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Level	Weight	Analytic conductor	Analytic rank	Dim.

Bad $p$	Char.	Primitive character	Character order	Is maximal/largest

Coefficient field	Self-twists	CM/RM discriminant	Inner twist count	Is self-dual

Coefficient ring index	Coefficient ring gens.	Is twist minimal	Projective image

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Results (1-50 of 132 matches)

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Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	Image	CM	RM	Self-dual	Twist minimal	Largest	Maximal	Minimal twist	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	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
728.1.l.a	$728$	$1$	728.l	728.l	$2$	$1$	$1$	$0.363$	$\Q$	$D_{3}$	$\Q(\sqrt{-182}) $	None	✓	✓			728.1.l.a	$2$	$0$	$-1$	$-1$	$0$	$-1$		$1$		$q-q^{2}-q^{3}+q^{4}+q^{6}-q^{7}-q^{8}+\cdots$
728.1.l.b	$728$	$1$	728.l	728.l	$2$	$1$	$1$	$0.363$	$\Q$	$D_{3}$	$\Q(\sqrt{-182}) $	None	✓	✓			728.1.l.a	$2$	$0$	$-1$	$1$	$0$	$1$		$1$		$q-q^{2}+q^{3}+q^{4}-q^{6}+q^{7}-q^{8}+\cdots$
728.1.l.c	$728$	$1$	728.l	728.l	$2$	$1$	$1$	$0.363$	$\Q$	$D_{3}$	$\Q(\sqrt{-182}) $	None	✓	✓			728.1.l.a	$2$	$0$	$1$	$-1$	$0$	$1$		$1$		$q+q^{2}-q^{3}+q^{4}-q^{6}+q^{7}+q^{8}+\cdots$
728.1.l.d	$728$	$1$	728.l	728.l	$2$	$1$	$1$	$0.363$	$\Q$	$D_{3}$	$\Q(\sqrt{-182}) $	None	✓	✓			728.1.l.a	$2$	$0$	$1$	$1$	$0$	$-1$		$1$		$q+q^{2}+q^{3}+q^{4}+q^{6}-q^{7}+q^{8}+\cdots$
728.1.l.e	$728$	$1$	728.l	728.l	$2$	$4$	$4$	$0.363$	$\Q(\zeta_{8})$	$D_{4}$	$\Q(\sqrt{-14}) $	None		✓	✓		728.1.l.e	$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q+\zeta_{8}^{2}q^{2}+(\zeta_{8}-\zeta_{8}^{3})q^{3}-q^{4}+(-\zeta_{8}+\cdots)q^{5}+\cdots$
728.1.bl.a	$728$	$1$	728.bl	728.al	$6$	$8$	$4$	$0.363$	$\Q(\zeta_{24})$	$D_{12}$	$\Q(\sqrt{-14}) $	None		✓	✓	✓	728.1.bl.a	$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q+\zeta_{24}^{2}q^{2}+(\zeta_{24}^{7}+\zeta_{24}^{9})q^{3}+\zeta_{24}^{4}q^{4}+\cdots$
728.1.bs.a	$728$	$1$	728.bs	728.as	$6$	$6$	$3$	$0.363$	$\Q(\zeta_{18})$	$D_{9}$	$\Q(\sqrt{-26}) $	None		✓			728.1.bs.a	$4$	$0$	$-3$	$0$	$0$	$0$		$1$		$q-\zeta_{18}^{3}q^{2}+(\zeta_{18}^{4}+\zeta_{18}^{8})q^{3}+\zeta_{18}^{6}q^{4}+\cdots$
728.1.bs.b	$728$	$1$	728.bs	728.as	$6$	$6$	$3$	$0.363$	$\Q(\zeta_{18})$	$D_{9}$	$\Q(\sqrt{-26}) $	None		✓			728.1.bs.a	$4$	$0$	$3$	$0$	$0$	$0$		$1$		$q+\zeta_{18}^{3}q^{2}+(\zeta_{18}^{4}+\zeta_{18}^{8})q^{3}+\zeta_{18}^{6}q^{4}+\cdots$
728.1.bx.a	$728$	$1$	728.bx	728.ax	$6$	$4$	$2$	$0.363$	$\Q(\zeta_{12})$	$A_{4}$	None	None		✓	✓	✓	728.1.bx.a	$4$	$0$	$-4$	$-2$	$0$	$0$		$1$		$q-q^{2}-\zeta_{12}^{2}q^{3}+q^{4}+\zeta_{12}^{5}q^{5}+\cdots$
728.1.ce.a	$728$	$1$	728.ce	728.be	$6$	$2$	$1$	$0.363$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-14}) $	None		✓			728.1.ce.a	$4$	$0$	$-1$	$-1$	$2$	$-1$		$1$		$q+\zeta_{6}^{2}q^{2}+\zeta_{6}^{2}q^{3}-\zeta_{6}q^{4}+q^{5}+\cdots$
728.1.ce.b	$728$	$1$	728.ce	728.be	$6$	$2$	$1$	$0.363$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-14}) $	None		✓			728.1.ce.a	$4$	$0$	$-1$	$1$	$-2$	$-1$		$1$		$q+\zeta_{6}^{2}q^{2}-\zeta_{6}^{2}q^{3}-\zeta_{6}q^{4}-q^{5}+\cdots$
728.1.ce.c	$728$	$1$	728.ce	728.be	$6$	$4$	$2$	$0.363$	$\Q(\zeta_{12})$	$D_{6}$	$\Q(\sqrt{-14}) $	None		✓	✓		728.1.ce.c	$8$	$0$	$2$	$0$	$0$	$2$		$1$		$q+\zeta_{12}^{2}q^{2}+(\zeta_{12}+\zeta_{12}^{3})q^{3}+\zeta_{12}^{4}q^{4}+\cdots$
728.1.di.a	$728$	$1$	728.di	728.ci	$6$	$4$	$2$	$0.363$	$\Q(\zeta_{12})$	$A_{4}$	None	None		✓	✓	✓	728.1.bx.a	$4$	$0$	$2$	$4$	$0$	$0$		$1$		$q-\zeta_{12}^{4}q^{2}+q^{3}-\zeta_{12}^{2}q^{4}+\zeta_{12}^{5}q^{5}+\cdots$
728.2.a.a	$728$	$2$	728.a	1.a	$1$	$1$	$1$	$5.813$	$\Q$	$_{}$	None	None	✓	✓	✓	✓	728.2.a.a	$1$	$1$	$0$	$-2$	$-1$	$1$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{3}-q^{5}+q^{7}+q^{9}+4q^{11}-q^{13}+\cdots$
728.2.a.b	$728$	$2$	728.a	1.a	$1$	$1$	$1$	$5.813$	$\Q$	$_{}$	None	None	✓	✓			728.2.a.b	$1$	$0$	$0$	$-1$	$0$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+q^{7}-2q^{9}+3q^{11}-q^{13}+\cdots$
728.2.a.c	$728$	$2$	728.a	1.a	$1$	$1$	$1$	$5.813$	$\Q$	$_{}$	None	None	✓	✓	✓	✓	728.2.a.c	$1$	$1$	$0$	$0$	$-1$	$-1$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{5}-q^{7}-3q^{9}+2q^{11}+q^{13}+\cdots$
728.2.a.d	$728$	$2$	728.a	1.a	$1$	$1$	$1$	$5.813$	$\Q$	$_{}$	None	None	✓	✓			728.2.a.d	$1$	$0$	$0$	$2$	$3$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{3}+3q^{5}+q^{7}+q^{9}-q^{13}+6q^{15}+\cdots$
728.2.a.e	$728$	$2$	728.a	1.a	$1$	$2$	$2$	$5.813$	$\Q(\sqrt{2}) $	$_{}$	None	None	✓	✓	✓	✓	728.2.a.e	$1$	$1$	$0$	$-4$	$-2$	$2$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-2+\beta )q^{3}+(-1+\beta )q^{5}+q^{7}+\cdots$
728.2.a.f	$728$	$2$	728.a	1.a	$1$	$2$	$2$	$5.813$	$\Q(\sqrt{3}) $	$_{}$	None	None	✓	✓	✓	✓	728.2.a.f	$1$	$1$	$0$	$-2$	$0$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta )q^{3}-\beta q^{5}-q^{7}+(1-2\beta )q^{9}+\cdots$
728.2.a.g	$728$	$2$	728.a	1.a	$1$	$2$	$2$	$5.813$	$\Q(\sqrt{17}) $	$_{}$	None	None	✓	✓	✓	✓	728.2.a.g	$1$	$0$	$0$	$1$	$-1$	$-2$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{3}+(-1+\beta )q^{5}-q^{7}+(1+\beta )q^{9}+\cdots$
728.2.a.h	$728$	$2$	728.a	1.a	$1$	$4$	$4$	$5.813$	4.4.183064.1	$_{}$	None	None	✓	✓	✓	✓	728.2.a.h	$1$	$0$	$0$	$1$	$0$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{3}-\beta _{3}q^{5}+q^{7}+(2+\beta _{2})q^{9}+\cdots$
728.2.a.i	$728$	$2$	728.a	1.a	$1$	$4$	$4$	$5.813$	4.4.64268.1	$_{}$	None	None	✓	✓	✓	✓	728.2.a.i	$1$	$0$	$0$	$1$	$2$	$-4$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{3}+(1+\beta _{2})q^{5}-q^{7}+(3+\beta _{1}+\cdots)q^{9}+\cdots$
728.2.b.a	$728$	$2$	728.b	728.b	$2$	$12$	$12$	$5.813$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	$_{}$	$\Q(\sqrt{-26}) $	None		✓			728.2.b.a	$8$	$0$	$0$	$0$	$0$	$0$		$2^{3}$	$\mathrm{U}(1)[D_{2}]$	$q-\beta _{3}q^{2}+(-\beta _{1}-\beta _{7})q^{3}+2q^{4}+(-\beta _{4}+\cdots)q^{5}+\cdots$
728.2.b.b	$728$	$2$	728.b	728.b	$2$	$96$	$96$	$5.813$		$_{}$	None	None		✓	✓		728.2.b.b	$8$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
728.2.c.a	$728$	$2$	728.c	8.b	$2$	$34$	$34$	$5.813$		$_{}$	None	None		✓			728.2.c.a	$2$	$0$	$2$	$0$	$0$	$-34$			$\mathrm{SU}(2)[C_{2}]$
728.2.c.b	$728$	$2$	728.c	8.b	$2$	$38$	$38$	$5.813$		$_{}$	None	None		✓	✓		728.2.c.b	$2$	$0$	$0$	$0$	$0$	$38$			$\mathrm{SU}(2)[C_{2}]$
728.2.h.a	$728$	$2$	728.h	56.e	$2$	$48$	$48$	$5.813$		$_{}$	None	None		✓			728.2.h.a	$2$	$0$	$1$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
728.2.h.b	$728$	$2$	728.h	56.e	$2$	$48$	$48$	$5.813$		$_{}$	None	None		✓			728.2.h.a	$2$	$0$	$1$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
728.2.i.a	$728$	$2$	728.i	104.e	$2$	$84$	$84$	$5.813$		$_{}$	None	None		✓	✓	✓	728.2.i.a	$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
728.2.k.a	$728$	$2$	728.k	13.b	$2$	$8$	$8$	$5.813$	$\mathbb{Q}[x]/(x^{8} + \cdots)$	$_{}$	None	None		✓			728.2.k.a	$2$	$0$	$0$	$-2$	$0$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{2}q^{3}+(-\beta _{1}+\beta _{5})q^{5}-\beta _{5}q^{7}+\cdots$
728.2.k.b	$728$	$2$	728.k	13.b	$2$	$12$	$12$	$5.813$	$\mathbb{Q}[x]/(x^{12} + \cdots)$	$_{}$	None	None		✓	✓		728.2.k.b	$2$	$0$	$0$	$2$	$0$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{2}q^{3}+(-\beta _{1}+\beta _{5}+\beta _{7})q^{5}-\beta _{4}q^{7}+\cdots$
728.2.q.a	$728$	$2$	728.q	91.h	$3$	$2$	$1$	$5.813$	$\Q(\sqrt{-3}) $	$_{}$	None	None		✓			728.2.q.a	$2$	$0$	$0$	$1$	$-3$	$4$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+\zeta_{6}q^{3}-3\zeta_{6}q^{5}+(1+2\zeta_{6})q^{7}+(2+\cdots)q^{9}+\cdots$
728.2.q.b	$728$	$2$	728.q	91.h	$3$	$6$	$3$	$5.813$	6.0.1156923.1	$_{}$	None	None		✓			728.2.q.b	$2$	$0$	$0$	$0$	$3$	$3$		$2^{2}$	$\mathrm{SU}(2)[C_{3}]$	$q+\beta _{4}q^{3}-\beta _{2}q^{5}+(1+\beta _{5})q^{7}+(-3+\cdots)q^{9}+\cdots$
728.2.q.c	$728$	$2$	728.q	91.h	$3$	$8$	$4$	$5.813$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	$_{}$	None	None		✓			728.2.q.c	$2$	$0$	$0$	$-3$	$1$	$-4$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(\beta _{1}-\beta _{6})q^{3}+(-\beta _{1}+\beta _{5})q^{5}+(1+\cdots)q^{7}+\cdots$
728.2.q.d	$728$	$2$	728.q	91.h	$3$	$18$	$9$	$5.813$	$\mathbb{Q}[x]/(x^{18} + \cdots)$	$_{}$	None	None		✓			728.2.q.d	$2$	$0$	$0$	$0$	$4$	$-1$		$2^{6}\cdot 3$	$\mathrm{SU}(2)[C_{3}]$	$q-\beta _{13}q^{3}+(-\beta _{4}-\beta _{12})q^{5}+(\beta _{1}+\beta _{2}+\cdots)q^{7}+\cdots$
728.2.q.e	$728$	$2$	728.q	91.h	$3$	$22$	$11$	$5.813$		$_{}$	None	None		✓	✓		728.2.q.e	$2$	$0$	$0$	$-2$	$-5$	$0$			$\mathrm{SU}(2)[C_{3}]$
728.2.r.a	$728$	$2$	728.r	7.c	$3$	$2$	$1$	$5.813$	$\Q(\sqrt{-3}) $	$_{}$	None	None		✓			728.2.r.a	$2$	$0$	$0$	$1$	$-3$	$4$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(1-\zeta_{6})q^{3}-3\zeta_{6}q^{5}+(3-2\zeta_{6})q^{7}+\cdots$
728.2.r.b	$728$	$2$	728.r	7.c	$3$	$2$	$1$	$5.813$	$\Q(\sqrt{-3}) $	$_{}$	None	None		✓			728.2.r.b	$2$	$0$	$0$	$1$	$-1$	$-4$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(1-\zeta_{6})q^{3}-\zeta_{6}q^{5}+(-3+2\zeta_{6})q^{7}+\cdots$
728.2.r.c	$728$	$2$	728.r	7.c	$3$	$2$	$1$	$5.813$	$\Q(\sqrt{-3}) $	$_{}$	None	None		✓			728.2.r.c	$2$	$0$	$0$	$1$	$3$	$-4$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(1-\zeta_{6})q^{3}+3\zeta_{6}q^{5}+(-3+2\zeta_{6})q^{7}+\cdots$
728.2.r.d	$728$	$2$	728.r	7.c	$3$	$4$	$2$	$5.813$	$\Q(\sqrt{-3}, \sqrt{7})$	$_{}$	None	None		✓			728.2.r.d	$2$	$0$	$0$	$-4$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+2\beta _{2}q^{3}-\beta _{1}q^{7}+(-1-\beta _{2})q^{9}+\cdots$
728.2.r.e	$728$	$2$	728.r	7.c	$3$	$8$	$4$	$5.813$	8.0.$\cdots$.1	$_{}$	None	None		✓			728.2.r.e	$2$	$0$	$0$	$1$	$-1$	$1$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-\beta _{1}-\beta _{6})q^{3}+(-\beta _{1}-\beta _{5})q^{5}+\cdots$
728.2.r.f	$728$	$2$	728.r	7.c	$3$	$14$	$7$	$5.813$	$\mathbb{Q}[x]/(x^{14} - \cdots)$	$_{}$	None	None		✓			728.2.r.f	$2$	$0$	$0$	$2$	$-2$	$-2$		$2^{2}$	$\mathrm{SU}(2)[C_{3}]$	$q+\beta _{1}q^{3}-\beta _{9}q^{5}-\beta _{4}q^{7}+(-1-\beta _{3}+\cdots)q^{9}+\cdots$
728.2.r.g	$728$	$2$	728.r	7.c	$3$	$16$	$8$	$5.813$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	$_{}$	None	None		✓	✓		728.2.r.g	$2$	$0$	$0$	$-2$	$0$	$1$		$2^{2}$	$\mathrm{SU}(2)[C_{3}]$	$q+(\beta _{1}-\beta _{2})q^{3}-\beta _{10}q^{5}+(\beta _{6}-\beta _{13}+\cdots)q^{7}+\cdots$
728.2.s.a	$728$	$2$	728.s	13.c	$3$	$2$	$1$	$5.813$	$\Q(\sqrt{-3}) $	$_{}$	None	None		✓			728.2.s.a	$2$	$0$	$0$	$-2$	$2$	$-1$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-2+2\zeta_{6})q^{3}+q^{5}-\zeta_{6}q^{7}-\zeta_{6}q^{9}+\cdots$
728.2.s.b	$728$	$2$	728.s	13.c	$3$	$4$	$2$	$5.813$	$\Q(\sqrt{-3}, \sqrt{5})$	$_{}$	None	None		✓			728.2.s.b	$2$	$0$	$0$	$-1$	$10$	$2$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q-\beta _{1}q^{3}+(2-\beta _{2})q^{5}-\beta _{3}q^{7}+(\beta _{1}+\cdots)q^{9}+\cdots$
728.2.s.c	$728$	$2$	728.s	13.c	$3$	$4$	$2$	$5.813$	$\Q(\zeta_{12})$	$_{}$	None	None		✓			728.2.s.c	$2$	$0$	$0$	$2$	$0$	$2$		$3$	$\mathrm{SU}(2)[C_{3}]$	$q+(\zeta_{12}-\zeta_{12}^{2})q^{3}-\zeta_{12}^{3}q^{5}+(1-\zeta_{12}+\cdots)q^{7}+\cdots$
728.2.s.d	$728$	$2$	728.s	13.c	$3$	$4$	$2$	$5.813$	$\Q(\zeta_{12})$	$_{}$	None	None		✓			728.2.s.d	$2$	$0$	$0$	$2$	$8$	$-2$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-\zeta_{12}+\zeta_{12}^{2}-\zeta_{12}^{3})q^{3}+(2+2\zeta_{12}+\cdots)q^{5}+\cdots$
728.2.s.e	$728$	$2$	728.s	13.c	$3$	$8$	$4$	$5.813$	8.0.4277552409.3	$_{}$	None	None		✓			728.2.s.e	$2$	$0$	$0$	$-3$	$-10$	$-4$		$2^{2}\cdot 3$	$\mathrm{SU}(2)[C_{3}]$	$q+(-\beta _{1}-\beta _{3})q^{3}+(-1+\beta _{1}+\beta _{7})q^{5}+\cdots$
728.2.s.f	$728$	$2$	728.s	13.c	$3$	$8$	$4$	$5.813$	8.0.$\cdots$.1	$_{}$	None	None		✓			728.2.s.f	$2$	$0$	$0$	$3$	$-10$	$-4$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-\beta _{1}-\beta _{4})q^{3}+(-1-\beta _{6})q^{5}+(-1+\cdots)q^{7}+\cdots$
728.2.s.g	$728$	$2$	728.s	13.c	$3$	$14$	$7$	$5.813$	$\mathbb{Q}[x]/(x^{14} - \cdots)$	$_{}$	None	None		✓	✓		728.2.s.g	$2$	$0$	$0$	$-1$	$4$	$7$		$2^{2}$	$\mathrm{SU}(2)[C_{3}]$	$q+(\beta _{1}-\beta _{2})q^{3}+\beta _{4}q^{5}+\beta _{7}q^{7}+(-\beta _{1}+\cdots)q^{9}+\cdots$

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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.