta_{10}q^{5}+\zeta_{10}^{3}q^{9}+(-\zeta_{10}^{3}+\cdots)q^{11}+\cdots$
1055.2.a.a	$1055$	$2$	1055.a	1.a	$1$	$1$	$1$	$8.424$	$\Q$	$_{}$	None	None	✓	✓			1055.2.a.a	$1$	$1$	$-1$	$-1$	$1$	$-3$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}-q^{4}+q^{5}+q^{6}-3q^{7}+\cdots$
1055.2.a.b	$1055$	$2$	1055.a	1.a	$1$	$2$	$2$	$8.424$	$\Q(\sqrt{2}) $	$_{}$	None	None	✓	✓			1055.2.a.b	$1$	$1$	$-2$	$-2$	$2$	$2$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta )q^{2}+(-1-\beta )q^{3}+(1-2\beta )q^{4}+\cdots$
1055.2.a.c	$1055$	$2$	1055.a	1.a	$1$	$2$	$2$	$8.424$	$\Q(\sqrt{5}) $	$_{}$	None	None	✓	✓			1055.2.a.c	$1$	$1$	$1$	$1$	$2$	$-1$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{2}+(1-\beta )q^{3}+(-1+\beta )q^{4}+q^{5}+\cdots$
1055.2.a.d	$1055$	$2$	1055.a	1.a	$1$	$3$	$3$	$8.424$	$\Q(\zeta_{14})^+$	$_{}$	None	None	✓	✓			1055.2.a.d	$1$	$1$	$2$	$-2$	$-3$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q+(1-\beta _{1})q^{2}+(-1-\beta _{2})q^{3}+(1-2\beta _{1}+\cdots)q^{4}+\cdots$
1055.2.a.e	$1055$	$2$	1055.a	1.a	$1$	$4$	$4$	$8.424$	4.4.7537.1	$_{}$	None	None	✓	✓	✓		1055.2.a.e	$1$	$1$	$-1$	$-3$	$4$	$-3$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+(-1-\beta _{2})q^{3}+(1+\beta _{2})q^{4}+\cdots$
1055.2.a.f	$1055$	$2$	1055.a	1.a	$1$	$6$	$6$	$8.424$	6.6.3195392.1	$_{}$	None	None	✓	✓	✓		1055.2.a.f	$1$	$1$	$-3$	$3$	$-6$	$-3$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta _{4}q^{2}+(1-\beta _{5})q^{3}+(\beta _{1}-\beta _{4})q^{4}+\cdots$
1055.2.a.g	$1055$	$2$	1055.a	1.a	$1$	$26$	$26$	$8.424$		$_{}$	None	None	✓	✓	✓	✓	1055.2.a.g	$1$	$0$	$6$	$9$	$26$	$13$	$-$		$\mathrm{SU}(2)$
1055.2.a.h	$1055$	$2$	1055.a	1.a	$1$	$27$	$27$	$8.424$		$_{}$	None	None	✓	✓	✓	✓	1055.2.a.h	$1$	$0$	$1$	$-1$	$-27$	$5$	$-$		$\mathrm{SU}(2)$
1055.2.b.a	$1055$	$2$	1055.b	5.b	$2$	$2$	$2$	$8.424$	$\Q(\sqrt{-1}) $	$_{}$	None	None		✓			1055.2.b.a	$2$	$0$	$0$	$0$	$2$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+i q^{2}-i q^{3}+q^{4}+(-2 i+1)q^{5}+\cdots$
1055.2.b.b	$1055$	$2$	1055.b	5.b	$2$	$4$	$4$	$8.424$	$\Q(\sqrt{-3}, \sqrt{-11})$	$_{}$	None	None		✓			1055.2.b.b	$2$	$0$	$0$	$0$	$-3$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{2}q^{2}+(-\beta _{1}-\beta _{2}+\beta _{3})q^{3}-q^{4}+\cdots$
1055.2.b.c	$1055$	$2$	1055.b	5.b	$2$	$4$	$4$	$8.424$	$\Q(\sqrt{-2}, \sqrt{3})$	$_{}$	None	None		✓			1055.2.b.c	$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{2}+(-\beta _{1}+2\beta _{3})q^{3}+\beta _{2}q^{4}+\cdots$
1055.2.b.d	$1055$	$2$	1055.b	5.b	$2$	$6$	$6$	$8.424$	6.0.4227136.1	$_{}$	None	None		✓			1055.2.b.d	$2$	$0$	$0$	$0$	$-2$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{4}q^{2}-\beta _{1}q^{3}+(-1+\beta _{3})q^{4}+(-\beta _{1}+\cdots)q^{5}+\cdots$
1055.2.b.e	$1055$	$2$	1055.b	5.b	$2$	$30$	$30$	$8.424$		$_{}$	None	None		✓			1055.2.b.e	$2$	$0$	$0$	$0$	$2$	$0$			$\mathrm{SU}(2)[C_{2}]$
1055.2.b.f	$1055$	$2$	1055.b	5.b	$2$	$58$	$58$	$8.424$		$_{}$	None	None		✓	✓		1055.2.b.f	$2$	$0$	$0$	$0$	$-1$	$0$			$\mathrm{SU}(2)[C_{2}]$
1055.4.a.a	$1055$	$4$	1055.a	1.a	$1$	$43$	$43$	$62.247$		$_{}$	None	None	✓	✓	✓	✓	1055.4.a.a	$1$	$1$	$-2$	$3$	$-215$	$-35$	$-$		$\mathrm{SU}(2)$
1055.4.a.b	$1055$	$4$	1055.a	1.a	$1$	$44$	$44$	$62.247$		$_{}$	None	None	✓	✓	✓	✓	1055.4.a.b	$1$	$1$	$-12$	$-27$	$220$	$-91$	$-$		$\mathrm{SU}(2)$
1055.4.a.c	$1055$	$4$	1055.a	1.a	$1$	$61$	$61$	$62.247$		$_{}$	None	None	✓	✓	✓	✓	1055.4.a.c	$1$	$0$	$2$	$-3$	$-305$	$35$	$+$		$\mathrm{SU}(2)$
1055.4.a.d	$1055$	$4$	1055.a	1.a	$1$	$62$	$62$	$62.247$		$_{}$	None	None	✓	✓	✓	✓	1055.4.a.d	$1$	$0$	$12$	$27$	$310$	$91$	$+$		$\mathrm{SU}(2)$
1055.6.a.a	$1055$	$6$	1055.a	1.a	$1$	$78$	$78$	$169.205$		$_{}$	None	None	✓	✓	✓	✓	1055.6.a.a	$1$	$1$	$-24$	$-81$	$1950$	$-637$	$+$		$\mathrm{SU}(2)$
1055.6.a.b	$1055$	$6$	1055.a	1.a	$1$	$79$	$79$	$169.205$		$_{}$	None	None	✓	✓	✓	✓	1055.6.a.b	$1$	$1$	$-4$	$9$	$-1975$	$-245$	$+$		$\mathrm{SU}(2)$
1055.6.a.c	$1055$	$6$	1055.a	1.a	$1$	$96$	$96$	$169.205$		$_{}$	None	None	✓	✓	✓	✓	1055.6.a.c	$1$	$0$	$24$	$81$	$2400$	$637$	$-$		$\mathrm{SU}(2)$
1055.6.a.d	$1055$	$6$	1055.a	1.a	$1$	$97$	$97$	$169.205$		$_{}$	None	None	✓	✓	✓	✓	1055.6.a.d	$1$	$0$	$4$	$-9$	$-2425$	$245$	$-$		$\mathrm{SU}(2)$

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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.