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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 (40 matches)

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Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	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	CM	Self-dual	Inner twists	Rank*	$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
262.2.a.a	$262$	$2$	262.a	1.a	$1$	$1$	$1$	$2.092$	$\Q$	None	✓	$1$	$1$	$-1$	$0$	$0$	$-5$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}-5q^{7}-q^{8}-3q^{9}+2q^{11}+\cdots$
262.2.a.b	$262$	$2$	262.a	1.a	$1$	$1$	$1$	$2.092$	$\Q$	None	✓	$1$	$1$	$1$	$-2$	$-2$	$-3$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-2q^{3}+q^{4}-2q^{5}-2q^{6}-3q^{7}+\cdots$
262.2.a.c	$262$	$2$	262.a	1.a	$1$	$2$	$2$	$2.092$	$\Q(\sqrt{13}) $	None	✓	$1$	$1$	$-2$	$-1$	$-5$	$3$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-\beta q^{3}+q^{4}+(-3+\beta )q^{5}+\beta q^{6}+\cdots$
262.2.a.d	$262$	$2$	262.a	1.a	$1$	$2$	$2$	$2.092$	$\Q(\sqrt{2}) $	None	✓	$1$	$0$	$-2$	$0$	$4$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+\beta q^{3}+q^{4}+(2-\beta )q^{5}-\beta q^{6}+\cdots$
262.2.a.e	$262$	$2$	262.a	1.a	$1$	$2$	$2$	$2.092$	$\Q(\sqrt{3}) $	None	✓	$1$	$0$	$2$	$-2$	$2$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+(-1+\beta )q^{3}+q^{4}+(1+\beta )q^{5}+\cdots$
262.2.a.f	$262$	$2$	262.a	1.a	$1$	$2$	$2$	$2.092$	$\Q(\sqrt{5}) $	None	✓	$1$	$0$	$2$	$3$	$-1$	$-1$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+(1+\beta )q^{3}+q^{4}-\beta q^{5}+(1+\beta )q^{6}+\cdots$
262.2.c.a	$262$	$2$	262.c	131.c	$5$	$4$	$1$	$2.092$	$\Q(\zeta_{10})$	None		$2$	$0$	$1$	$5$	$-5$	$5$		$1$	$\mathrm{SU}(2)[C_{5}]$	$q+(1-\zeta_{10}+\zeta_{10}^{2}-\zeta_{10}^{3})q^{2}+(2+\cdots)q^{3}+\cdots$
262.2.c.b	$262$	$2$	262.c	131.c	$5$	$16$	$4$	$2.092$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	None		$2$	$0$	$4$	$-4$	$6$	$-5$		$1$	$\mathrm{SU}(2)[C_{5}]$	$q+\beta _{11}q^{2}+(\beta _{5}+\beta _{9}-\beta _{11})q^{3}+(-1+\cdots)q^{4}+\cdots$
262.2.c.c	$262$	$2$	262.c	131.c	$5$	$24$	$6$	$2.092$		None		$2$	$0$	$-6$	$-3$	$-5$	$2$			$\mathrm{SU}(2)[C_{5}]$
262.2.e.a	$262$	$2$	262.e	131.e	$13$	$60$	$5$	$2.092$		None		$2$	$0$	$5$	$1$	$1$	$0$			$\mathrm{SU}(2)[C_{13}]$
262.2.e.b	$262$	$2$	262.e	131.e	$13$	$72$	$6$	$2.092$		None		$2$	$0$	$-6$	$-3$	$-5$	$-8$			$\mathrm{SU}(2)[C_{13}]$
262.2.g.a	$262$	$2$	262.g	131.g	$65$	$240$	$5$	$2.092$		None		$2$	$0$	$-5$	$-1$	$-1$	$0$			$\mathrm{SU}(2)[C_{65}]$
262.2.g.b	$262$	$2$	262.g	131.g	$65$	$288$	$6$	$2.092$		None		$2$	$0$	$6$	$3$	$5$	$-2$			$\mathrm{SU}(2)[C_{65}]$
262.3.b.a	$262$	$3$	262.b	131.b	$2$	$22$	$22$	$7.139$		None		$2$	$0$	$0$	$-4$	$-4$	$4$			$\mathrm{SU}(2)[C_{2}]$
262.3.d.a	$262$	$3$	262.d	131.d	$10$	$88$	$22$	$7.139$		None		$2$	$0$	$0$	$4$	$4$	$26$			$\mathrm{SU}(2)[C_{10}]$
262.3.f.a	$262$	$3$	262.f	131.f	$26$	$264$	$22$	$7.139$		None		$2$	$0$	$0$	$4$	$4$	$-4$			$\mathrm{SU}(2)[C_{26}]$
262.3.h.a	$262$	$3$	262.h	131.h	$130$	$1056$	$22$	$7.139$		None		$2$	$0$	$0$	$-4$	$-4$	$-26$			$\mathrm{SU}(2)[C_{130}]$
262.4.a.a	$262$	$4$	262.a	1.a	$1$	$6$	$6$	$15.459$	$\mathbb{Q}[x]/(x^{6} - \cdots)$	None	✓	$1$	$1$	$12$	$-9$	$-26$	$-56$	$-$	$2^{2}$	$\mathrm{SU}(2)$	$q+2q^{2}+(-1-\beta _{2})q^{3}+4q^{4}+(-5+\cdots)q^{5}+\cdots$
262.4.a.b	$262$	$4$	262.a	1.a	$1$	$8$	$8$	$15.459$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	None	✓	$1$	$0$	$-16$	$1$	$18$	$19$	$+$	$2^{2}$	$\mathrm{SU}(2)$	$q-2q^{2}+\beta _{1}q^{3}+4q^{4}+(2+\beta _{3}-\beta _{5}+\cdots)q^{5}+\cdots$
262.4.a.c	$262$	$4$	262.a	1.a	$1$	$9$	$9$	$15.459$	$\mathbb{Q}[x]/(x^{9} - \cdots)$	None	✓	$1$	$1$	$-18$	$-2$	$-27$	$-9$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{2}-\beta _{1}q^{3}+4q^{4}+(-3+\beta _{5}+\cdots)q^{5}+\cdots$
262.4.a.d	$262$	$4$	262.a	1.a	$1$	$10$	$10$	$15.459$	$\mathbb{Q}[x]/(x^{10} - \cdots)$	None	✓	$1$	$0$	$20$	$12$	$19$	$42$	$+$	$3\cdot 5$	$\mathrm{SU}(2)$	$q+2q^{2}+(1+\beta _{1})q^{3}+4q^{4}+(2+\beta _{2}+\cdots)q^{5}+\cdots$
262.5.b.a	$262$	$5$	262.b	131.b	$2$	$44$	$44$	$27.083$		None		$2$	$0$	$0$	$8$	$36$	$20$			$\mathrm{SU}(2)[C_{2}]$
262.6.a.a	$262$	$6$	262.a	1.a	$1$	$12$	$12$	$42.021$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	None	✓	$1$	$1$	$48$	$-32$	$-120$	$-427$	$+$	$2^{3}\cdot 3$	$\mathrm{SU}(2)$	$q+4q^{2}+(-3+\beta _{1})q^{3}+2^{4}q^{4}+(-10+\cdots)q^{5}+\cdots$
262.6.a.b	$262$	$6$	262.a	1.a	$1$	$13$	$13$	$42.021$	$\mathbb{Q}[x]/(x^{13} - \cdots)$	None	✓	$1$	$0$	$-52$	$-6$	$142$	$26$	$-$	$2^{3}\cdot 13$	$\mathrm{SU}(2)$	$q-4q^{2}-\beta _{1}q^{3}+2^{4}q^{4}+(11-\beta _{9}+\cdots)q^{5}+\cdots$
262.6.a.c	$262$	$6$	262.a	1.a	$1$	$14$	$14$	$42.021$	$\mathbb{Q}[x]/(x^{14} - \cdots)$	None	✓	$1$	$1$	$-56$	$-15$	$-83$	$-170$	$+$	$2^{5}\cdot 3$	$\mathrm{SU}(2)$	$q-4q^{2}+(-1-\beta _{1})q^{3}+2^{4}q^{4}+(-6+\cdots)q^{5}+\cdots$
262.6.a.d	$262$	$6$	262.a	1.a	$1$	$16$	$16$	$42.021$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	None	✓	$1$	$0$	$64$	$31$	$105$	$259$	$-$	$2^{5}$	$\mathrm{SU}(2)$	$q+4q^{2}+(2-\beta _{1})q^{3}+2^{4}q^{4}+(7+\beta _{7}+\cdots)q^{5}+\cdots$
262.7.b.a	$262$	$7$	262.b	131.b	$2$	$66$	$66$	$60.274$		None		$2$	$0$	$0$	$20$	$-224$	$-696$			$\mathrm{SU}(2)[C_{2}]$
262.8.a.a	$262$	$8$	262.a	1.a	$1$	$17$	$17$	$81.845$	$\mathbb{Q}[x]/(x^{17} - \cdots)$	None	✓	$1$	$1$	$136$	$-123$	$-637$	$-1929$	$-$	$2^{7}\cdot 3^{4}$	$\mathrm{SU}(2)$	$q+8q^{2}+(-7-\beta _{1})q^{3}+2^{6}q^{4}+(-38+\cdots)q^{5}+\cdots$
262.8.a.b	$262$	$8$	262.a	1.a	$1$	$18$	$18$	$81.845$	$\mathbb{Q}[x]/(x^{18} - \cdots)$	None	✓	$1$	$0$	$-144$	$43$	$849$	$266$	$+$	$2^{8}\cdot 3^{5}$	$\mathrm{SU}(2)$	$q-8q^{2}+(2+\beta _{1})q^{3}+2^{6}q^{4}+(47-\beta _{4}+\cdots)q^{5}+\cdots$
262.8.a.c	$262$	$8$	262.a	1.a	$1$	$19$	$19$	$81.845$	$\mathbb{Q}[x]/(x^{19} - \cdots)$	None	✓	$1$	$1$	$-152$	$16$	$-276$	$-1106$	$-$	$2^{11}\cdot 3^{3}$	$\mathrm{SU}(2)$	$q-8q^{2}+(1-\beta _{1})q^{3}+2^{6}q^{4}+(-15+\cdots)q^{5}+\cdots$
262.8.a.d	$262$	$8$	262.a	1.a	$1$	$21$	$21$	$81.845$		None	✓	$1$	$0$	$168$	$66$	$488$	$2873$	$+$		$\mathrm{SU}(2)$
262.9.b.a	$262$	$9$	262.b	131.b	$2$	$88$	$88$	$106.733$		None		$2$	$0$	$0$	$-112$	$1116$	$4540$			$\mathrm{SU}(2)[C_{2}]$
262.10.a.a	$262$	$10$	262.a	1.a	$1$	$22$	$22$	$134.939$		None	✓	$1$	$1$	$352$	$-98$	$-2853$	$-12978$	$+$		$\mathrm{SU}(2)$
262.10.a.b	$262$	$10$	262.a	1.a	$1$	$24$	$24$	$134.939$		None	✓	$1$	$0$	$-384$	$84$	$1415$	$859$	$-$		$\mathrm{SU}(2)$
262.10.a.c	$262$	$10$	262.a	1.a	$1$	$25$	$25$	$134.939$		None	✓	$1$	$1$	$-400$	$3$	$-4210$	$-8745$	$+$		$\mathrm{SU}(2)$
262.10.a.d	$262$	$10$	262.a	1.a	$1$	$26$	$26$	$134.939$		None	✓	$1$	$0$	$416$	$469$	$2772$	$20636$	$-$		$\mathrm{SU}(2)$
262.12.a.a	$262$	$12$	262.a	1.a	$1$	$28$	$28$	$201.306$		None	✓	$1$	$1$	$896$	$-1005$	$-14371$	$-165585$	$-$		$\mathrm{SU}(2)$
262.12.a.b	$262$	$12$	262.a	1.a	$1$	$30$	$30$	$201.306$		None	✓	$1$	$0$	$-960$	$13$	$19433$	$58938$	$+$		$\mathrm{SU}(2)$
262.12.a.c	$262$	$12$	262.a	1.a	$1$	$31$	$31$	$201.306$		None	✓	$1$	$1$	$-992$	$-230$	$-8692$	$-8290$	$-$		$\mathrm{SU}(2)$
262.12.a.d	$262$	$12$	262.a	1.a	$1$	$32$	$32$	$201.306$		None	✓	$1$	$0$	$1024$	$696$	$13754$	$69713$	$+$		$\mathrm{SU}(2)$

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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.