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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 173 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
40.2.a.a	$40$	$2$	40.a	1.a	$1$	$1$	$1$	$0.319$	$\Q$	None	✓	$1$	$0$	$0$	$0$	$1$	$-4$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{5}-4q^{7}-3q^{9}+4q^{11}-2q^{13}+\cdots$
40.2.c.a	$40$	$2$	40.c	5.b	$2$	$2$	$2$	$0.319$	$\Q(\sqrt{-1}) $	None		$2$	$0$	$0$	$0$	$-2$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q+iq^{3}+(-1-i)q^{5}-iq^{7}-q^{9}+\cdots$
40.2.d.a	$40$	$2$	40.d	8.b	$2$	$4$	$4$	$0.319$	$\Q(\zeta_{12})$	None		$2$	$0$	$-2$	$0$	$0$	$-4$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q+(-\zeta_{12}+\zeta_{12}^{2})q^{2}+(-1+\zeta_{12}+\cdots)q^{3}+\cdots$
40.2.f.a	$40$	$2$	40.f	40.f	$2$	$4$	$4$	$0.319$	$\Q(\sqrt{2}, \sqrt{-3})$	None		$4$	$0$	$0$	$0$	$0$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{2}+\beta _{2}q^{3}+(-1+\beta _{3})q^{4}+(-\beta _{2}+\cdots)q^{5}+\cdots$
40.2.k.a	$40$	$2$	40.k	40.k	$4$	$8$	$4$	$0.319$	$\Q(\zeta_{20})$	None		$4$	$0$	$-2$	$-4$	$0$	$0$		$2^{4}$	$\mathrm{SU}(2)[C_{4}]$	$q-\zeta_{20}^{7}q^{2}+(-1+\zeta_{20}^{3}+\zeta_{20}^{5}+\cdots)q^{3}+\cdots$
40.3.e.a	$40$	$3$	40.e	40.e	$2$	$1$	$1$	$1.090$	$\Q$	$\Q(\sqrt{-10}) $	✓	$2$	$0$	$-2$	$0$	$5$	$6$		$1$	$\mathrm{U}(1)[D_{2}]$	$q-2q^{2}+4q^{4}+5q^{5}+6q^{7}-8q^{8}+\cdots$
40.3.e.b	$40$	$3$	40.e	40.e	$2$	$1$	$1$	$1.090$	$\Q$	$\Q(\sqrt{-10}) $	✓	$2$	$0$	$2$	$0$	$-5$	$-6$		$1$	$\mathrm{U}(1)[D_{2}]$	$q+2q^{2}+4q^{4}-5q^{5}-6q^{7}+8q^{8}+\cdots$
40.3.e.c	$40$	$3$	40.e	40.e	$2$	$8$	$8$	$1.090$	8.0.$\cdots$.2	None		$4$	$0$	$0$	$0$	$0$	$0$		$2^{5}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{2}q^{2}-\beta _{7}q^{3}+(-2-\beta _{3}-\beta _{6}+\cdots)q^{4}+\cdots$
40.3.g.a	$40$	$3$	40.g	8.d	$2$	$8$	$8$	$1.090$	8.0.$\cdots$.1	None		$2$	$0$	$2$	$0$	$0$	$0$		$2^{5}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{4}q^{2}-\beta _{6}q^{3}+(-1+\beta _{1}+\beta _{4}+\cdots)q^{4}+\cdots$
40.3.i.a	$40$	$3$	40.i	40.i	$4$	$20$	$10$	$1.090$	$\mathbb{Q}[x]/(x^{20} - \cdots)$	None		$4$	$0$	$-2$	$0$	$0$	$-4$		$2^{20}$	$\mathrm{SU}(2)[C_{4}]$	$q+\beta _{4}q^{2}+\beta _{16}q^{3}+\beta _{3}q^{4}+\beta _{8}q^{5}+\cdots$
40.3.l.a	$40$	$3$	40.l	5.c	$4$	$2$	$1$	$1.090$	$\Q(\sqrt{-1}) $	None		$2$	$0$	$0$	$2$	$10$	$-6$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+(1-i)q^{3}+5q^{5}+(-3-3i)q^{7}+\cdots$
40.3.l.b	$40$	$3$	40.l	5.c	$4$	$4$	$2$	$1.090$	$\Q(i, \sqrt{41})$	None		$2$	$0$	$0$	$-2$	$-6$	$14$		$2$	$\mathrm{SU}(2)[C_{4}]$	$q+(-1+\beta _{2})q^{3}+(-1-2\beta _{1}+\beta _{3})q^{5}+\cdots$
40.4.a.a	$40$	$4$	40.a	1.a	$1$	$1$	$1$	$2.360$	$\Q$	None	✓	$1$	$1$	$0$	$-6$	$-5$	$-34$	$-$	$1$	$\mathrm{SU}(2)$	$q-6q^{3}-5q^{5}-34q^{7}+9q^{9}+2^{4}q^{11}+\cdots$
40.4.a.b	$40$	$4$	40.a	1.a	$1$	$1$	$1$	$2.360$	$\Q$	None	✓	$1$	$0$	$0$	$4$	$5$	$16$	$+$	$1$	$\mathrm{SU}(2)$	$q+4q^{3}+5q^{5}+2^{4}q^{7}-11q^{9}+6^{2}q^{11}+\cdots$
40.4.a.c	$40$	$4$	40.a	1.a	$1$	$1$	$1$	$2.360$	$\Q$	None	✓	$1$	$0$	$0$	$10$	$-5$	$-18$	$+$	$1$	$\mathrm{SU}(2)$	$q+10q^{3}-5q^{5}-18q^{7}+73q^{9}-2^{4}q^{11}+\cdots$
40.4.c.a	$40$	$4$	40.c	5.b	$2$	$4$	$4$	$2.360$	$\Q(i, \sqrt{6})$	None		$2$	$0$	$0$	$0$	$-4$	$0$		$2^{7}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{3}+(-1-\beta _{2}-\beta _{3})q^{5}+(2\beta _{1}+\cdots)q^{7}+\cdots$
40.4.d.a	$40$	$4$	40.d	8.b	$2$	$12$	$12$	$2.360$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	None		$2$	$0$	$2$	$0$	$0$	$28$		$2^{14}\cdot 5^{4}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{2}+\beta _{5}q^{3}+(1-\beta _{4})q^{4}-\beta _{8}q^{5}+\cdots$
40.4.f.a	$40$	$4$	40.f	40.f	$2$	$16$	$16$	$2.360$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	None		$4$	$0$	$0$	$0$	$0$	$0$		$2^{21}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{2}-\beta _{13}q^{3}+\beta _{2}q^{4}+\beta _{12}q^{5}+\cdots$
40.4.k.a	$40$	$4$	40.k	40.k	$4$	$32$	$16$	$2.360$		None		$4$	$0$	$-2$	$-4$	$0$	$0$			$\mathrm{SU}(2)[C_{4}]$
40.5.e.a	$40$	$5$	40.e	40.e	$2$	$1$	$1$	$4.135$	$\Q$	$\Q(\sqrt{-10}) $	✓	$2$	$0$	$-4$	$0$	$-25$	$62$		$1$	$\mathrm{U}(1)[D_{2}]$	$q-4q^{2}+2^{4}q^{4}-5^{2}q^{5}+62q^{7}-2^{6}q^{8}+\cdots$
40.5.e.b	$40$	$5$	40.e	40.e	$2$	$1$	$1$	$4.135$	$\Q$	$\Q(\sqrt{-10}) $	✓	$2$	$0$	$4$	$0$	$25$	$-62$		$1$	$\mathrm{U}(1)[D_{2}]$	$q+4q^{2}+2^{4}q^{4}+5^{2}q^{5}-62q^{7}+2^{6}q^{8}+\cdots$
40.5.e.c	$40$	$5$	40.e	40.e	$2$	$20$	$20$	$4.135$	$\mathbb{Q}[x]/(x^{20} + \cdots)$	None		$4$	$0$	$0$	$0$	$0$	$0$		$2^{33}\cdot 5^{5}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{2}+\beta _{11}q^{3}+(-1+\beta _{2})q^{4}+\cdots$
40.5.g.a	$40$	$5$	40.g	8.d	$2$	$16$	$16$	$4.135$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	None		$2$	$0$	$-6$	$0$	$0$	$0$		$2^{25}\cdot 5^{5}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{1}q^{2}+\beta _{3}q^{3}+\beta _{2}q^{4}-\beta _{5}q^{5}+\cdots$
40.5.i.a	$40$	$5$	40.i	40.i	$4$	$44$	$22$	$4.135$		None		$4$	$0$	$-2$	$0$	$0$	$-4$			$\mathrm{SU}(2)[C_{4}]$
40.5.l.a	$40$	$5$	40.l	5.c	$4$	$2$	$1$	$4.135$	$\Q(\sqrt{-1}) $	None		$2$	$0$	$0$	$20$	$40$	$-84$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+(10-10i)q^{3}+(20+15i)q^{5}+(-42+\cdots)q^{7}+\cdots$
40.5.l.b	$40$	$5$	40.l	5.c	$4$	$4$	$2$	$4.135$	$\Q(i, \sqrt{29})$	None		$2$	$0$	$0$	$-12$	$-12$	$44$		$2^{4}\cdot 5$	$\mathrm{SU}(2)[C_{4}]$	$q+(-3+3\beta _{1})q^{3}+(-3-6\beta _{1}-\beta _{3})q^{5}+\cdots$
40.5.l.c	$40$	$5$	40.l	5.c	$4$	$6$	$3$	$4.135$	6.0.313431616.3	None		$2$	$0$	$0$	$-8$	$-4$	$-40$		$2^{5}\cdot 5^{2}$	$\mathrm{SU}(2)[C_{4}]$	$q+(-1-\beta _{1}-\beta _{3})q^{3}+(-1+7\beta _{1}+\cdots)q^{5}+\cdots$
40.6.a.a	$40$	$6$	40.a	1.a	$1$	$1$	$1$	$6.415$	$\Q$	None	✓	$1$	$0$	$0$	$-18$	$-25$	$242$	$-$	$1$	$\mathrm{SU}(2)$	$q-18q^{3}-5^{2}q^{5}+242q^{7}+3^{4}q^{9}+\cdots$
40.6.a.b	$40$	$6$	40.a	1.a	$1$	$1$	$1$	$6.415$	$\Q$	None	✓	$1$	$1$	$0$	$-8$	$25$	$-108$	$+$	$1$	$\mathrm{SU}(2)$	$q-8q^{3}+5^{2}q^{5}-108q^{7}-179q^{9}+\cdots$
40.6.a.c	$40$	$6$	40.a	1.a	$1$	$1$	$1$	$6.415$	$\Q$	None	✓	$1$	$1$	$0$	$-2$	$-25$	$-62$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{3}-5^{2}q^{5}-62q^{7}-239q^{9}+\cdots$
40.6.a.d	$40$	$6$	40.a	1.a	$1$	$2$	$2$	$6.415$	$\Q(\sqrt{129}) $	None	✓	$1$	$0$	$0$	$-12$	$50$	$52$	$-$	$2^{2}$	$\mathrm{SU}(2)$	$q+(-6-\beta )q^{3}+5^{2}q^{5}+(26-3\beta )q^{7}+\cdots$
40.6.c.a	$40$	$6$	40.c	5.b	$2$	$8$	$8$	$6.415$	$\mathbb{Q}[x]/(x^{8} + \cdots)$	None		$2$	$0$	$0$	$0$	$8$	$0$		$2^{31}\cdot 5^{3}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{1}q^{3}+(1-\beta _{2})q^{5}+(\beta _{2}+\beta _{6})q^{7}+\cdots$
40.6.d.a	$40$	$6$	40.d	8.b	$2$	$20$	$20$	$6.415$	$\mathbb{Q}[x]/(x^{20} - \cdots)$	None		$2$	$0$	$2$	$0$	$0$	$-196$		$2^{42}\cdot 3^{4}\cdot 5^{12}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{1}q^{2}-\beta _{2}q^{3}+(-2+\beta _{3})q^{4}+\beta _{5}q^{5}+\cdots$
40.6.f.a	$40$	$6$	40.f	40.f	$2$	$28$	$28$	$6.415$		None		$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
40.6.k.a	$40$	$6$	40.k	40.k	$4$	$56$	$28$	$6.415$		None		$4$	$0$	$-2$	$-4$	$0$	$0$			$\mathrm{SU}(2)[C_{4}]$
40.7.e.a	$40$	$7$	40.e	40.e	$2$	$1$	$1$	$9.202$	$\Q$	$\Q(\sqrt{-10}) $	✓	$2$	$0$	$-8$	$0$	$125$	$-666$		$1$	$\mathrm{U}(1)[D_{2}]$	$q-8q^{2}+2^{6}q^{4}+5^{3}q^{5}-666q^{7}+\cdots$
40.7.e.b	$40$	$7$	40.e	40.e	$2$	$1$	$1$	$9.202$	$\Q$	$\Q(\sqrt{-10}) $	✓	$2$	$0$	$8$	$0$	$-125$	$666$		$1$	$\mathrm{U}(1)[D_{2}]$	$q+8q^{2}+2^{6}q^{4}-5^{3}q^{5}+666q^{7}+\cdots$
40.7.e.c	$40$	$7$	40.e	40.e	$2$	$32$	$32$	$9.202$		None		$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
40.7.g.a	$40$	$7$	40.g	8.d	$2$	$24$	$24$	$9.202$		None		$2$	$0$	$10$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
40.7.i.a	$40$	$7$	40.i	40.i	$4$	$68$	$34$	$9.202$		None		$4$	$0$	$-2$	$0$	$0$	$-4$			$\mathrm{SU}(2)[C_{4}]$
40.7.l.a	$40$	$7$	40.l	5.c	$4$	$8$	$4$	$9.202$	$\mathbb{Q}[x]/(x^{8} + \cdots)$	None		$2$	$0$	$0$	$-14$	$-50$	$-46$		$2^{12}\cdot 5^{4}$	$\mathrm{SU}(2)[C_{4}]$	$q+(-2-2\beta _{1}+\beta _{4})q^{3}+(-6+11\beta _{1}+\cdots)q^{5}+\cdots$
40.7.l.b	$40$	$7$	40.l	5.c	$4$	$10$	$5$	$9.202$	$\mathbb{Q}[x]/(x^{10} - \cdots)$	None		$2$	$0$	$0$	$14$	$94$	$454$		$2^{19}\cdot 5^{4}$	$\mathrm{SU}(2)[C_{4}]$	$q+(1+\beta _{1}-\beta _{3})q^{3}+(9-2^{4}\beta _{1}+\beta _{2}+\cdots)q^{5}+\cdots$
40.8.a.a	$40$	$8$	40.a	1.a	$1$	$1$	$1$	$12.495$	$\Q$	None	✓	$1$	$1$	$0$	$-36$	$125$	$776$	$-$	$1$	$\mathrm{SU}(2)$	$q-6^{2}q^{3}+5^{3}q^{5}+776q^{7}-891q^{9}+\cdots$
40.8.a.b	$40$	$8$	40.a	1.a	$1$	$2$	$2$	$12.495$	$\Q(\sqrt{46}) $	None	✓	$1$	$0$	$0$	$4$	$-250$	$844$	$+$	$2^{3}$	$\mathrm{SU}(2)$	$q+(2+\beta )q^{3}-5^{3}q^{5}+(422+17\beta )q^{7}+\cdots$
40.8.a.c	$40$	$8$	40.a	1.a	$1$	$2$	$2$	$12.495$	$\Q(\sqrt{6}) $	None	✓	$1$	$1$	$0$	$36$	$-250$	$-404$	$-$	$2^{3}$	$\mathrm{SU}(2)$	$q+(18+\beta )q^{3}-5^{3}q^{5}+(-202-63\beta )q^{7}+\cdots$
40.8.a.d	$40$	$8$	40.a	1.a	$1$	$2$	$2$	$12.495$	$\Q(\sqrt{601}) $	None	✓	$1$	$0$	$0$	$76$	$250$	$796$	$+$	$2^{2}$	$\mathrm{SU}(2)$	$q+(38-\beta )q^{3}+5^{3}q^{5}+(398-7\beta )q^{7}+\cdots$
40.8.c.a	$40$	$8$	40.c	5.b	$2$	$2$	$2$	$12.495$	$\Q(\sqrt{-1}) $	None		$2$	$0$	$0$	$0$	$550$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q+17iq^{3}+(275+5^{2}i)q^{5}-53iq^{7}+\cdots$
40.8.c.b	$40$	$8$	40.c	5.b	$2$	$8$	$8$	$12.495$	$\mathbb{Q}[x]/(x^{8} + \cdots)$	None		$2$	$0$	$0$	$0$	$-744$	$0$		$2^{38}\cdot 5^{3}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{3}+(-93-\beta _{1}+\beta _{3})q^{5}+(3\beta _{1}+\cdots)q^{7}+\cdots$
40.8.d.a	$40$	$8$	40.d	8.b	$2$	$28$	$28$	$12.495$		None		$2$	$0$	$-14$	$0$	$0$	$1372$			$\mathrm{SU}(2)[C_{2}]$
40.8.f.a	$40$	$8$	40.f	40.f	$2$	$40$	$40$	$12.495$		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.