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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 136 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
540.1.f.a	$540$	$1$	540.f	20.d	$2$	$4$	$4$	$0.269$	$\Q(\zeta_{12})$	$D_{6}$	$\Q(\sqrt{-15}) $	None		$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{12}q^{2}+\zeta_{12}^{2}q^{4}+\zeta_{12}^{3}q^{5}-\zeta_{12}^{3}q^{8}+\cdots$
540.1.p.a	$540$	$1$	540.p	180.p	$6$	$2$	$1$	$0.269$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-5}) $	None		$4$	$0$	$-1$	$0$	$1$	$-1$		$1$		$q-\zeta_{6}q^{2}+\zeta_{6}^{2}q^{4}-\zeta_{6}^{2}q^{5}-\zeta_{6}q^{7}+\cdots$
540.1.p.b	$540$	$1$	540.p	180.p	$6$	$2$	$1$	$0.269$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-5}) $	None		$4$	$0$	$1$	$0$	$1$	$1$		$1$		$q+\zeta_{6}q^{2}+\zeta_{6}^{2}q^{4}-\zeta_{6}^{2}q^{5}+\zeta_{6}q^{7}+\cdots$
540.1.bf.a	$540$	$1$	540.bf	540.af	$18$	$6$	$1$	$0.269$	$\Q(\zeta_{18})$	$D_{9}$	$\Q(\sqrt{-5}) $	None		$4$	$0$	$0$	$0$	$0$	$-3$		$1$		$q-\zeta_{18}q^{2}-\zeta_{18}^{5}q^{3}+\zeta_{18}^{2}q^{4}-\zeta_{18}^{5}q^{5}+\cdots$
540.1.bf.b	$540$	$1$	540.bf	540.af	$18$	$6$	$1$	$0.269$	$\Q(\zeta_{18})$	$D_{9}$	$\Q(\sqrt{-5}) $	None		$4$	$0$	$0$	$0$	$0$	$3$		$1$		$q+\zeta_{18}q^{2}+\zeta_{18}^{5}q^{3}+\zeta_{18}^{2}q^{4}-\zeta_{18}^{5}q^{5}+\cdots$
540.2.a.a	$540$	$2$	540.a	1.a	$1$	$1$	$1$	$4.312$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$0$	$0$	$-1$	$-4$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{5}-4q^{7}+6q^{11}-4q^{13}-3q^{17}+\cdots$
540.2.a.b	$540$	$2$	540.a	1.a	$1$	$1$	$1$	$4.312$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$0$	$0$	$-1$	$-1$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{5}-q^{7}-6q^{11}-q^{13}-q^{19}+\cdots$
540.2.a.c	$540$	$2$	540.a	1.a	$1$	$1$	$1$	$4.312$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$0$	$0$	$-1$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{5}+2q^{7}+2q^{13}+3q^{17}+5q^{19}+\cdots$
540.2.a.d	$540$	$2$	540.a	1.a	$1$	$1$	$1$	$4.312$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$0$	$0$	$1$	$-4$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{5}-4q^{7}-6q^{11}-4q^{13}+3q^{17}+\cdots$
540.2.a.e	$540$	$2$	540.a	1.a	$1$	$1$	$1$	$4.312$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$0$	$0$	$1$	$-1$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{5}-q^{7}+6q^{11}-q^{13}-q^{19}+\cdots$
540.2.a.f	$540$	$2$	540.a	1.a	$1$	$1$	$1$	$4.312$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$0$	$0$	$1$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{5}+2q^{7}+2q^{13}-3q^{17}+5q^{19}+\cdots$
540.2.d.a	$540$	$2$	540.d	5.b	$2$	$2$	$2$	$4.312$	$\Q(\sqrt{-1}) $	$_{}$	None	None		$2$	$0$	$0$	$0$	$-4$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+(-2+i)q^{5}-2iq^{7}+2q^{11}-6iq^{13}+\cdots$
540.2.d.b	$540$	$2$	540.d	5.b	$2$	$2$	$2$	$4.312$	$\Q(\sqrt{-1}) $	$_{}$	None	None		$2$	$0$	$0$	$0$	$4$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+(2+i)q^{5}+2iq^{7}-2q^{11}+6iq^{13}+\cdots$
540.2.d.c	$540$	$2$	540.d	5.b	$2$	$4$	$4$	$4.312$	$\Q(i, \sqrt{10})$	$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{5}+\beta _{2}q^{7}+(\beta _{1}-\beta _{3})q^{11}-3\beta _{2}q^{13}+\cdots$
540.2.e.a	$540$	$2$	540.e	12.b	$2$	$16$	$16$	$4.312$	16.0.$\cdots$.1	$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$0$		$2^{12}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{11}q^{2}+\beta _{2}q^{4}+\beta _{3}q^{5}+(\beta _{4}+\beta _{6}+\cdots)q^{7}+\cdots$
540.2.e.b	$540$	$2$	540.e	12.b	$2$	$16$	$16$	$4.312$	16.0.$\cdots$.1	$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$0$		$2^{12}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{2}+(\beta _{2}+\beta _{7})q^{4}+\beta _{3}q^{5}+(\beta _{6}+\cdots)q^{7}+\cdots$
540.2.h.a	$540$	$2$	540.h	60.h	$2$	$4$	$4$	$4.312$	$\Q(\sqrt{-3}, \sqrt{5})$	$_{}$	$\Q(\sqrt{-15}) $	None		$4$	$0$	$-3$	$0$	$0$	$0$		$2$	$\mathrm{U}(1)[D_{2}]$	$q+(-1+\beta _{1})q^{2}+(-\beta _{1}+\beta _{2})q^{4}+(\beta _{1}+\cdots)q^{5}+\cdots$
540.2.h.b	$540$	$2$	540.h	60.h	$2$	$4$	$4$	$4.312$	$\Q(\sqrt{-3}, \sqrt{5})$	$_{}$	$\Q(\sqrt{-15}) $	None		$4$	$0$	$3$	$0$	$0$	$0$		$2$	$\mathrm{U}(1)[D_{2}]$	$q+(1-\beta _{1})q^{2}+(-\beta _{1}+\beta _{2})q^{4}+(-\beta _{1}+\cdots)q^{5}+\cdots$
540.2.h.c	$540$	$2$	540.h	60.h	$2$	$16$	$16$	$4.312$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	$_{}$	None	None		$8$	$0$	$0$	$0$	$0$	$0$		$2^{10}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{7}q^{2}-\beta _{11}q^{4}+(-\beta _{6}-\beta _{10})q^{5}+\cdots$
540.2.h.d	$540$	$2$	540.h	60.h	$2$	$24$	$24$	$4.312$		$_{}$	None	None		$8$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
540.2.i.a	$540$	$2$	540.i	9.c	$3$	$2$	$1$	$4.312$	$\Q(\sqrt{-3}) $	$_{}$	None	None		$2$	$0$	$0$	$0$	$1$	$1$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+\zeta_{6}q^{5}+(1-\zeta_{6})q^{7}+4\zeta_{6}q^{13}+6q^{17}+\cdots$
540.2.i.b	$540$	$2$	540.i	9.c	$3$	$6$	$3$	$4.312$	6.0.954288.1	$_{}$	None	None		$2$	$0$	$0$	$0$	$-3$	$-3$		$3^{3}$	$\mathrm{SU}(2)[C_{3}]$	$q+(-1-\beta _{2})q^{5}+(\beta _{2}+\beta _{4})q^{7}+(\beta _{3}+\cdots)q^{11}+\cdots$
540.2.j.a	$540$	$2$	540.j	15.e	$4$	$8$	$4$	$4.312$	8.0.$\cdots$.8	$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$-8$		$5$	$\mathrm{SU}(2)[C_{4}]$	$q+\beta _{2}q^{5}+(-1-\beta _{1}+\beta _{4})q^{7}+(-\beta _{5}+\cdots)q^{11}+\cdots$
540.2.j.b	$540$	$2$	540.j	15.e	$4$	$8$	$4$	$4.312$	8.0.$\cdots$.1	$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$4$		$2^{2}$	$\mathrm{SU}(2)[C_{4}]$	$q+(-\beta _{1}+\beta _{4}+\beta _{7})q^{5}+(1+\beta _{6})q^{7}+\cdots$
540.2.k.a	$540$	$2$	540.k	20.e	$4$	$4$	$2$	$4.312$	$\Q(\zeta_{8})$	$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$-8$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+(\zeta_{8}+\zeta_{8}^{3})q^{2}-2q^{4}+(-2\zeta_{8}+\zeta_{8}^{3})q^{5}+\cdots$
540.2.k.b	$540$	$2$	540.k	20.e	$4$	$4$	$2$	$4.312$	$\Q(\zeta_{8})$	$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$4$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+(\zeta_{8}+\zeta_{8}^{3})q^{2}-2q^{4}+(\zeta_{8}-2\zeta_{8}^{3})q^{5}+\cdots$
540.2.k.c	$540$	$2$	540.k	20.e	$4$	$4$	$2$	$4.312$	$\Q(\zeta_{8})$	$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$-4$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+(-\zeta_{8}+\zeta_{8}^{3})q^{2}+2q^{4}+(-\zeta_{8}+2\zeta_{8}^{3})q^{5}+\cdots$
540.2.k.d	$540$	$2$	540.k	20.e	$4$	$4$	$2$	$4.312$	$\Q(\zeta_{8})$	$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$8$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+(-\zeta_{8}+\zeta_{8}^{3})q^{2}+2q^{4}+(2\zeta_{8}-\zeta_{8}^{3})q^{5}+\cdots$
540.2.k.e	$540$	$2$	540.k	20.e	$4$	$32$	$16$	$4.312$		$_{}$	None	None		$8$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{4}]$
540.2.k.f	$540$	$2$	540.k	20.e	$4$	$48$	$24$	$4.312$		$_{}$	None	None		$8$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{4}]$
540.2.n.a	$540$	$2$	540.n	180.n	$6$	$4$	$2$	$4.312$	$\Q(\sqrt{2}, \sqrt{-3})$	$_{}$	None	None		$4$	$0$	$0$	$0$	$-6$	$-6$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q+\beta _{1}q^{2}+2\beta _{2}q^{4}+(-2-\beta _{1}-\beta _{2}+\cdots)q^{5}+\cdots$
540.2.n.b	$540$	$2$	540.n	180.n	$6$	$4$	$2$	$4.312$	$\Q(\sqrt{2}, \sqrt{-3})$	$_{}$	None	None		$4$	$0$	$0$	$0$	$-6$	$6$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q+\beta _{1}q^{2}+2\beta _{2}q^{4}+(-2-\beta _{1}-\beta _{2}+\cdots)q^{5}+\cdots$
540.2.n.c	$540$	$2$	540.n	180.n	$6$	$8$	$4$	$4.312$	8.0.3317760000.8	$_{}$	$\Q(\sqrt{-5}) $	None		$8$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{U}(1)[D_{6}]$	$q+(\beta _{4}+\beta _{5})q^{2}+(2-2\beta _{3})q^{4}+\beta _{6}q^{5}+\cdots$
540.2.n.d	$540$	$2$	540.n	180.n	$6$	$48$	$24$	$4.312$		$_{}$	None	None		$8$	$0$	$0$	$0$	$18$	$0$			$\mathrm{SU}(2)[C_{6}]$
540.2.q.a	$540$	$2$	540.q	36.h	$6$	$48$	$24$	$4.312$		$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{6}]$
540.2.r.a	$540$	$2$	540.r	45.j	$6$	$12$	$6$	$4.312$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	$_{}$	None	None		$4$	$0$	$0$	$0$	$-1$	$0$		$3^{2}$	$\mathrm{SU}(2)[C_{6}]$	$q+(-\beta _{5}+\beta _{10})q^{5}+(\beta _{7}-\beta _{9}+\beta _{10}+\cdots)q^{7}+\cdots$
540.2.u.a	$540$	$2$	540.u	27.e	$9$	$30$	$5$	$4.312$		$_{}$	None	None		$2$	$0$	$0$	$-3$	$0$	$0$			$\mathrm{SU}(2)[C_{9}]$
540.2.u.b	$540$	$2$	540.u	27.e	$9$	$42$	$7$	$4.312$		$_{}$	None	None		$2$	$0$	$0$	$3$	$0$	$0$			$\mathrm{SU}(2)[C_{9}]$
540.2.x.a	$540$	$2$	540.x	45.l	$12$	$24$	$6$	$4.312$		$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{12}]$
540.2.y.a	$540$	$2$	540.y	180.x	$12$	$128$	$32$	$4.312$		$_{}$	None	None		$8$	$0$	$2$	$0$	$4$	$0$			$\mathrm{SU}(2)[C_{12}]$
540.2.bb.a	$540$	$2$	540.bb	540.ab	$18$	$24$	$4$	$4.312$		$_{}$	$\Q(\sqrt{-5}) $	None		$8$	$0$	$0$	$0$	$0$	$0$			$\mathrm{U}(1)[D_{18}]$
540.2.bb.b	$540$	$2$	540.bb	540.ab	$18$	$600$	$100$	$4.312$		$_{}$	None	None		$8$	$0$	$0$	$0$	$-12$	$0$			$\mathrm{SU}(2)[C_{18}]$
540.2.bd.a	$540$	$2$	540.bd	135.p	$18$	$108$	$18$	$4.312$		$_{}$	None	None		$4$	$0$	$0$	$0$	$-3$	$0$			$\mathrm{SU}(2)[C_{18}]$
540.2.be.a	$540$	$2$	540.be	108.l	$18$	$432$	$72$	$4.312$		$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{18}]$
540.2.bh.a	$540$	$2$	540.bh	540.ah	$36$	$1248$	$104$	$4.312$		$_{}$	None	None		$8$	$0$	$-12$	$0$	$-24$	$0$			$\mathrm{SU}(2)[C_{36}]$
540.2.bj.a	$540$	$2$	540.bj	135.q	$36$	$216$	$18$	$4.312$		$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{36}]$
540.3.b.a	$540$	$3$	540.b	15.d	$2$	$4$	$4$	$14.714$	$\Q(\sqrt{-11}, \sqrt{-19})$	$_{}$	None	None		$2$	$0$	$0$	$0$	$-3$	$0$		$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	$q+(-1-\beta _{3})q^{5}-\beta _{2}q^{7}+(-2\beta _{1}-3\beta _{2}+\cdots)q^{11}+\cdots$
540.3.b.b	$540$	$3$	540.b	15.d	$2$	$4$	$4$	$14.714$	$\Q(\sqrt{-11}, \sqrt{-19})$	$_{}$	None	None		$2$	$0$	$0$	$0$	$3$	$0$		$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	$q+(1+\beta _{3})q^{5}-\beta _{2}q^{7}+(2\beta _{1}+3\beta _{2}+\cdots)q^{11}+\cdots$
540.3.b.c	$540$	$3$	540.b	15.d	$2$	$8$	$8$	$14.714$	8.0.$\cdots$.13	$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$0$		$2^{2}\cdot 3^{4}\cdot 5$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{2}q^{5}+(-\beta _{1}-\beta _{3})q^{7}-\beta _{6}q^{11}+\cdots$
540.3.c.a	$540$	$3$	540.c	4.b	$2$	$32$	$32$	$14.714$		$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$

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Elliptic curves over $\Q$
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Genus 2 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.