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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 (20 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
2627.1.b.a	$2627$	$1$	2627.b	2627.b	$2$	$1$	$1$	$1.311$	$\Q$	$D_{2}$	$\Q(\sqrt{-71}) $, $\Q(\sqrt{-2627}) $	$\Q(\sqrt{37}) $	✓	✓			2627.1.b.a	$4$	$0$	$0$	$-2$	$0$	$0$		$1$		$q-2q^{3}+q^{4}+3q^{9}-2q^{12}+q^{16}+\cdots$
2627.1.b.b	$2627$	$1$	2627.b	2627.b	$2$	$1$	$1$	$1.311$	$\Q$	$D_{3}$	$\Q(\sqrt{-2627}) $	None	✓	✓			2627.1.b.b	$2$	$0$	$0$	$-1$	$0$	$0$		$1$		$q-q^{3}+q^{4}-q^{12}-2q^{13}+q^{16}+\cdots$
2627.1.b.c	$2627$	$1$	2627.b	2627.b	$2$	$1$	$1$	$1.311$	$\Q$	$D_{3}$	$\Q(\sqrt{-2627}) $	None	✓	✓			2627.1.b.b	$2$	$0$	$0$	$-1$	$0$	$0$		$1$		$q-q^{3}+q^{4}-q^{12}+2q^{13}+q^{16}+\cdots$
2627.1.b.d	$2627$	$1$	2627.b	2627.b	$2$	$2$	$2$	$1.311$	$\Q(\sqrt{3}) $	$D_{6}$	$\Q(\sqrt{-2627}) $	None	✓	✓			2627.1.b.d	$4$	$0$	$0$	$2$	$0$	$0$		$1$		$q+q^{3}+q^{4}+q^{12}+q^{16}-\beta q^{17}+\cdots$
2627.1.b.e	$2627$	$1$	2627.b	2627.b	$2$	$6$	$6$	$1.311$	$\Q(\zeta_{14})$	$D_{14}$	$\Q(\sqrt{-71}) $	None		✓	✓		2627.1.b.e	$4$	$0$	$0$	$2$	$0$	$0$		$1$		$q+(\zeta_{14}^{2}+\zeta_{14}^{5})q^{2}+(\zeta_{14}-\zeta_{14}^{6}+\cdots)q^{3}+\cdots$
2627.1.i.a	$2627$	$1$	2627.i	2627.i	$6$	$2$	$1$	$1.311$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-71}) $	None		✓			2627.1.i.a	$4$	$0$	$-2$	$1$	$1$	$0$		$1$		$q-\zeta_{6}q^{2}-\zeta_{6}^{2}q^{3}+3\zeta_{6}^{2}q^{4}-\zeta_{6}^{2}q^{5}+\cdots$
2627.1.i.b	$2627$	$1$	2627.i	2627.i	$6$	$12$	$6$	$1.311$	$\Q(\zeta_{21})$	$D_{21}$	$\Q(\sqrt{-71}) $	None		✓	✓		2627.1.i.b	$4$	$0$	$2$	$-1$	$-1$	$0$		$1$		$q+(-\zeta_{42}-\zeta_{42}^{13})q^{2}+(-\zeta_{42}^{3}+\zeta_{42}^{4}+\cdots)q^{3}+\cdots$
2627.1.k.a	$2627$	$1$	2627.k	2627.k	$6$	$2$	$1$	$1.311$	$\Q(\sqrt{-3}) $	$D_{6}$	$\Q(\sqrt{-71}) $	None		✓			2627.1.k.a	$4$	$0$	$0$	$-1$	$3$	$0$		$1$		$q+\zeta_{6}^{2}q^{3}+\zeta_{6}^{2}q^{4}+(1+\zeta_{6})q^{5}-\zeta_{6}q^{12}+\cdots$
2627.1.k.b	$2627$	$1$	2627.k	2627.k	$6$	$12$	$6$	$1.311$	$\Q(\zeta_{21})$	$D_{42}$	$\Q(\sqrt{-71}) $	None		✓	✓		2627.1.k.b	$4$	$0$	$0$	$1$	$-3$	$0$		$1$		$q+(-\zeta_{42}^{2}-\zeta_{42}^{5})q^{2}+(\zeta_{42}^{15}-\zeta_{42}^{20}+\cdots)q^{3}+\cdots$
2627.1.p.a	$2627$	$1$	2627.p	2627.p	$10$	$4$	$1$	$1.311$	$\Q(\zeta_{10})$	$D_{10}$	None	$\Q(\sqrt{37}) $		✓	✓	✓	2627.1.p.a	$4$	$0$	$0$	$-3$	$0$	$0$		$1$		$q+(-1-\zeta_{10}^{2})q^{3}+\zeta_{10}^{2}q^{4}+(\zeta_{10}^{3}+\cdots)q^{7}+\cdots$
2627.1.x.a	$2627$	$1$	2627.x	2627.x	$18$	$6$	$1$	$1.311$	$\Q(\zeta_{18})$	$D_{18}$	$\Q(\sqrt{-71}) $	None		✓			2627.1.x.a	$4$	$0$	$0$	$-6$	$-3$	$0$		$1$		$q+(-1-\zeta_{18}^{4})q^{3}-\zeta_{18}^{5}q^{4}+(-\zeta_{18}^{3}+\cdots)q^{5}+\cdots$
2627.1.x.b	$2627$	$1$	2627.x	2627.x	$18$	$36$	$6$	$1.311$	$\Q(\zeta_{63})$	$D_{126}$	$\Q(\sqrt{-71}) $	None		✓	✓		2627.1.x.b	$4$	$0$	$0$	$6$	$3$	$0$		$1$		$q+(-\zeta_{126}^{13}-\zeta_{126}^{22})q^{2}+(-\zeta_{126}^{10}+\cdots)q^{3}+\cdots$
2627.1.y.a	$2627$	$1$	2627.y	2627.y	$18$	$6$	$1$	$1.311$	$\Q(\zeta_{18})$	$D_{9}$	$\Q(\sqrt{-71}) $	None		✓			2627.1.y.a	$4$	$0$	$0$	$6$	$-3$	$0$		$1$		$q-\zeta_{18}^{5}q^{2}+(1+\zeta_{18}^{8})q^{3}-3\zeta_{18}q^{4}+\cdots$
2627.1.y.b	$2627$	$1$	2627.y	2627.y	$18$	$36$	$6$	$1.311$	$\Q(\zeta_{63})$	$D_{63}$	$\Q(\sqrt{-71}) $	None		✓	✓		2627.1.y.b	$4$	$0$	$0$	$-6$	$3$	$0$		$1$		$q+(-\zeta_{126}^{11}+\zeta_{126}^{38})q^{2}+(-\zeta_{126}^{5}+\cdots)q^{3}+\cdots$
2627.2.a.a	$2627$	$2$	2627.a	1.a	$1$	$1$	$1$	$20.977$	$\Q$	$_{}$	None	None	✓	✓			2627.2.a.a	$1$	$0$	$1$	$-1$	$0$	$-2$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}-q^{4}-q^{6}-2q^{7}-3q^{8}+\cdots$
2627.2.a.b	$2627$	$2$	2627.a	1.a	$1$	$1$	$1$	$20.977$	$\Q$	$_{}$	None	None	✓	✓			2627.2.a.b	$1$	$0$	$1$	$3$	$4$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+3q^{3}-q^{4}+4q^{5}+3q^{6}+2q^{7}+\cdots$
2627.2.a.c	$2627$	$2$	2627.a	1.a	$1$	$47$	$47$	$20.977$		$_{}$	None	None	✓	✓	✓	✓	2627.2.a.c	$1$	$1$	$-7$	$-13$	$-16$	$-13$	$+$		$\mathrm{SU}(2)$
2627.2.a.d	$2627$	$2$	2627.a	1.a	$1$	$47$	$47$	$20.977$		$_{}$	None	None	✓	✓	✓	✓	2627.2.a.d	$1$	$1$	$-3$	$-9$	$-6$	$-21$	$+$		$\mathrm{SU}(2)$
2627.2.a.e	$2627$	$2$	2627.a	1.a	$1$	$57$	$57$	$20.977$		$_{}$	None	None	✓	✓	✓		2627.2.a.e	$1$	$0$	$5$	$13$	$6$	$15$	$-$		$\mathrm{SU}(2)$
2627.2.a.f	$2627$	$2$	2627.a	1.a	$1$	$58$	$58$	$20.977$		$_{}$	None	None	✓	✓	✓	✓	2627.2.a.f	$1$	$0$	$4$	$7$	$10$	$15$	$-$		$\mathrm{SU}(2)$

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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.