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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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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
115.2.a.a	$115$	$2$	115.a	1.a	$1$	$1$	$1$	$0.918$	$\Q$	None	✓	$1$	$0$	$2$	$0$	$-1$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{2}+2q^{4}-q^{5}+q^{7}-3q^{9}-2q^{10}+\cdots$
115.2.a.b	$115$	$2$	115.a	1.a	$1$	$2$	$2$	$0.918$	$\Q(\sqrt{5}) $	None	✓	$1$	$1$	$-3$	$-2$	$-2$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1-\beta )q^{2}-q^{3}+3\beta q^{4}-q^{5}+\cdots$
115.2.a.c	$115$	$2$	115.a	1.a	$1$	$4$	$4$	$0.918$	4.4.15317.1	None	✓	$1$	$0$	$2$	$-2$	$4$	$-3$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+(-1-\beta _{2})q^{3}+(1+\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots$
115.2.b.a	$115$	$2$	115.b	5.b	$2$	$2$	$2$	$0.918$	$\Q(\sqrt{-1}) $	None		$2$	$0$	$0$	$0$	$4$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+2iq^{2}-2iq^{3}-2q^{4}+(2+i)q^{5}+\cdots$
115.2.b.b	$115$	$2$	115.b	5.b	$2$	$8$	$8$	$0.918$	8.0.527896576.2	None		$2$	$0$	$0$	$0$	$-6$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{7}q^{2}+(-\beta _{1}-\beta _{3}+\beta _{5})q^{3}+(-1+\cdots)q^{4}+\cdots$
115.2.e.a	$115$	$2$	115.e	115.e	$4$	$20$	$10$	$0.918$	$\mathbb{Q}[x]/(x^{20} - \cdots)$	None		$4$	$0$	$-4$	$-8$	$0$	$0$		$5$	$\mathrm{SU}(2)[C_{4}]$	$q-\beta _{3}q^{2}+\beta _{2}q^{3}+\beta _{4}q^{4}+\beta _{18}q^{5}+\cdots$
115.2.g.a	$115$	$2$	115.g	23.c	$11$	$10$	$1$	$0.918$	$\Q(\zeta_{22})$	None		$2$	$0$	$5$	$1$	$1$	$5$		$1$	$\mathrm{SU}(2)[C_{11}]$	$q+(\zeta_{22}+\zeta_{22}^{3}-\zeta_{22}^{4}+\zeta_{22}^{5}+\zeta_{22}^{7}+\cdots)q^{2}+\cdots$
115.2.g.b	$115$	$2$	115.g	23.c	$11$	$20$	$2$	$0.918$	$\mathbb{Q}[x]/(x^{20} - \cdots)$	None		$2$	$0$	$-4$	$1$	$2$	$-4$		$1$	$\mathrm{SU}(2)[C_{11}]$	$q+(-1+\beta _{2}+\beta _{3}+\beta _{4}+\beta _{6}+\beta _{8}+\cdots)q^{2}+\cdots$
115.2.g.c	$115$	$2$	115.g	23.c	$11$	$50$	$5$	$0.918$		None		$2$	$0$	$-5$	$-2$	$-5$	$-5$			$\mathrm{SU}(2)[C_{11}]$
115.2.j.a	$115$	$2$	115.j	115.j	$22$	$100$	$10$	$0.918$		None		$4$	$0$	$0$	$0$	$-9$	$0$			$\mathrm{SU}(2)[C_{22}]$
115.2.l.a	$115$	$2$	115.l	115.l	$44$	$200$	$10$	$0.918$		None		$4$	$0$	$-18$	$-14$	$-22$	$-22$			$\mathrm{SU}(2)[C_{44}]$
115.3.c.a	$115$	$3$	115.c	115.c	$2$	$1$	$1$	$3.134$	$\Q$	$\Q(\sqrt{-115}) $	✓	$2$	$0$	$0$	$0$	$-5$	$9$		$1$	$\mathrm{U}(1)[D_{2}]$	$q+4q^{4}-5q^{5}+9q^{7}+9q^{9}+2^{4}q^{16}+\cdots$
115.3.c.b	$115$	$3$	115.c	115.c	$2$	$1$	$1$	$3.134$	$\Q$	$\Q(\sqrt{-115}) $	✓	$2$	$0$	$0$	$0$	$5$	$-9$		$1$	$\mathrm{U}(1)[D_{2}]$	$q+4q^{4}+5q^{5}-9q^{7}+9q^{9}+2^{4}q^{16}+\cdots$
115.3.c.c	$115$	$3$	115.c	115.c	$2$	$20$	$20$	$3.134$	$\mathbb{Q}[x]/(x^{20} + \cdots)$	None		$4$	$0$	$0$	$0$	$0$	$0$		$2^{4}\cdot 5$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{3}q^{2}-\beta _{4}q^{3}+(-3+\beta _{7}-\beta _{8}+\cdots)q^{4}+\cdots$
115.3.d.a	$115$	$3$	115.d	23.b	$2$	$6$	$6$	$3.134$	$\mathbb{Q}[x]/(x^{6} - \cdots)$	None		$2$	$0$	$-6$	$2$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q-q^{2}+\beta _{4}q^{3}-3q^{4}-\beta _{3}q^{5}-\beta _{4}q^{6}+\cdots$
115.3.d.b	$115$	$3$	115.d	23.b	$2$	$10$	$10$	$3.134$	$\mathbb{Q}[x]/(x^{10} - \cdots)$	None		$2$	$0$	$2$	$-2$	$0$	$0$		$5$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{4}q^{2}-\beta _{7}q^{3}+(3+\beta _{6})q^{4}+\beta _{5}q^{5}+\cdots$
115.3.f.a	$115$	$3$	115.f	5.c	$4$	$44$	$22$	$3.134$		None		$2$	$0$	$-4$	$0$	$-8$	$-16$			$\mathrm{SU}(2)[C_{4}]$
115.3.h.a	$115$	$3$	115.h	23.d	$22$	$160$	$16$	$3.134$		None		$2$	$0$	$4$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{22}]$
115.3.i.a	$115$	$3$	115.i	115.i	$22$	$220$	$22$	$3.134$		None		$4$	$0$	$0$	$0$	$-11$	$0$			$\mathrm{SU}(2)[C_{22}]$
115.3.k.a	$115$	$3$	115.k	115.k	$44$	$440$	$22$	$3.134$		None		$4$	$0$	$-18$	$-22$	$-14$	$-6$			$\mathrm{SU}(2)[C_{44}]$
115.4.a.a	$115$	$4$	115.a	1.a	$1$	$1$	$1$	$6.785$	$\Q$	None	✓	$1$	$1$	$1$	$4$	$-5$	$-32$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+4q^{3}-7q^{4}-5q^{5}+4q^{6}+\cdots$
115.4.a.b	$115$	$4$	115.a	1.a	$1$	$1$	$1$	$6.785$	$\Q$	None	✓	$1$	$1$	$2$	$-3$	$5$	$-2$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{2}-3q^{3}-4q^{4}+5q^{5}-6q^{6}+\cdots$
115.4.a.c	$115$	$4$	115.a	1.a	$1$	$2$	$2$	$6.785$	$\Q(\sqrt{109}) $	None	✓	$1$	$1$	$-6$	$-3$	$10$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q-3q^{2}+(-1-\beta )q^{3}+q^{4}+5q^{5}+\cdots$
115.4.a.d	$115$	$4$	115.a	1.a	$1$	$5$	$5$	$6.785$	$\mathbb{Q}[x]/(x^{5} - \cdots)$	None	✓	$1$	$1$	$-5$	$-6$	$-25$	$-15$	$-$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta _{1})q^{2}+(-1-\beta _{2}-\beta _{3}-\beta _{4})q^{3}+\cdots$
115.4.a.e	$115$	$4$	115.a	1.a	$1$	$5$	$5$	$6.785$	$\mathbb{Q}[x]/(x^{5} - \cdots)$	None	✓	$1$	$0$	$6$	$4$	$-25$	$-3$	$+$	$1$	$\mathrm{SU}(2)$	$q+(1+\beta _{1})q^{2}+(1+\beta _{1}-\beta _{2}+\beta _{3})q^{3}+\cdots$
115.4.a.f	$115$	$4$	115.a	1.a	$1$	$8$	$8$	$6.785$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	None	✓	$1$	$0$	$6$	$0$	$40$	$11$	$+$	$1$	$\mathrm{SU}(2)$	$q+(1-\beta _{1})q^{2}+\beta _{6}q^{3}+(5+\beta _{2})q^{4}+\cdots$
115.4.b.a	$115$	$4$	115.b	5.b	$2$	$34$	$34$	$6.785$		None		$2$	$0$	$0$	$0$	$14$	$0$			$\mathrm{SU}(2)[C_{2}]$
115.4.e.a	$115$	$4$	115.e	115.e	$4$	$68$	$34$	$6.785$		None		$4$	$0$	$-4$	$4$	$0$	$0$			$\mathrm{SU}(2)[C_{4}]$
115.4.g.a	$115$	$4$	115.g	23.c	$11$	$110$	$11$	$6.785$		None		$2$	$0$	$-2$	$6$	$-55$	$-10$			$\mathrm{SU}(2)[C_{11}]$
115.4.g.b	$115$	$4$	115.g	23.c	$11$	$130$	$13$	$6.785$		None		$2$	$0$	$6$	$-6$	$65$	$38$			$\mathrm{SU}(2)[C_{11}]$
115.4.j.a	$115$	$4$	115.j	115.j	$22$	$340$	$34$	$6.785$		None		$4$	$0$	$0$	$0$	$-25$	$0$			$\mathrm{SU}(2)[C_{22}]$
115.4.l.a	$115$	$4$	115.l	115.l	$44$	$680$	$34$	$6.785$		None		$4$	$0$	$-18$	$-26$	$-22$	$-22$			$\mathrm{SU}(2)[C_{44}]$
115.5.c.a	$115$	$5$	115.c	115.c	$2$	$1$	$1$	$11.888$	$\Q$	$\Q(\sqrt{-115}) $	✓	$2$	$0$	$0$	$0$	$-25$	$17$		$1$	$\mathrm{U}(1)[D_{2}]$	$q+2^{4}q^{4}-5^{2}q^{5}+17q^{7}+3^{4}q^{9}+\cdots$
115.5.c.b	$115$	$5$	115.c	115.c	$2$	$1$	$1$	$11.888$	$\Q$	$\Q(\sqrt{-115}) $	✓	$2$	$0$	$0$	$0$	$25$	$-17$		$1$	$\mathrm{U}(1)[D_{2}]$	$q+2^{4}q^{4}+5^{2}q^{5}-17q^{7}+3^{4}q^{9}+\cdots$
115.5.c.c	$115$	$5$	115.c	115.c	$2$	$44$	$44$	$11.888$		None		$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
115.5.d.a	$115$	$5$	115.d	23.b	$2$	$32$	$32$	$11.888$		None		$2$	$0$	$12$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
115.5.f.a	$115$	$5$	115.f	5.c	$4$	$88$	$44$	$11.888$		None		$2$	$0$	$0$	$0$	$-48$	$160$			$\mathrm{SU}(2)[C_{4}]$
115.5.h.a	$115$	$5$	115.h	23.d	$22$	$320$	$32$	$11.888$		None		$2$	$0$	$-12$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{22}]$
115.5.i.a	$115$	$5$	115.i	115.i	$22$	$460$	$46$	$11.888$		None		$4$	$0$	$0$	$0$	$-11$	$0$			$\mathrm{SU}(2)[C_{22}]$
115.5.k.a	$115$	$5$	115.k	115.k	$44$	$920$	$46$	$11.888$		None		$4$	$0$	$-18$	$2$	$-54$	$-78$			$\mathrm{SU}(2)[C_{44}]$
115.6.a.a	$115$	$6$	115.a	1.a	$1$	$2$	$2$	$18.444$	$\Q(\sqrt{1821}) $	None	✓	$1$	$0$	$4$	$3$	$-50$	$53$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{2}+(2-\beta )q^{3}-28q^{4}-5^{2}q^{5}+\cdots$
115.6.a.b	$115$	$6$	115.a	1.a	$1$	$7$	$7$	$18.444$	$\mathbb{Q}[x]/(x^{7} - \cdots)$	None	✓	$1$	$1$	$-12$	$4$	$175$	$-275$	$+$	$2\cdot 3$	$\mathrm{SU}(2)$	$q+(-2+\beta _{1})q^{2}+(1-\beta _{1}-\beta _{6})q^{3}+\cdots$
115.6.a.c	$115$	$6$	115.a	1.a	$1$	$7$	$7$	$18.444$	$\mathbb{Q}[x]/(x^{7} - \cdots)$	None	✓	$1$	$0$	$4$	$-3$	$-175$	$33$	$-$	$2$	$\mathrm{SU}(2)$	$q+(1-\beta _{1})q^{2}+(-1+\beta _{1}-\beta _{2})q^{3}+\cdots$
115.6.a.d	$115$	$6$	115.a	1.a	$1$	$10$	$10$	$18.444$	$\mathbb{Q}[x]/(x^{10} - \cdots)$	None	✓	$1$	$1$	$-12$	$-18$	$-250$	$-15$	$+$	$2\cdot 3$	$\mathrm{SU}(2)$	$q+(-1-\beta _{1})q^{2}+(-2+\beta _{3})q^{3}+(14+\cdots)q^{4}+\cdots$
115.6.a.e	$115$	$6$	115.a	1.a	$1$	$12$	$12$	$18.444$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	None	✓	$1$	$0$	$8$	$22$	$300$	$16$	$-$	$2$	$\mathrm{SU}(2)$	$q+(1-\beta _{1})q^{2}+(2-\beta _{1}-\beta _{4})q^{3}+(5^{2}+\cdots)q^{4}+\cdots$
115.6.b.a	$115$	$6$	115.b	5.b	$2$	$54$	$54$	$18.444$		None		$2$	$0$	$0$	$0$	$98$	$0$			$\mathrm{SU}(2)[C_{2}]$
115.7.c.a	$115$	$7$	115.c	115.c	$2$	$1$	$1$	$26.456$	$\Q$	$\Q(\sqrt{-115}) $	✓	$2$	$0$	$0$	$0$	$-125$	$-594$		$1$	$\mathrm{U}(1)[D_{2}]$	$q+2^{6}q^{4}-5^{3}q^{5}-594q^{7}+3^{6}q^{9}+\cdots$
115.7.c.b	$115$	$7$	115.c	115.c	$2$	$1$	$1$	$26.456$	$\Q$	$\Q(\sqrt{-115}) $	✓	$2$	$0$	$0$	$0$	$125$	$594$		$1$	$\mathrm{U}(1)[D_{2}]$	$q+2^{6}q^{4}+5^{3}q^{5}+594q^{7}+3^{6}q^{9}+\cdots$
115.7.c.c	$115$	$7$	115.c	115.c	$2$	$68$	$68$	$26.456$		None		$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
115.7.d.a	$115$	$7$	115.d	23.b	$2$	$48$	$48$	$26.456$		None		$2$	$0$	$-20$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$

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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.