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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 (1-50 of 67 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
889.1.n.a	$889$	$1$	889.n	889.n	$6$	$4$	$2$	$0.444$	$\Q(\zeta_{12})$	$A_{4}$	None	None		$4$	$0$	$-2$	$0$	$0$	$0$		$1$		$q-\zeta_{12}^{2}q^{2}-\zeta_{12}q^{3}+\zeta_{12}^{5}q^{5}+\zeta_{12}^{3}q^{6}+\cdots$
889.1.t.a	$889$	$1$	889.t	889.t	$6$	$2$	$1$	$0.444$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-7}) $	None		$4$	$0$	$-2$	$0$	$0$	$-1$		$1$		$q-q^{2}-\zeta_{6}q^{7}+q^{8}+\zeta_{6}^{2}q^{9}-\zeta_{6}^{2}q^{11}+\cdots$
889.1.ba.a	$889$	$1$	889.ba	889.aa	$14$	$6$	$1$	$0.444$	$\Q(\zeta_{14})$	$D_{7}$	$\Q(\sqrt{-7}) $	None		$4$	$0$	$5$	$0$	$0$	$-1$		$1$		$q+(1+\zeta_{14}^{4})q^{2}+(1-\zeta_{14}+\zeta_{14}^{4}+\cdots)q^{4}+\cdots$
889.1.bj.a	$889$	$1$	889.bj	889.aj	$18$	$6$	$1$	$0.444$	$\Q(\zeta_{18})$	$D_{9}$	$\Q(\sqrt{-7}) $	None		$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q+(-\zeta_{18}+\zeta_{18}^{8})q^{2}+(1+\zeta_{18}^{2}-\zeta_{18}^{7}+\cdots)q^{4}+\cdots$
889.1.bo.a	$889$	$1$	889.bo	889.ao	$42$	$12$	$1$	$0.444$	$\Q(\zeta_{21})$	$D_{21}$	$\Q(\sqrt{-7}) $	None		$4$	$0$	$-5$	$0$	$0$	$1$		$1$		$q+(\zeta_{42}^{14}+\zeta_{42}^{16})q^{2}+(-\zeta_{42}^{7}-\zeta_{42}^{9}+\cdots)q^{4}+\cdots$
889.1.ce.a	$889$	$1$	889.ce	889.be	$126$	$36$	$1$	$0.444$	$\Q(\zeta_{63})$	$D_{63}$	$\Q(\sqrt{-7}) $	None		$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q+(\zeta_{126}^{14}+\zeta_{126}^{58})q^{2}+(-\zeta_{126}^{9}+\zeta_{126}^{28}+\cdots)q^{4}+\cdots$
889.2.a.a	$889$	$2$	889.a	1.a	$1$	$12$	$12$	$7.099$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	$_{}$	None	None	✓	$1$	$1$	$-7$	$-4$	$-7$	$12$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta _{1})q^{2}-\beta _{10}q^{3}+(1-\beta _{1}+\cdots)q^{4}+\cdots$
889.2.a.b	$889$	$2$	889.a	1.a	$1$	$15$	$15$	$7.099$	$\mathbb{Q}[x]/(x^{15} - \cdots)$	$_{}$	None	None	✓	$1$	$0$	$0$	$4$	$7$	$-15$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+\beta _{9}q^{3}+(1+\beta _{2})q^{4}+\beta _{8}q^{5}+\cdots$
889.2.a.c	$889$	$2$	889.a	1.a	$1$	$16$	$16$	$7.099$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	$_{}$	None	None	✓	$1$	$1$	$-2$	$-4$	$-9$	$-16$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+\beta _{10}q^{3}+(1+\beta _{2})q^{4}+(-1+\cdots)q^{5}+\cdots$
889.2.a.d	$889$	$2$	889.a	1.a	$1$	$20$	$20$	$7.099$	$\mathbb{Q}[x]/(x^{20} - \cdots)$	$_{}$	None	None	✓	$1$	$0$	$8$	$0$	$3$	$20$	$-$	$2$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+\beta _{9}q^{3}+(1+\beta _{2})q^{4}-\beta _{16}q^{5}+\cdots$
889.2.d.a	$889$	$2$	889.d	889.d	$2$	$2$	$2$	$7.099$	$\Q(\sqrt{-7}) $	$_{}$	$\Q(\sqrt{-7}) $	None		$4$	$0$	$-2$	$0$	$0$	$0$		$2$	$\mathrm{U}(1)[D_{2}]$	$q-q^{2}-q^{4}+\beta q^{7}+3q^{8}-3q^{9}+4q^{11}+\cdots$
889.2.d.b	$889$	$2$	889.d	889.d	$2$	$80$	$80$	$7.099$		$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
889.2.e.a	$889$	$2$	889.e	889.e	$3$	$168$	$84$	$7.099$		$_{}$	None	None		$2$	$0$	$-3$	$3$	$2$	$-5$			$\mathrm{SU}(2)[C_{3}]$
889.2.f.a	$889$	$2$	889.f	7.c	$3$	$4$	$2$	$7.099$	$\Q(\sqrt{-3}, \sqrt{5})$	$_{}$	None	None		$2$	$0$	$-3$	$4$	$-3$	$10$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-1-\beta _{1}-\beta _{3})q^{2}-2\beta _{3}q^{3}+(3\beta _{1}+\cdots)q^{4}+\cdots$
889.2.f.b	$889$	$2$	889.f	7.c	$3$	$8$	$4$	$7.099$	8.0.142635249.1	$_{}$	None	None		$2$	$0$	$-2$	$1$	$-3$	$-4$		$3$	$\mathrm{SU}(2)[C_{3}]$	$q+(\beta _{3}-\beta _{5}-\beta _{7})q^{2}+(-\beta _{4}-\beta _{7})q^{3}+\cdots$
889.2.f.c	$889$	$2$	889.f	7.c	$3$	$76$	$38$	$7.099$		$_{}$	None	None		$2$	$0$	$2$	$-11$	$-16$	$3$			$\mathrm{SU}(2)[C_{3}]$
889.2.f.d	$889$	$2$	889.f	7.c	$3$	$80$	$40$	$7.099$		$_{}$	None	None		$2$	$0$	$3$	$6$	$24$	$-11$			$\mathrm{SU}(2)[C_{3}]$
889.2.g.a	$889$	$2$	889.g	889.g	$3$	$168$	$84$	$7.099$		$_{}$	None	None		$2$	$0$	$-3$	$-6$	$2$	$7$			$\mathrm{SU}(2)[C_{3}]$
889.2.h.a	$889$	$2$	889.h	127.c	$3$	$62$	$31$	$7.099$		$_{}$	None	None		$2$	$0$	$-4$	$0$	$2$	$31$			$\mathrm{SU}(2)[C_{3}]$
889.2.h.b	$889$	$2$	889.h	127.c	$3$	$66$	$33$	$7.099$		$_{}$	None	None		$2$	$0$	$2$	$0$	$-2$	$-33$			$\mathrm{SU}(2)[C_{3}]$
889.2.k.a	$889$	$2$	889.k	889.k	$6$	$168$	$84$	$7.099$		$_{}$	None	None		$2$	$0$	$-1$	$-3$	$0$	$3$			$\mathrm{SU}(2)[C_{6}]$
889.2.l.a	$889$	$2$	889.l	889.l	$6$	$168$	$84$	$7.099$		$_{}$	None	None		$4$	$0$	$-4$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{6}]$
889.2.q.a	$889$	$2$	889.q	889.q	$6$	$168$	$84$	$7.099$		$_{}$	None	None		$2$	$0$	$-1$	$-6$	$0$	$-3$			$\mathrm{SU}(2)[C_{6}]$
889.2.r.a	$889$	$2$	889.r	889.r	$6$	$4$	$2$	$7.099$	$\Q(\sqrt{-3}, \sqrt{-7})$	$_{}$	$\Q(\sqrt{-7}) $	None		$4$	$0$	$2$	$0$	$0$	$0$		$1$	$\mathrm{U}(1)[D_{6}]$	$q+(1-\beta _{1}-\beta _{3})q^{2}+(4-\beta _{1}-\beta _{3})q^{4}+\cdots$
889.2.r.b	$889$	$2$	889.r	889.r	$6$	$160$	$80$	$7.099$		$_{}$	None	None		$4$	$0$	$-12$	$0$	$0$	$-9$			$\mathrm{SU}(2)[C_{6}]$
889.2.u.a	$889$	$2$	889.u	127.e	$7$	$6$	$1$	$7.099$	$\Q(\zeta_{14})$	$_{}$	None	None		$2$	$0$	$-3$	$3$	$-4$	$-1$		$1$	$\mathrm{SU}(2)[C_{7}]$	$q+(-\zeta_{14}+\zeta_{14}^{4}-\zeta_{14}^{5})q^{2}+(1-\zeta_{14}+\cdots)q^{3}+\cdots$
889.2.u.b	$889$	$2$	889.u	127.e	$7$	$186$	$31$	$7.099$		$_{}$	None	None		$2$	$0$	$2$	$0$	$-5$	$31$			$\mathrm{SU}(2)[C_{7}]$
889.2.u.c	$889$	$2$	889.u	127.e	$7$	$192$	$32$	$7.099$		$_{}$	None	None		$2$	$0$	$6$	$-3$	$9$	$-32$			$\mathrm{SU}(2)[C_{7}]$
889.2.v.a	$889$	$2$	889.v	889.v	$9$	$498$	$83$	$7.099$		$_{}$	None	None		$2$	$0$	$-6$	$-3$	$15$	$0$			$\mathrm{SU}(2)[C_{9}]$
889.2.w.a	$889$	$2$	889.w	889.w	$9$	$498$	$83$	$7.099$		$_{}$	None	None		$2$	$0$	$-6$	$-3$	$-30$	$-18$			$\mathrm{SU}(2)[C_{9}]$
889.2.x.a	$889$	$2$	889.x	127.f	$9$	$186$	$31$	$7.099$		$_{}$	None	None		$2$	$0$	$-12$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{9}]$
889.2.x.b	$889$	$2$	889.x	127.f	$9$	$198$	$33$	$7.099$		$_{}$	None	None		$2$	$0$	$12$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{9}]$
889.2.y.a	$889$	$2$	889.y	889.y	$14$	$6$	$1$	$7.099$	$\Q(\zeta_{14})$	$_{}$	$\Q(\sqrt{-7}) $	None		$4$	$0$	$-6$	$0$	$0$	$7$		$1$	$\mathrm{U}(1)[D_{14}]$	$q+(-2+\zeta_{14}-2\zeta_{14}^{2}+\zeta_{14}^{3}-2\zeta_{14}^{4}+\cdots)q^{2}+\cdots$
889.2.y.b	$889$	$2$	889.y	889.y	$14$	$6$	$1$	$7.099$	$\Q(\zeta_{14})$	$_{}$	$\Q(\sqrt{-7}) $	None		$4$	$0$	$1$	$0$	$0$	$-7$		$1$	$\mathrm{U}(1)[D_{14}]$	$q+(1-\zeta_{14}+2\zeta_{14}^{2}-\zeta_{14}^{3}+\zeta_{14}^{4}+\cdots)q^{2}+\cdots$
889.2.y.c	$889$	$2$	889.y	889.y	$14$	$480$	$80$	$7.099$		$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$14$			$\mathrm{SU}(2)[C_{14}]$
889.2.bd.a	$889$	$2$	889.bd	889.ad	$18$	$498$	$83$	$7.099$		$_{}$	None	None		$2$	$0$	$-6$	$-9$	$-9$	$0$			$\mathrm{SU}(2)[C_{18}]$
889.2.bg.a	$889$	$2$	889.bg	889.ag	$18$	$498$	$83$	$7.099$		$_{}$	None	None		$2$	$0$	$-6$	$-9$	$-18$	$-18$			$\mathrm{SU}(2)[C_{18}]$
889.2.bh.a	$889$	$2$	889.bh	889.ah	$18$	$12$	$2$	$7.099$	12.0.$\cdots$.1	$_{}$	$\Q(\sqrt{-7}) $	None		$4$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{U}(1)[D_{18}]$	$q+(\beta _{1}-\beta _{4}+\beta _{6}-\beta _{7}-\beta _{11})q^{2}+(2+\cdots)q^{4}+\cdots$
889.2.bh.b	$889$	$2$	889.bh	889.ah	$18$	$492$	$82$	$7.099$		$_{}$	None	None		$4$	$0$	$-24$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{18}]$
889.2.bk.a	$889$	$2$	889.bk	127.i	$21$	$372$	$31$	$7.099$		$_{}$	None	None		$2$	$0$	$4$	$0$	$5$	$-31$			$\mathrm{SU}(2)[C_{21}]$
889.2.bk.b	$889$	$2$	889.bk	127.i	$21$	$396$	$33$	$7.099$		$_{}$	None	None		$2$	$0$	$-9$	$0$	$-5$	$33$			$\mathrm{SU}(2)[C_{21}]$
889.2.bl.a	$889$	$2$	889.bl	889.al	$21$	$1008$	$84$	$7.099$		$_{}$	None	None		$2$	$0$	$3$	$-1$	$-9$	$-7$			$\mathrm{SU}(2)[C_{21}]$
889.2.bm.a	$889$	$2$	889.bm	889.am	$21$	$1008$	$84$	$7.099$		$_{}$	None	None		$4$	$0$	$0$	$-7$	$-9$	$-19$			$\mathrm{SU}(2)[C_{21}]$
889.2.bn.a	$889$	$2$	889.bn	889.an	$21$	$1008$	$84$	$7.099$		$_{}$	None	None		$2$	$0$	$-18$	$-10$	$-9$	$-16$			$\mathrm{SU}(2)[C_{21}]$
889.2.bq.a	$889$	$2$	889.bq	889.aq	$42$	$12$	$1$	$7.099$	$\Q(\zeta_{21})$	$_{}$	$\Q(\sqrt{-7}) $	None		$4$	$0$	$-1$	$0$	$0$	$7$		$1$	$\mathrm{U}(1)[D_{42}]$	$q+(\zeta_{21}^{7}+\zeta_{21}^{8}-\zeta_{21}^{9}+\zeta_{21}^{10}+\cdots)q^{2}+\cdots$
889.2.bq.b	$889$	$2$	889.bq	889.aq	$42$	$12$	$1$	$7.099$	$\Q(\zeta_{21})$	$_{}$	$\Q(\sqrt{-7}) $	None		$4$	$0$	$6$	$0$	$0$	$-7$		$1$	$\mathrm{U}(1)[D_{42}]$	$q+(1-\zeta_{21}^{4}-\zeta_{21}^{8}+\zeta_{21}^{9}-\zeta_{21}^{10}+\cdots)q^{2}+\cdots$
889.2.bq.c	$889$	$2$	889.bq	889.aq	$42$	$960$	$80$	$7.099$		$_{}$	None	None		$4$	$0$	$-30$	$0$	$0$	$-26$			$\mathrm{SU}(2)[C_{42}]$
889.2.br.a	$889$	$2$	889.br	889.ar	$42$	$1008$	$84$	$7.099$		$_{}$	None	None		$2$	$0$	$-13$	$-15$	$-21$	$-25$			$\mathrm{SU}(2)[C_{42}]$
889.2.bw.a	$889$	$2$	889.bw	889.aw	$42$	$1008$	$84$	$7.099$		$_{}$	None	None		$4$	$0$	$-10$	$-21$	$-21$	$-7$			$\mathrm{SU}(2)[C_{42}]$
889.2.bx.a	$889$	$2$	889.bx	889.ax	$42$	$1008$	$84$	$7.099$		$_{}$	None	None		$2$	$0$	$8$	$-18$	$-21$	$-10$			$\mathrm{SU}(2)[C_{42}]$

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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.