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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				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
263.1.b.a	$263$	$1$	263.b	263.b	$2$	$6$	$6$	$0.131$	$\Q(\zeta_{26})^+$	$D_{13}$	$\Q(\sqrt{-263}) $	None	✓	$2$	$0$	$-1$	$-1$	$0$	$0$	$1$		$q-\beta _{3}q^{2}+\beta _{2}q^{3}+(\beta _{1}-\beta _{2}+\beta _{3}-\beta _{4}+\cdots)q^{4}+\cdots$
2104.1.d.a	$2104$	$1$	2104.d	2104.d	$2$	$1$	$1$	$1.050$	$\Q$	$D_{2}$	$\Q(\sqrt{-263}) $, $\Q(\sqrt{-526}) $	$\Q(\sqrt{2}) $	✓	$4$	$0$	$-1$	$0$	$0$	$0$	$1$		$q-q^{2}+q^{4}-q^{8}+q^{9}+q^{16}+2q^{17}+\cdots$
2104.1.d.e	$2104$	$1$	2104.d	2104.d	$2$	$12$	$12$	$1.050$	$\Q(\zeta_{26})$	$D_{26}$	$\Q(\sqrt{-263}) $	None		$4$	$0$	$1$	$0$	$0$	$0$	$1$		$q-\zeta_{26}^{10}q^{2}+(\zeta_{26}^{2}+\zeta_{26}^{11})q^{3}+\cdots$
2367.1.d.a	$2367$	$1$	2367.d	263.b	$2$	$6$	$6$	$1.181$	$\Q(\zeta_{26})^+$	$D_{13}$	$\Q(\sqrt{-263}) $	None	✓	$2$	$0$	$1$	$0$	$0$	$0$	$1$		$q+\beta _{3}q^{2}+(\beta _{1}-\beta _{2}+\beta _{3}-\beta _{4}+\beta _{5})q^{4}+\cdots$
2367.1.f.a	$2367$	$1$	2367.f	2367.f	$6$	$2$	$1$	$1.181$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-263}) $	None		$4$	$0$	$1$	$-1$	$0$	$0$	$1$		$q-\zeta_{6}^{2}q^{2}-\zeta_{6}q^{3}-q^{6}+q^{8}+\zeta_{6}^{2}q^{9}+\cdots$
2367.1.f.c	$2367$	$1$	2367.f	2367.f	$6$	$24$	$12$	$1.181$	$\Q(\zeta_{39})$	$D_{39}$	$\Q(\sqrt{-263}) $	None		$4$	$0$	$-1$	$1$	$0$	$0$	$1$		$q+(-\zeta_{78}^{25}-\zeta_{78}^{27})q^{2}-\zeta_{78}^{31}q^{3}+\cdots$
2893.1.f.a	$2893$	$1$	2893.f	2893.f	$10$	$4$	$1$	$1.444$	$\Q(\zeta_{10})$	$D_{5}$	$\Q(\sqrt{-263}) $	None		$4$	$0$	$3$	$-2$	$0$	$0$	$1$		$q+(1+\zeta_{10}^{4})q^{2}-\zeta_{10}q^{3}+(1-\zeta_{10}^{3}+\cdots)q^{4}+\cdots$
2893.1.f.b	$2893$	$1$	2893.f	2893.f	$10$	$48$	$12$	$1.444$	$\Q(\zeta_{65})$	$D_{65}$	$\Q(\sqrt{-263}) $	None		$4$	$0$	$-3$	$2$	$0$	$0$	$1$		$q+(-\zeta_{130}^{5}+\zeta_{130}^{8})q^{2}+(\zeta_{130}^{12}-\zeta_{130}^{27}+\cdots)q^{3}+\cdots$
3156.1.h.a	$3156$	$1$	3156.h	3156.h	$2$	$1$	$1$	$1.575$	$\Q$	$D_{2}$	$\Q(\sqrt{-263}) $, $\Q(\sqrt{-789}) $	$\Q(\sqrt{3}) $	✓	$4$	$0$	$-1$	$-1$	$0$	$0$	$1$		$q-q^{2}-q^{3}+q^{4}+q^{6}-q^{8}+q^{9}+\cdots$
3156.1.h.b	$3156$	$1$	3156.h	3156.h	$2$	$1$	$1$	$1.575$	$\Q$	$D_{2}$	$\Q(\sqrt{-263}) $, $\Q(\sqrt{-789}) $	$\Q(\sqrt{3}) $	✓	$4$	$0$	$1$	$1$	$0$	$0$	$1$		$q+q^{2}+q^{3}+q^{4}+q^{6}+q^{8}+q^{9}+\cdots$
3156.1.h.g	$3156$	$1$	3156.h	3156.h	$2$	$12$	$12$	$1.575$	$\Q(\zeta_{26})$	$D_{26}$	$\Q(\sqrt{-263}) $	None		$4$	$0$	$-1$	$-1$	$0$	$0$	$1$		$q+\zeta_{26}^{10}q^{2}+\zeta_{26}^{2}q^{3}-\zeta_{26}^{7}q^{4}+\cdots$
3156.1.h.h	$3156$	$1$	3156.h	3156.h	$2$	$12$	$12$	$1.575$	$\Q(\zeta_{26})$	$D_{26}$	$\Q(\sqrt{-263}) $	None		$4$	$0$	$1$	$1$	$0$	$0$	$1$		$q-\zeta_{26}^{10}q^{2}+\zeta_{26}^{11}q^{3}-\zeta_{26}^{7}q^{4}+\cdots$
3419.1.c.a	$3419$	$1$	3419.c	3419.c	$2$	$1$	$1$	$1.706$	$\Q$	$D_{2}$	$\Q(\sqrt{-263}) $, $\Q(\sqrt{-3419}) $	$\Q(\sqrt{13}) $	✓	$4$	$0$	$0$	$2$	$0$	$0$	$1$		$q+2q^{3}+q^{4}+3q^{9}+2q^{12}-q^{13}+\cdots$
3419.1.c.e	$3419$	$1$	3419.c	3419.c	$2$	$12$	$12$	$1.706$	$\Q(\zeta_{26})$	$D_{26}$	$\Q(\sqrt{-263}) $	None		$4$	$0$	$0$	$-2$	$0$	$0$	$1$		$q+(\zeta_{26}^{6}+\zeta_{26}^{7})q^{2}+(\zeta_{26}^{4}-\zeta_{26}^{9}+\cdots)q^{3}+\cdots$
3419.1.h.a	$3419$	$1$	3419.h	3419.h	$6$	$2$	$1$	$1.706$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-263}) $	None		$4$	$0$	$-2$	$1$	$0$	$0$	$1$		$q+\zeta_{6}^{2}q^{2}-\zeta_{6}^{2}q^{3}-3\zeta_{6}q^{4}+2\zeta_{6}q^{6}+\cdots$
3419.1.h.b	$3419$	$1$	3419.h	3419.h	$6$	$24$	$12$	$1.706$	$\Q(\zeta_{39})$	$D_{39}$	$\Q(\sqrt{-263}) $	None		$4$	$0$	$2$	$-1$	$0$	$0$	$1$		$q+(-\zeta_{78}^{5}+\zeta_{78}^{8})q^{2}+(-\zeta_{78}^{25}+\cdots)q^{3}+\cdots$
3419.1.j.a	$3419$	$1$	3419.j	3419.j	$6$	$2$	$1$	$1.706$	$\Q(\sqrt{-3}) $	$D_{6}$	$\Q(\sqrt{-263}) $	None		$4$	$0$	$0$	$1$	$0$	$0$	$1$		$q+\zeta_{6}q^{3}+\zeta_{6}^{2}q^{4}+(-1+\zeta_{6}^{2})q^{11}+\cdots$
3419.1.j.b	$3419$	$1$	3419.j	3419.j	$6$	$24$	$12$	$1.706$	$\Q(\zeta_{39})$	$D_{78}$	$\Q(\sqrt{-263}) $	None		$4$	$0$	$0$	$-1$	$0$	$0$	$1$		$q+(\zeta_{78}^{23}-\zeta_{78}^{29})q^{2}+(-\zeta_{78}^{15}+\cdots)q^{3}+\cdots$
789.2.c.a	$789$	$2$	789.c	789.c	$2$	$26$	$26$	$6.300$		$_{}$	$\Q(\sqrt{-263}) $	None		$4$	$0$	$0$	$0$	$0$	$0$		$\mathrm{U}(1)[D_{2}]$
263.3.b.a	$263$	$3$	263.b	263.b	$2$	$13$	$13$	$7.166$	$\mathbb{Q}[x]/(x^{13} - \cdots)$	$_{}$	$\Q(\sqrt{-263}) $	None	✓	$2$	$0$	$0$	$0$	$0$	$0$	$1$	$\mathrm{U}(1)[D_{2}]$	$q+\beta _{2}q^{2}-\beta _{10}q^{3}+(4+\beta _{8}+\beta _{9})q^{4}+\cdots$
263.5.b.a	$263$	$5$	263.b	263.b	$2$	$13$	$13$	$27.186$	$\mathbb{Q}[x]/(x^{13} - \cdots)$	$_{}$	$\Q(\sqrt{-263}) $	None	✓	$2$	$0$	$0$	$0$	$0$	$0$	$1$	$\mathrm{U}(1)[D_{2}]$	$q+(\beta _{8}+\beta _{9})q^{2}+(3\beta _{5}-\beta _{6})q^{3}+(2^{4}+\cdots)q^{4}+\cdots$

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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.