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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 (27 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
1011.1.c.a	$1011$	$1$	1011.c	1011.c	$2$	$1$	$1$	$0.505$	$\Q$	$D_{2}$	$\Q(\sqrt{-3}) $, $\Q(\sqrt{-1011}) $	$\Q(\sqrt{337}) $	✓	$4$	$0$	$0$	$-1$	$0$	$2$		$1$		$q-q^{3}+q^{4}+2q^{7}+q^{9}-q^{12}-2q^{13}+\cdots$
1011.1.c.b	$1011$	$1$	1011.c	1011.c	$2$	$1$	$1$	$0.505$	$\Q$	$D_{3}$	$\Q(\sqrt{-1011}) $	None	✓	$2$	$0$	$0$	$1$	$-1$	$-1$		$1$		$q+q^{3}+q^{4}-q^{5}-q^{7}+q^{9}+2q^{11}+\cdots$
1011.1.c.c	$1011$	$1$	1011.c	1011.c	$2$	$1$	$1$	$0.505$	$\Q$	$D_{3}$	$\Q(\sqrt{-1011}) $	None	✓	$2$	$0$	$0$	$1$	$1$	$-1$		$1$		$q+q^{3}+q^{4}+q^{5}-q^{7}+q^{9}-2q^{11}+\cdots$
1011.1.c.d	$1011$	$1$	1011.c	1011.c	$2$	$2$	$2$	$0.505$	$\Q(\sqrt{3}) $	$D_{6}$	$\Q(\sqrt{-1011}) $	None	✓	$4$	$0$	$0$	$-2$	$0$	$-2$		$1$		$q-q^{3}+q^{4}-\beta q^{5}-q^{7}+q^{9}-q^{12}+\cdots$
1011.1.f.a	$1011$	$1$	1011.f	1011.f	$4$	$2$	$1$	$0.505$	$\Q(\sqrt{-1}) $	$D_{4}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q-iq^{3}+q^{4}-q^{9}-iq^{12}+q^{16}+\cdots$
1011.1.f.b	$1011$	$1$	1011.f	1011.f	$4$	$4$	$2$	$0.505$	$\Q(\zeta_{8})$	$S_{4}$	None	None		$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q+(-\zeta_{8}-\zeta_{8}^{3})q^{2}+\zeta_{8}^{2}q^{3}-q^{4}+\cdots$
1011.1.l.a	$1011$	$1$	1011.l	1011.l	$8$	$4$	$1$	$0.505$	$\Q(\zeta_{8})$	$D_{8}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$0$	$0$	$-4$		$1$		$q-\zeta_{8}^{3}q^{3}+q^{4}+(-1-\zeta_{8}^{2})q^{7}-\zeta_{8}^{2}q^{9}+\cdots$
1011.1.q.a	$1011$	$1$	1011.q	1011.q	$14$	$6$	$1$	$0.505$	$\Q(\zeta_{14})$	$D_{14}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$1$	$0$	$-2$		$1$		$q-\zeta_{14}^{6}q^{3}+\zeta_{14}^{6}q^{4}+(-\zeta_{14}-\zeta_{14}^{5}+\cdots)q^{7}+\cdots$
1011.1.r.a	$1011$	$1$	1011.r	1011.r	$14$	$6$	$1$	$0.505$	$\Q(\zeta_{14})$	$D_{7}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$-1$	$0$	$-2$		$1$		$q-\zeta_{14}^{3}q^{3}-\zeta_{14}^{3}q^{4}+(\zeta_{14}^{4}+\zeta_{14}^{6}+\cdots)q^{7}+\cdots$
1011.1.y.a	$1011$	$1$	1011.y	1011.y	$28$	$12$	$1$	$0.505$	$\Q(\zeta_{28})$	$D_{28}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{28}^{3}q^{3}-\zeta_{28}^{10}q^{4}+(-\zeta_{28}^{4}+\cdots)q^{7}+\cdots$
1011.1.bf.a	$1011$	$1$	1011.bf	1011.af	$56$	$24$	$1$	$0.505$	$\Q(\zeta_{56})$	$D_{56}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$0$	$0$	$4$		$1$		$q-\zeta_{56}^{15}q^{3}+\zeta_{56}^{8}q^{4}+(\zeta_{56}^{6}-\zeta_{56}^{16}+\cdots)q^{7}+\cdots$
1011.2.a.a	$1011$	$2$	1011.a	1.a	$1$	$1$	$1$	$8.073$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$-1$	$1$	$0$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}-q^{4}-q^{6}+4q^{7}+3q^{8}+\cdots$
1011.2.a.b	$1011$	$2$	1011.a	1.a	$1$	$1$	$1$	$8.073$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$1$	$-1$	$-3$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}-q^{4}-3q^{5}-q^{6}+q^{7}+\cdots$
1011.2.a.c	$1011$	$2$	1011.a	1.a	$1$	$7$	$7$	$8.073$	7.7.20134393.1	$_{}$	None	None	✓	$1$	$1$	$-1$	$7$	$-6$	$-11$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+q^{3}+\beta _{2}q^{4}+(-1+\beta _{1}+\cdots)q^{5}+\cdots$
1011.2.a.d	$1011$	$2$	1011.a	1.a	$1$	$10$	$10$	$8.073$	$\mathbb{Q}[x]/(x^{10} - \cdots)$	$_{}$	None	None	✓	$1$	$1$	$-2$	$-10$	$-8$	$9$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}-q^{3}+\beta _{2}q^{4}+(-1+\beta _{2}+\cdots)q^{5}+\cdots$
1011.2.a.e	$1011$	$2$	1011.a	1.a	$1$	$17$	$17$	$8.073$	$\mathbb{Q}[x]/(x^{17} - \cdots)$	$_{}$	None	None	✓	$1$	$0$	$3$	$-17$	$13$	$-12$	$-$	$2^{2}$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}+(1+\beta _{11}+\cdots)q^{5}+\cdots$
1011.2.a.f	$1011$	$2$	1011.a	1.a	$1$	$21$	$21$	$8.073$		$_{}$	None	None	✓	$1$	$0$	$3$	$21$	$6$	$13$	$-$		$\mathrm{SU}(2)$
1011.2.d.a	$1011$	$2$	1011.d	337.b	$2$	$28$	$28$	$8.073$		$_{}$	None	None		$2$	$0$	$-2$	$28$	$0$	$-6$			$\mathrm{SU}(2)[C_{2}]$
1011.2.d.b	$1011$	$2$	1011.d	337.b	$2$	$30$	$30$	$8.073$		$_{}$	None	None		$2$	$0$	$0$	$-30$	$0$	$2$			$\mathrm{SU}(2)[C_{2}]$
1011.4.a.a	$1011$	$4$	1011.a	1.a	$1$	$34$	$34$	$59.651$		$_{}$	None	None	✓	$1$	$1$	$-7$	$102$	$-34$	$-128$	$-$		$\mathrm{SU}(2)$
1011.4.a.b	$1011$	$4$	1011.a	1.a	$1$	$38$	$38$	$59.651$		$_{}$	None	None	✓	$1$	$1$	$-5$	$-114$	$-48$	$68$	$-$		$\mathrm{SU}(2)$
1011.4.a.c	$1011$	$4$	1011.a	1.a	$1$	$46$	$46$	$59.651$		$_{}$	None	None	✓	$1$	$0$	$7$	$-138$	$42$	$-72$	$+$		$\mathrm{SU}(2)$
1011.4.a.d	$1011$	$4$	1011.a	1.a	$1$	$50$	$50$	$59.651$		$_{}$	None	None	✓	$1$	$0$	$5$	$150$	$56$	$124$	$+$		$\mathrm{SU}(2)$
1011.6.a.a	$1011$	$6$	1011.a	1.a	$1$	$62$	$62$	$162.148$		$_{}$	None	None	✓	$1$	$1$	$-7$	$558$	$-250$	$-823$	$+$		$\mathrm{SU}(2)$
1011.6.a.b	$1011$	$6$	1011.a	1.a	$1$	$66$	$66$	$162.148$		$_{}$	None	None	✓	$1$	$1$	$-17$	$-594$	$-222$	$549$	$+$		$\mathrm{SU}(2)$
1011.6.a.c	$1011$	$6$	1011.a	1.a	$1$	$74$	$74$	$162.148$		$_{}$	None	None	✓	$1$	$0$	$7$	$-666$	$228$	$-431$	$-$		$\mathrm{SU}(2)$
1011.6.a.d	$1011$	$6$	1011.a	1.a	$1$	$78$	$78$	$162.148$		$_{}$	None	None	✓	$1$	$0$	$17$	$702$	$200$	$941$	$-$		$\mathrm{SU}(2)$

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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.