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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 (45 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
268.1.b.a	$268$	$1$	268.b	67.b	$2$	$1$	$1$	$0.134$	$\Q$	$D_{3}$	$\Q(\sqrt{-67}) $	None	✓	$2$	$0$	$0$	$0$	$0$	$0$		$1$		$q+q^{9}-q^{17}-q^{19}-q^{23}+q^{25}+\cdots$
268.2.a.a	$268$	$2$	268.a	1.a	$1$	$1$	$1$	$2.140$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$0$	$2$	$2$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{3}+2q^{5}+2q^{7}+q^{9}-4q^{11}+\cdots$
268.2.a.b	$268$	$2$	268.a	1.a	$1$	$2$	$2$	$2.140$	$\Q(\sqrt{5}) $	$_{}$	None	None	✓	$1$	$1$	$0$	$-3$	$0$	$-5$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1-\beta )q^{3}+(-1+2\beta )q^{5}+(-2+\cdots)q^{7}+\cdots$
268.2.a.c	$268$	$2$	268.a	1.a	$1$	$2$	$2$	$2.140$	$\Q(\sqrt{21}) $	$_{}$	None	None	✓	$1$	$0$	$0$	$1$	$-2$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{3}-q^{5}+(1-\beta )q^{7}+(2+\beta )q^{9}+\cdots$
268.2.d.a	$268$	$2$	268.d	268.d	$2$	$32$	$32$	$2.140$		$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
268.2.e.a	$268$	$2$	268.e	67.c	$3$	$12$	$6$	$2.140$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	$_{}$	None	None		$2$	$0$	$0$	$-4$	$6$	$-3$		$3$	$\mathrm{SU}(2)[C_{3}]$	$q+\beta _{2}q^{3}-\beta _{8}q^{5}+(\beta _{6}-\beta _{7})q^{7}+\beta _{3}q^{9}+\cdots$
268.2.h.a	$268$	$2$	268.h	268.h	$6$	$64$	$32$	$2.140$		$_{}$	None	None		$4$	$0$	$-3$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{6}]$
268.2.i.a	$268$	$2$	268.i	67.e	$11$	$50$	$5$	$2.140$		$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$2$			$\mathrm{SU}(2)[C_{11}]$
268.2.j.a	$268$	$2$	268.j	268.j	$22$	$320$	$32$	$2.140$		$_{}$	None	None		$4$	$0$	$-11$	$0$	$-22$	$0$			$\mathrm{SU}(2)[C_{22}]$
268.2.m.a	$268$	$2$	268.m	67.g	$33$	$120$	$6$	$2.140$		$_{}$	None	None		$2$	$0$	$0$	$4$	$-6$	$3$			$\mathrm{SU}(2)[C_{33}]$
268.2.n.a	$268$	$2$	268.n	268.n	$66$	$640$	$32$	$2.140$		$_{}$	None	None		$4$	$0$	$-19$	$0$	$-44$	$0$			$\mathrm{SU}(2)[C_{66}]$
268.3.b.a	$268$	$3$	268.b	67.b	$2$	$2$	$2$	$7.302$	$\Q(\sqrt{201}) $	$_{}$	$\Q(\sqrt{-67}) $	None	✓	$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{U}(1)[D_{2}]$	$q+9q^{9}+(17-\beta )q^{17}+(13+3\beta )q^{19}+\cdots$
268.3.b.b	$268$	$3$	268.b	67.b	$2$	$10$	$10$	$7.302$	$\mathbb{Q}[x]/(x^{10} + \cdots)$	$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{3}-\beta _{4}q^{5}+\beta _{5}q^{7}+(-4-2\beta _{3}+\cdots)q^{9}+\cdots$
268.3.c.a	$268$	$3$	268.c	4.b	$2$	$66$	$66$	$7.302$		$_{}$	None	None		$2$	$0$	$0$	$0$	$-4$	$0$			$\mathrm{SU}(2)[C_{2}]$
268.3.f.a	$268$	$3$	268.f	67.d	$6$	$22$	$11$	$7.302$		$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$-9$			$\mathrm{SU}(2)[C_{6}]$
268.3.g.a	$268$	$3$	268.g	268.g	$6$	$132$	$66$	$7.302$		$_{}$	None	None		$4$	$0$	$-3$	$0$	$-8$	$0$			$\mathrm{SU}(2)[C_{6}]$
268.3.k.a	$268$	$3$	268.k	268.k	$22$	$660$	$66$	$7.302$		$_{}$	None	None		$4$	$0$	$-11$	$0$	$-18$	$0$			$\mathrm{SU}(2)[C_{22}]$
268.3.l.a	$268$	$3$	268.l	67.f	$22$	$120$	$12$	$7.302$		$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{22}]$
268.3.o.a	$268$	$3$	268.o	268.o	$66$	$1320$	$66$	$7.302$		$_{}$	None	None		$4$	$0$	$-19$	$0$	$-36$	$0$			$\mathrm{SU}(2)[C_{66}]$
268.3.p.a	$268$	$3$	268.p	67.h	$66$	$220$	$11$	$7.302$		$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$9$			$\mathrm{SU}(2)[C_{66}]$
268.4.a.a	$268$	$4$	268.a	1.a	$1$	$8$	$8$	$15.813$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	$_{}$	None	None	✓	$1$	$1$	$0$	$-9$	$-9$	$-20$	$-$	$2^{2}$	$\mathrm{SU}(2)$	$q+(-1-\beta _{5})q^{3}+(-1+\beta _{4})q^{5}+(-3+\cdots)q^{7}+\cdots$
268.4.a.b	$268$	$4$	268.a	1.a	$1$	$9$	$9$	$15.813$	$\mathbb{Q}[x]/(x^{9} - \cdots)$	$_{}$	None	None	✓	$1$	$0$	$0$	$9$	$-9$	$36$	$+$	$2^{2}$	$\mathrm{SU}(2)$	$q+(1+\beta _{1})q^{3}+(-1+\beta _{7})q^{5}+(4+\beta _{1}+\cdots)q^{7}+\cdots$
268.4.d.a	$268$	$4$	268.d	268.d	$2$	$100$	$100$	$15.813$		$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
268.4.e.a	$268$	$4$	268.e	67.c	$3$	$34$	$17$	$15.813$		$_{}$	None	None		$2$	$0$	$0$	$6$	$-12$	$-10$			$\mathrm{SU}(2)[C_{3}]$
268.5.b.a	$268$	$5$	268.b	67.b	$2$	$2$	$2$	$27.703$	$\Q(\sqrt{201}) $	$_{}$	$\Q(\sqrt{-67}) $	None	✓	$2$	$0$	$0$	$0$	$0$	$0$		$3$	$\mathrm{U}(1)[D_{2}]$	$q+3^{4}q^{9}+(-250+11\beta )q^{17}+(-74+\cdots)q^{19}+\cdots$
268.5.b.b	$268$	$5$	268.b	67.b	$2$	$20$	$20$	$27.703$	$\mathbb{Q}[x]/(x^{20} + \cdots)$	$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$0$		$2^{7}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{3}-\beta _{11}q^{5}-\beta _{7}q^{7}+(-30+\cdots)q^{9}+\cdots$
268.5.f.a	$268$	$5$	268.f	67.d	$6$	$46$	$23$	$27.703$		$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$-3$			$\mathrm{SU}(2)[C_{6}]$
268.6.a.a	$268$	$6$	268.a	1.a	$1$	$13$	$13$	$42.983$	$\mathbb{Q}[x]/(x^{13} - \cdots)$	$_{}$	None	None	✓	$1$	$1$	$0$	$-27$	$0$	$-217$	$+$	$2^{9}$	$\mathrm{SU}(2)$	$q+(-2-\beta _{1})q^{3}-\beta _{6}q^{5}+(-17-\beta _{1}+\cdots)q^{7}+\cdots$
268.6.a.b	$268$	$6$	268.a	1.a	$1$	$14$	$14$	$42.983$	$\mathbb{Q}[x]/(x^{14} - \cdots)$	$_{}$	None	None	✓	$1$	$0$	$0$	$27$	$0$	$175$	$-$	$2^{11}$	$\mathrm{SU}(2)$	$q+(2-\beta _{1})q^{3}-\beta _{6}q^{5}+(12+2\beta _{1}-\beta _{6}+\cdots)q^{7}+\cdots$
268.6.e.a	$268$	$6$	268.e	67.c	$3$	$56$	$28$	$42.983$		$_{}$	None	None		$2$	$0$	$0$	$36$	$42$	$-47$			$\mathrm{SU}(2)[C_{3}]$
268.7.b.a	$268$	$7$	268.b	67.b	$2$	$2$	$2$	$61.654$	$\Q(\sqrt{201}) $	$_{}$	$\Q(\sqrt{-67}) $	None	✓	$2$	$0$	$0$	$0$	$0$	$0$		$2^{3}\cdot 5$	$\mathrm{U}(1)[D_{2}]$	$q+3^{6}q^{9}+(3663-20\beta )q^{17}+(-3509+\cdots)q^{19}+\cdots$
268.7.b.b	$268$	$7$	268.b	67.b	$2$	$32$	$32$	$61.654$		$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
268.7.f.a	$268$	$7$	268.f	67.d	$6$	$68$	$34$	$61.654$		$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$-840$			$\mathrm{SU}(2)[C_{6}]$
268.8.a.a	$268$	$8$	268.a	1.a	$1$	$19$	$19$	$83.719$	$\mathbb{Q}[x]/(x^{19} - \cdots)$	$_{}$	None	None	✓	$1$	$1$	$0$	$-81$	$-54$	$-1849$	$-$	$2^{23}\cdot 3^{3}\cdot 5$	$\mathrm{SU}(2)$	$q+(-4-\beta _{1})q^{3}+(-3+\beta _{4})q^{5}+(-98+\cdots)q^{7}+\cdots$
268.8.a.b	$268$	$8$	268.a	1.a	$1$	$20$	$20$	$83.719$	$\mathbb{Q}[x]/(x^{20} - \cdots)$	$_{}$	None	None	✓	$1$	$0$	$0$	$81$	$-54$	$895$	$+$	$2^{26}\cdot 3$	$\mathrm{SU}(2)$	$q+(4+\beta _{1})q^{3}+(-3-\beta _{3})q^{5}+(45-\beta _{1}+\cdots)q^{7}+\cdots$
268.8.e.a	$268$	$8$	268.e	67.c	$3$	$80$	$40$	$83.719$		$_{}$	None	None		$2$	$0$	$0$	$-132$	$-642$	$529$			$\mathrm{SU}(2)[C_{3}]$
268.9.b.a	$268$	$9$	268.b	67.b	$2$	$2$	$2$	$109.177$	$\Q(\sqrt{201}) $	$_{}$	$\Q(\sqrt{-67}) $	None	✓	$2$	$0$	$0$	$0$	$0$	$0$		$3\cdot 7$	$\mathrm{U}(1)[D_{2}]$	$q+3^{8}q^{9}+(-46638+803\beta )q^{17}+\cdots$
268.9.b.b	$268$	$9$	268.b	67.b	$2$	$44$	$44$	$109.177$		$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
268.9.f.a	$268$	$9$	268.f	67.d	$6$	$90$	$45$	$109.177$		$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$2427$			$\mathrm{SU}(2)[C_{6}]$
268.10.a.a	$268$	$10$	268.a	1.a	$1$	$24$	$24$	$138.030$		$_{}$	None	None	✓	$1$	$1$	$0$	$-243$	$495$	$-2820$	$+$		$\mathrm{SU}(2)$
268.10.a.b	$268$	$10$	268.a	1.a	$1$	$25$	$25$	$138.030$		$_{}$	None	None	✓	$1$	$0$	$0$	$243$	$495$	$16388$	$-$		$\mathrm{SU}(2)$
268.11.b.a	$268$	$11$	268.b	67.b	$2$	$2$	$2$	$170.276$	$\Q(\sqrt{201}) $	$_{}$	$\Q(\sqrt{-67}) $	None	✓	$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{U}(1)[D_{2}]$	$q+3^{10}q^{9}+(331057+325279\beta )q^{17}+\cdots$
268.11.b.b	$268$	$11$	268.b	67.b	$2$	$54$	$54$	$170.276$		$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
268.12.a.a	$268$	$12$	268.a	1.a	$1$	$30$	$30$	$205.916$		$_{}$	None	None	✓	$1$	$1$	$0$	$-729$	$6426$	$-102165$	$-$		$\mathrm{SU}(2)$
268.12.a.b	$268$	$12$	268.a	1.a	$1$	$31$	$31$	$205.916$		$_{}$	None	None	✓	$1$	$0$	$0$	$729$	$6426$	$32291$	$+$		$\mathrm{SU}(2)$

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Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
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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.