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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 111 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
58.2.a.a	$58$	$2$	58.a	1.a	$1$	$1$	$1$	$0.463$	$\Q$	None	✓	$1$	$1$	$-1$	$-3$	$-3$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-3q^{3}+q^{4}-3q^{5}+3q^{6}-2q^{7}+\cdots$
58.2.a.b	$58$	$2$	58.a	1.a	$1$	$1$	$1$	$0.463$	$\Q$	None	✓	$1$	$0$	$1$	$-1$	$1$	$-2$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}+q^{5}-q^{6}-2q^{7}+\cdots$
58.2.b.a	$58$	$2$	58.b	29.b	$2$	$2$	$2$	$0.463$	$\Q(\sqrt{-1}) $	None		$2$	$0$	$0$	$0$	$2$	$-4$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+iq^{2}+iq^{3}-q^{4}+q^{5}-q^{6}-2q^{7}+\cdots$
58.2.d.a	$58$	$2$	58.d	29.d	$7$	$6$	$1$	$0.463$	$\Q(\zeta_{14})$	None		$2$	$0$	$1$	$3$	$-4$	$-5$		$1$	$\mathrm{SU}(2)[C_{7}]$	$q-\zeta_{14}^{4}q^{2}+(1-\zeta_{14}+\zeta_{14}^{4}-\zeta_{14}^{5})q^{3}+\cdots$
58.2.d.b	$58$	$2$	58.d	29.d	$7$	$12$	$2$	$0.463$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	None		$2$	$0$	$-2$	$-3$	$0$	$1$		$1$	$\mathrm{SU}(2)[C_{7}]$	$q+\beta _{2}q^{2}+\beta _{11}q^{3}+\beta _{6}q^{4}+(\beta _{1}+\beta _{3}+\cdots)q^{5}+\cdots$
58.2.e.a	$58$	$2$	58.e	29.e	$14$	$12$	$2$	$0.463$	$\Q(\zeta_{28})$	None		$2$	$0$	$0$	$0$	$-2$	$4$		$1$	$\mathrm{SU}(2)[C_{14}]$	$q-\zeta_{28}^{9}q^{2}+(-\zeta_{28}-\zeta_{28}^{3}-\zeta_{28}^{5}+\cdots)q^{3}+\cdots$
58.3.c.a	$58$	$3$	58.c	29.c	$4$	$4$	$2$	$1.580$	$\Q(i, \sqrt{6})$	None		$2$	$0$	$4$	$4$	$0$	$8$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+(1-\beta _{2})q^{2}+(1-\beta _{2}+\beta _{3})q^{3}-2\beta _{2}q^{4}+\cdots$
58.3.c.b	$58$	$3$	58.c	29.c	$4$	$6$	$3$	$1.580$	6.0.9296045056.1	None		$2$	$0$	$-6$	$-4$	$0$	$-8$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+(-1+\beta _{4})q^{2}+(-1+\beta _{1}+\beta _{4})q^{3}+\cdots$
58.3.f.a	$58$	$3$	58.f	29.f	$28$	$24$	$2$	$1.580$		None		$2$	$0$	$-4$	$-4$	$28$	$34$			$\mathrm{SU}(2)[C_{28}]$
58.3.f.b	$58$	$3$	58.f	29.f	$28$	$36$	$3$	$1.580$		None		$2$	$0$	$6$	$4$	$-28$	$-34$			$\mathrm{SU}(2)[C_{28}]$
58.4.a.a	$58$	$4$	58.a	1.a	$1$	$1$	$1$	$3.422$	$\Q$	None	✓	$1$	$0$	$-2$	$7$	$5$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{2}+7q^{3}+4q^{4}+5q^{5}-14q^{6}+\cdots$
58.4.a.b	$58$	$4$	58.a	1.a	$1$	$1$	$1$	$3.422$	$\Q$	None	✓	$1$	$1$	$2$	$-7$	$-15$	$-18$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{2}-7q^{3}+4q^{4}-15q^{5}-14q^{6}+\cdots$
58.4.a.c	$58$	$4$	58.a	1.a	$1$	$2$	$2$	$3.422$	$\Q(\sqrt{6}) $	None	✓	$1$	$1$	$-4$	$-2$	$-10$	$-16$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{2}+(-1+\beta )q^{3}+4q^{4}+(-5+\cdots)q^{5}+\cdots$
58.4.a.d	$58$	$4$	58.a	1.a	$1$	$3$	$3$	$3.422$	3.3.19816.1	None	✓	$1$	$0$	$6$	$2$	$20$	$24$	$+$	$1$	$\mathrm{SU}(2)$	$q+2q^{2}+(1-\beta _{1})q^{3}+4q^{4}+(6+2\beta _{1}+\cdots)q^{5}+\cdots$
58.4.b.a	$58$	$4$	58.b	29.b	$2$	$8$	$8$	$3.422$	$\mathbb{Q}[x]/(x^{8} + \cdots)$	None		$2$	$0$	$0$	$0$	$-22$	$12$		$2^{6}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{5}q^{2}+\beta _{1}q^{3}-4q^{4}+(-3-\beta _{4}+\cdots)q^{5}+\cdots$
58.4.d.a	$58$	$4$	58.d	29.d	$7$	$18$	$3$	$3.422$	$\mathbb{Q}[x]/(x^{18} - \cdots)$	None		$2$	$0$	$6$	$-5$	$-16$	$-59$		$2^{6}$	$\mathrm{SU}(2)[C_{7}]$	$q+2\beta _{8}q^{2}+(-1-\beta _{2}-\beta _{3}+\beta _{5}+\beta _{8}+\cdots)q^{3}+\cdots$
58.4.d.b	$58$	$4$	58.d	29.d	$7$	$24$	$4$	$3.422$		None		$2$	$0$	$-8$	$5$	$16$	$71$			$\mathrm{SU}(2)[C_{7}]$
58.4.e.a	$58$	$4$	58.e	29.e	$14$	$48$	$8$	$3.422$		None		$2$	$0$	$0$	$0$	$22$	$-12$			$\mathrm{SU}(2)[C_{14}]$
58.5.c.a	$58$	$5$	58.c	29.c	$4$	$10$	$5$	$5.995$	$\mathbb{Q}[x]/(x^{10} - \cdots)$	None		$2$	$0$	$-20$	$16$	$0$	$-96$		$2^{2}$	$\mathrm{SU}(2)[C_{4}]$	$q+(-2-2\beta _{3})q^{2}+(2-\beta _{1}+2\beta _{3})q^{3}+\cdots$
58.5.c.b	$58$	$5$	58.c	29.c	$4$	$10$	$5$	$5.995$	$\mathbb{Q}[x]/(x^{10} - \cdots)$	None		$2$	$0$	$20$	$-16$	$0$	$96$		$2^{2}$	$\mathrm{SU}(2)[C_{4}]$	$q+(2-2\beta _{5})q^{2}+(-2+\beta _{1}+2\beta _{5})q^{3}+\cdots$
58.5.f.a	$58$	$5$	58.f	29.f	$28$	$60$	$5$	$5.995$		None		$2$	$0$	$-20$	$16$	$-56$	$72$			$\mathrm{SU}(2)[C_{28}]$
58.5.f.b	$58$	$5$	58.f	29.f	$28$	$60$	$5$	$5.995$		None		$2$	$0$	$20$	$-16$	$56$	$-72$			$\mathrm{SU}(2)[C_{28}]$
58.6.a.a	$58$	$6$	58.a	1.a	$1$	$2$	$2$	$9.302$	$\Q(\sqrt{22}) $	None	✓	$1$	$1$	$8$	$-14$	$-82$	$-160$	$+$	$1$	$\mathrm{SU}(2)$	$q+4q^{2}+(-7+\beta )q^{3}+2^{4}q^{4}+(-41+\cdots)q^{5}+\cdots$
58.6.a.b	$58$	$6$	58.a	1.a	$1$	$3$	$3$	$9.302$	3.3.431464.1	None	✓	$1$	$0$	$-12$	$14$	$68$	$24$	$-$	$1$	$\mathrm{SU}(2)$	$q-4q^{2}+(4+\beta _{1}+\beta _{2})q^{3}+2^{4}q^{4}+\cdots$
58.6.a.c	$58$	$6$	58.a	1.a	$1$	$4$	$4$	$9.302$	$\mathbb{Q}[x]/(x^{4} - \cdots)$	None	✓	$1$	$1$	$-16$	$-13$	$-7$	$-74$	$+$	$2^{2}$	$\mathrm{SU}(2)$	$q-4q^{2}+(-3-\beta _{1}+\beta _{2})q^{3}+2^{4}q^{4}+\cdots$
58.6.a.d	$58$	$6$	58.a	1.a	$1$	$4$	$4$	$9.302$	$\mathbb{Q}[x]/(x^{4} - \cdots)$	None	✓	$1$	$0$	$16$	$13$	$93$	$134$	$-$	$2^{2}$	$\mathrm{SU}(2)$	$q+4q^{2}+(3+\beta _{1})q^{3}+2^{4}q^{4}+(23-\beta _{2}+\cdots)q^{5}+\cdots$
58.6.b.a	$58$	$6$	58.b	29.b	$2$	$12$	$12$	$9.302$	$\mathbb{Q}[x]/(x^{12} + \cdots)$	None		$2$	$0$	$0$	$0$	$-10$	$76$		$2^{16}\cdot 5^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{7}q^{2}+(\beta _{6}+\beta _{7})q^{3}-2^{4}q^{4}+(-1+\cdots)q^{5}+\cdots$
58.6.d.a	$58$	$6$	58.d	29.d	$7$	$36$	$6$	$9.302$		None		$2$	$0$	$-24$	$1$	$-228$	$-9$			$\mathrm{SU}(2)[C_{7}]$
58.6.d.b	$58$	$6$	58.d	29.d	$7$	$42$	$7$	$9.302$		None		$2$	$0$	$28$	$-1$	$156$	$85$			$\mathrm{SU}(2)[C_{7}]$
58.6.e.a	$58$	$6$	58.e	29.e	$14$	$72$	$12$	$9.302$		None		$2$	$0$	$0$	$0$	$10$	$-76$			$\mathrm{SU}(2)[C_{14}]$
58.7.c.a	$58$	$7$	58.c	29.c	$4$	$14$	$7$	$13.343$	$\mathbb{Q}[x]/(x^{14} - \cdots)$	None		$2$	$0$	$-56$	$-28$	$0$	$776$		$2^{4}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{4}]$	$q+(-4-4\beta _{2})q^{2}+(-2-\beta _{1}-2\beta _{2}+\cdots)q^{3}+\cdots$
58.7.c.b	$58$	$7$	58.c	29.c	$4$	$16$	$8$	$13.343$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	None		$2$	$0$	$64$	$28$	$0$	$-776$		$2^{5}$	$\mathrm{SU}(2)[C_{4}]$	$q+(4+4\beta _{2})q^{2}+(2-\beta _{1}+2\beta _{2})q^{3}+\cdots$
58.7.f.a	$58$	$7$	58.f	29.f	$28$	$84$	$7$	$13.343$		None		$2$	$0$	$56$	$28$	$588$	$610$			$\mathrm{SU}(2)[C_{28}]$
58.7.f.b	$58$	$7$	58.f	29.f	$28$	$96$	$8$	$13.343$		None		$2$	$0$	$-64$	$-28$	$-588$	$-610$			$\mathrm{SU}(2)[C_{28}]$
58.8.a.a	$58$	$8$	58.a	1.a	$1$	$3$	$3$	$18.118$	3.3.1792765.1	None	✓	$1$	$0$	$-24$	$13$	$195$	$110$	$+$	$2^{3}$	$\mathrm{SU}(2)$	$q-8q^{2}+(4-\beta _{1}-\beta _{2})q^{3}+2^{6}q^{4}+\cdots$
58.8.a.b	$58$	$8$	58.a	1.a	$1$	$3$	$3$	$18.118$	3.3.732765.1	None	✓	$1$	$1$	$24$	$-25$	$-305$	$-1138$	$-$	$2^{3}$	$\mathrm{SU}(2)$	$q+8q^{2}+(-8+\beta _{2})q^{3}+2^{6}q^{4}+(-104+\cdots)q^{5}+\cdots$
58.8.a.c	$58$	$8$	58.a	1.a	$1$	$4$	$4$	$18.118$	$\mathbb{Q}[x]/(x^{4} - \cdots)$	None	✓	$1$	$1$	$-32$	$-68$	$-180$	$-576$	$-$	$2^{4}\cdot 3$	$\mathrm{SU}(2)$	$q-8q^{2}+(-17+\beta _{2})q^{3}+2^{6}q^{4}+(-45+\cdots)q^{5}+\cdots$
58.8.a.d	$58$	$8$	58.a	1.a	$1$	$5$	$5$	$18.118$	$\mathbb{Q}[x]/(x^{5} - \cdots)$	None	✓	$1$	$0$	$40$	$56$	$570$	$920$	$+$	$2^{4}$	$\mathrm{SU}(2)$	$q+8q^{2}+(11+\beta _{1})q^{3}+2^{6}q^{4}+(114+\cdots)q^{5}+\cdots$
58.8.b.a	$58$	$8$	58.b	29.b	$2$	$18$	$18$	$18.118$	$\mathbb{Q}[x]/(x^{18} + \cdots)$	None		$2$	$0$	$0$	$0$	$-82$	$-1348$		$2^{53}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{10}q^{2}+(-\beta _{9}+\beta _{10})q^{3}-2^{6}q^{4}+\cdots$
58.8.d.a	$58$	$8$	58.d	29.d	$7$	$48$	$8$	$18.118$		None		$2$	$0$	$-64$	$-31$	$-356$	$-3695$			$\mathrm{SU}(2)[C_{7}]$
58.8.d.b	$58$	$8$	58.d	29.d	$7$	$54$	$9$	$18.118$		None		$2$	$0$	$72$	$31$	$496$	$2347$			$\mathrm{SU}(2)[C_{7}]$
58.8.e.a	$58$	$8$	58.e	29.e	$14$	$108$	$18$	$18.118$		None		$2$	$0$	$0$	$0$	$82$	$1348$			$\mathrm{SU}(2)[C_{14}]$
58.9.c.a	$58$	$9$	58.c	29.c	$4$	$20$	$10$	$23.628$	$\mathbb{Q}[x]/(x^{20} + \cdots)$	None		$2$	$0$	$-160$	$-32$	$0$	$1728$		$2^{13}$	$\mathrm{SU}(2)[C_{4}]$	$q+(-8+8\beta _{1})q^{2}+(-2+2\beta _{1}+\beta _{2}+\cdots)q^{3}+\cdots$
58.9.c.b	$58$	$9$	58.c	29.c	$4$	$20$	$10$	$23.628$	$\mathbb{Q}[x]/(x^{20} - \cdots)$	None		$2$	$0$	$160$	$32$	$0$	$-1728$		$2^{13}\cdot 3^{4}$	$\mathrm{SU}(2)[C_{4}]$	$q+(8+8\beta _{3})q^{2}+(2-\beta _{2}+2\beta _{3})q^{3}+\cdots$
58.9.f.a	$58$	$9$	58.f	29.f	$28$	$120$	$10$	$23.628$		None		$2$	$0$	$-160$	$-32$	$2576$	$-12048$			$\mathrm{SU}(2)[C_{28}]$
58.9.f.b	$58$	$9$	58.f	29.f	$28$	$120$	$10$	$23.628$		None		$2$	$0$	$160$	$32$	$-2576$	$12048$			$\mathrm{SU}(2)[C_{28}]$
58.10.a.a	$58$	$10$	58.a	1.a	$1$	$4$	$4$	$29.872$	$\mathbb{Q}[x]/(x^{4} - \cdots)$	None	✓	$1$	$1$	$64$	$4$	$-3012$	$-12576$	$+$	$2^{4}\cdot 3$	$\mathrm{SU}(2)$	$q+2^{4}q^{2}+(1+\beta _{2})q^{3}+2^{8}q^{4}+(-753+\cdots)q^{5}+\cdots$
58.10.a.b	$58$	$10$	58.a	1.a	$1$	$5$	$5$	$29.872$	$\mathbb{Q}[x]/(x^{5} - \cdots)$	None	✓	$1$	$0$	$-80$	$152$	$738$	$3848$	$-$	$2^{4}\cdot 3$	$\mathrm{SU}(2)$	$q-2^{4}q^{2}+(30+\beta _{4})q^{3}+2^{8}q^{4}+(147+\cdots)q^{5}+\cdots$
58.10.a.c	$58$	$10$	58.a	1.a	$1$	$6$	$6$	$29.872$	$\mathbb{Q}[x]/(x^{6} - \cdots)$	None	✓	$1$	$1$	$-96$	$-91$	$-1137$	$-954$	$+$	$2^{7}\cdot 3^{3}$	$\mathrm{SU}(2)$	$q-2^{4}q^{2}+(-15+\beta _{1})q^{3}+2^{8}q^{4}+\cdots$
58.10.a.d	$58$	$10$	58.a	1.a	$1$	$6$	$6$	$29.872$	$\mathbb{Q}[x]/(x^{6} - \cdots)$	None	✓	$1$	$0$	$96$	$247$	$1363$	$1830$	$-$	$2^{7}\cdot 3$	$\mathrm{SU}(2)$	$q+2^{4}q^{2}+(41+\beta _{1})q^{3}+2^{8}q^{4}+(226+\cdots)q^{5}+\cdots$

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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.