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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 (26 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				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*	$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$	Coefficient ring index	Sato-Tate	$q$-expansion
251.1.b.a	$251$	$1$	251.b	251.b	$2$	$3$	$3$	$0.125$	$\Q(\zeta_{14})^+$	$D_{7}$	$\Q(\sqrt{-251}) $	None	✓	$2$	$0$	$0$	$-1$	$-1$	$-1$	$1$		$q-\beta _{1}q^{3}+q^{4}+(-1+\beta _{1}-\beta _{2})q^{5}+\cdots$
1004.1.d.a	$1004$	$1$	1004.d	251.b	$2$	$1$	$1$	$0.501$	$\Q$	$D_{3}$	$\Q(\sqrt{-251}) $	None	✓	$2$	$0$	$0$	$2$	$-1$	$-1$	$1$		$q+2q^{3}-q^{5}-q^{7}+3q^{9}+2q^{13}+\cdots$
1004.1.d.b	$1004$	$1$	1004.d	251.b	$2$	$6$	$6$	$0.501$	$\Q(\zeta_{21})^+$	$D_{21}$	$\Q(\sqrt{-251}) $	None	✓	$2$	$0$	$0$	$-2$	$1$	$1$	$1$		$q+(-1-\beta _{3}+\beta _{5})q^{3}+\beta _{4}q^{5}+(-\beta _{2}+\cdots)q^{7}+\cdots$
1255.1.d.b	$1255$	$1$	1255.d	1255.d	$2$	$1$	$1$	$0.626$	$\Q$	$D_{2}$	$\Q(\sqrt{-251}) $, $\Q(\sqrt{-1255}) $	$\Q(\sqrt{5}) $	✓	$4$	$0$	$0$	$0$	$-1$	$0$	$1$		$q-q^{4}-q^{5}+q^{9}+q^{16}+q^{20}+q^{25}+\cdots$
1255.1.d.e	$1255$	$1$	1255.d	1255.d	$2$	$6$	$6$	$0.626$	$\Q(\zeta_{14})$	$D_{14}$	$\Q(\sqrt{-251}) $	None		$4$	$0$	$0$	$0$	$1$	$0$	$1$		$q+(\zeta_{14}^{2}+\zeta_{14}^{5})q^{3}-q^{4}+\zeta_{14}q^{5}+\cdots$
1757.1.h.a	$1757$	$1$	1757.h	1757.h	$6$	$2$	$1$	$0.877$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-251}) $	None		$4$	$0$	$0$	$1$	$1$	$2$	$1$		$q-\zeta_{6}^{2}q^{3}+\zeta_{6}^{2}q^{4}+\zeta_{6}q^{5}+q^{7}+\cdots$
1757.1.h.b	$1757$	$1$	1757.h	1757.h	$6$	$12$	$6$	$0.877$	$\Q(\zeta_{21})$	$D_{21}$	$\Q(\sqrt{-251}) $	None		$4$	$0$	$0$	$-1$	$-1$	$-2$	$1$		$q+(-\zeta_{42}^{3}+\zeta_{42}^{4})q^{3}+\zeta_{42}^{14}q^{4}+\cdots$
2259.1.c.a	$2259$	$1$	2259.c	251.b	$2$	$3$	$3$	$1.127$	$\Q(\zeta_{14})^+$	$D_{7}$	$\Q(\sqrt{-251}) $	None	✓	$2$	$0$	$0$	$0$	$1$	$-1$	$1$		$q+q^{4}+\beta _{1}q^{5}+(-1+\beta _{1}-\beta _{2})q^{7}+\cdots$
2259.1.h.a	$2259$	$1$	2259.h	2259.h	$6$	$2$	$1$	$1.127$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-251}) $	None		$4$	$0$	$0$	$-1$	$1$	$1$	$1$		$q+\zeta_{6}^{2}q^{3}+\zeta_{6}^{2}q^{4}-\zeta_{6}^{2}q^{5}+\zeta_{6}q^{7}+\cdots$
2259.1.h.c	$2259$	$1$	2259.h	2259.h	$6$	$12$	$6$	$1.127$	$\Q(\zeta_{21})$	$D_{21}$	$\Q(\sqrt{-251}) $	None		$4$	$0$	$0$	$1$	$-1$	$-1$	$1$		$q-\zeta_{42}^{19}q^{3}-\zeta_{42}^{7}q^{4}+(\zeta_{42}^{6}+\zeta_{42}^{8}+\cdots)q^{5}+\cdots$
3263.1.d.b	$3263$	$1$	3263.d	3263.d	$2$	$1$	$1$	$1.628$	$\Q$	$D_{2}$	$\Q(\sqrt{-251}) $, $\Q(\sqrt{-3263}) $	$\Q(\sqrt{13}) $	✓	$4$	$0$	$0$	$-2$	$0$	$0$	$1$		$q-2q^{3}-q^{4}+3q^{9}+2q^{12}+q^{13}+\cdots$
3263.1.d.h	$3263$	$1$	3263.d	3263.d	$2$	$6$	$6$	$1.628$	$\Q(\zeta_{14})$	$D_{14}$	$\Q(\sqrt{-251}) $	None		$4$	$0$	$0$	$2$	$0$	$0$	$1$		$q+(\zeta_{14}^{3}-\zeta_{14}^{4})q^{3}-q^{4}+(\zeta_{14}^{2}+\zeta_{14}^{5}+\cdots)q^{5}+\cdots$
3263.1.i.a	$3263$	$1$	3263.i	3263.i	$6$	$2$	$1$	$1.628$	$\Q(\sqrt{-3}) $	$D_{6}$	$\Q(\sqrt{-251}) $	None		$4$	$0$	$0$	$-1$	$0$	$3$	$1$		$q+\zeta_{6}^{2}q^{3}+\zeta_{6}q^{4}+(\zeta_{6}+\zeta_{6}^{2})q^{5}+\cdots$
3263.1.i.b	$3263$	$1$	3263.i	3263.i	$6$	$12$	$6$	$1.628$	$\Q(\zeta_{21})$	$D_{42}$	$\Q(\sqrt{-251}) $	None		$4$	$0$	$0$	$1$	$0$	$-3$	$1$		$q+(\zeta_{42}^{3}-\zeta_{42}^{4})q^{3}+\zeta_{42}^{7}q^{4}+(\zeta_{42}^{2}+\cdots)q^{5}+\cdots$
3263.1.k.a	$3263$	$1$	3263.k	3263.k	$6$	$2$	$1$	$1.628$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-251}) $	None		$4$	$0$	$0$	$1$	$-2$	$1$	$1$		$q-\zeta_{6}^{2}q^{3}-\zeta_{6}q^{4}-q^{5}+\zeta_{6}q^{7}-q^{12}+\cdots$
3263.1.k.b	$3263$	$1$	3263.k	3263.k	$6$	$12$	$6$	$1.628$	$\Q(\zeta_{21})$	$D_{21}$	$\Q(\sqrt{-251}) $	None		$4$	$0$	$0$	$-1$	$2$	$-1$	$1$		$q+(-\zeta_{42}^{3}+\zeta_{42}^{4})q^{3}-\zeta_{42}^{7}q^{4}+\cdots$
3765.1.l.a	$3765$	$1$	3765.l	3765.l	$4$	$2$	$1$	$1.879$	$\Q(\sqrt{-1}) $	$D_{4}$	$\Q(\sqrt{-251}) $	None		$4$	$0$	$0$	$0$	$0$	$2$	$1$		$q+iq^{3}+iq^{4}-iq^{5}+(1-i)q^{7}-q^{9}+\cdots$
3765.1.l.b	$3765$	$1$	3765.l	3765.l	$4$	$2$	$1$	$1.879$	$\Q(\sqrt{-1}) $	$D_{4}$	$\Q(\sqrt{-251}) $	None		$4$	$0$	$0$	$2$	$0$	$2$	$1$		$q+q^{3}+iq^{4}+iq^{5}+(1-i)q^{7}+q^{9}+\cdots$
3765.1.l.c	$3765$	$1$	3765.l	3765.l	$4$	$12$	$6$	$1.879$	$\Q(\zeta_{28})$	$D_{28}$	$\Q(\sqrt{-251}) $	None		$4$	$0$	$0$	$-2$	$0$	$-2$	$1$		$q-\zeta_{28}^{2}q^{3}-\zeta_{28}^{7}q^{4}+\zeta_{28}q^{5}+(\zeta_{28}^{3}+\cdots)q^{7}+\cdots$
3765.1.l.d	$3765$	$1$	3765.l	3765.l	$4$	$12$	$6$	$1.879$	$\Q(\zeta_{28})$	$D_{28}$	$\Q(\sqrt{-251}) $	None		$4$	$0$	$0$	$0$	$0$	$-2$	$1$		$q+\zeta_{28}^{13}q^{3}-\zeta_{28}^{7}q^{4}+\zeta_{28}^{11}q^{5}+\cdots$
753.2.d.a	$753$	$2$	753.d	753.d	$2$	$14$	$14$	$6.013$	$\mathbb{Q}[x]/(x^{14} - \cdots)$	$_{}$	$\Q(\sqrt{-251}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$2\cdot 3^{3}$	$\mathrm{U}(1)[D_{2}]$	$q+\beta _{1}q^{3}-2q^{4}-\beta _{4}q^{5}-\beta _{5}q^{7}+\beta _{2}q^{9}+\cdots$
251.3.b.a	$251$	$3$	251.b	251.b	$2$	$7$	$7$	$6.839$	$\mathbb{Q}[x]/(x^{7} - \cdots)$	$_{}$	$\Q(\sqrt{-251}) $	None	✓	$2$	$0$	$0$	$0$	$0$	$0$	$1$	$\mathrm{U}(1)[D_{2}]$	$q+\beta _{2}q^{3}+4q^{4}+(\beta _{1}-\beta _{6})q^{5}+(-3\beta _{3}+\cdots)q^{7}+\cdots$
3012.2.e.c	$3012$	$2$	3012.e	753.d	$2$	$28$	$28$	$24.051$		$_{}$	$\Q(\sqrt{-251}) $	None		$4$	$0$	$0$	$0$	$0$	$0$		$\mathrm{U}(1)[D_{2}]$
251.5.b.a	$251$	$5$	251.b	251.b	$2$	$7$	$7$	$25.946$	$\mathbb{Q}[x]/(x^{7} - \cdots)$	$_{}$	$\Q(\sqrt{-251}) $	None	✓	$2$	$0$	$0$	$0$	$0$	$0$	$1$	$\mathrm{U}(1)[D_{2}]$	$q+(4\beta _{3}+\beta _{5})q^{3}+2^{4}q^{4}+(-6\beta _{2}-7\beta _{4}+\cdots)q^{5}+\cdots$
1004.3.d.a	$1004$	$3$	1004.d	251.b	$2$	$14$	$14$	$27.357$	$\mathbb{Q}[x]/(x^{14} - \cdots)$	$_{}$	$\Q(\sqrt{-251}) $	None	✓	$2$	$0$	$0$	$0$	$0$	$0$	$2^{9}\cdot 3$	$\mathrm{U}(1)[D_{2}]$	$q+\beta _{1}q^{3}+\beta _{11}q^{5}-\beta _{4}q^{7}+(9+\beta _{3}+\cdots)q^{9}+\cdots$
1004.5.d.a	$1004$	$5$	1004.d	251.b	$2$	$14$	$14$	$103.783$	$\mathbb{Q}[x]/(x^{14} - \cdots)$	$_{}$	$\Q(\sqrt{-251}) $	None	✓	$2$	$0$	$0$	$0$	$0$	$0$	$2^{12}\cdot 3$	$\mathrm{U}(1)[D_{2}]$	$q+(-\beta _{2}+\beta _{4}-\beta _{8})q^{3}+(2\beta _{1}+\beta _{3}+\cdots)q^{5}+\cdots$

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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.