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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 80 matches)

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Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	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	CM	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
29.2.a.a	$29$	$2$	29.a	1.a	$1$	$2$	$2$	$0.232$	$\Q(\sqrt{2}) $	None	✓	✓	✓	✓	29.2.a.a	$1$	$0$	$-2$	$2$	$-2$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta )q^{2}+(1-\beta )q^{3}+(1-2\beta )q^{4}+\cdots$
29.2.b.a	$29$	$2$	29.b	29.b	$2$	$2$	$2$	$0.232$	$\Q(\sqrt{-5}) $	None		✓	✓	✓	29.2.b.a	$2$	$0$	$0$	$0$	$-6$	$4$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta q^{2}-\beta q^{3}-3q^{4}-3q^{5}+5q^{6}+\cdots$
29.2.d.a	$29$	$2$	29.d	29.d	$7$	$6$	$1$	$0.232$	$\Q(\zeta_{14})$	None		✓	✓	✓	29.2.d.a	$2$	$0$	$-2$	$-5$	$1$	$1$		$1$	$\mathrm{SU}(2)[C_{7}]$	$q+(-1+\zeta_{14}+\zeta_{14}^{3}-\zeta_{14}^{4}+\zeta_{14}^{5})q^{2}+\cdots$
29.2.e.a	$29$	$2$	29.e	29.e	$14$	$12$	$2$	$0.232$	12.0.$\cdots$.1	None		✓	✓	✓	29.2.e.a	$2$	$0$	$-7$	$-7$	$-1$	$-11$		$1$	$\mathrm{SU}(2)[C_{14}]$	$q+(-1+\beta _{3}+\beta _{7}+\beta _{9}+\beta _{10})q^{2}+\cdots$
29.3.c.a	$29$	$3$	29.c	29.c	$4$	$8$	$4$	$0.790$	$\mathbb{Q}[x]/(x^{8} + \cdots)$	None		✓	✓	✓	29.3.c.a	$2$	$0$	$2$	$-2$	$0$	$-4$		$2^{2}$	$\mathrm{SU}(2)[C_{4}]$	$q-\beta _{6}q^{2}+(\beta _{2}+\beta _{6})q^{3}+(\beta _{3}+\beta _{4}-\beta _{5}+\cdots)q^{4}+\cdots$
29.3.f.a	$29$	$3$	29.f	29.f	$28$	$48$	$4$	$0.790$		None		✓	✓	✓	29.3.f.a	$2$	$0$	$-16$	$-12$	$-14$	$-10$			$\mathrm{SU}(2)[C_{28}]$
29.4.a.a	$29$	$4$	29.a	1.a	$1$	$2$	$2$	$1.711$	$\Q(\sqrt{2}) $	None	✓	✓	✓	✓	29.4.a.a	$1$	$1$	$-2$	$-10$	$-10$	$-16$	$-$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta )q^{2}+(-5-3\beta )q^{3}+(-5+\cdots)q^{4}+\cdots$
29.4.a.b	$29$	$4$	29.a	1.a	$1$	$5$	$5$	$1.711$	5.5.13458092.1	None	✓	✓	✓	✓	29.4.a.b	$1$	$0$	$0$	$8$	$10$	$40$	$+$	$2^{2}$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+(1-\beta _{1}-\beta _{3}-\beta _{4})q^{3}+(6+\cdots)q^{4}+\cdots$
29.4.b.a	$29$	$4$	29.b	29.b	$2$	$6$	$6$	$1.711$	$\mathbb{Q}[x]/(x^{6} + \cdots)$	None		✓	✓	✓	29.4.b.a	$2$	$0$	$0$	$0$	$22$	$-28$		$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{2}-\beta _{2}q^{3}+(-5+\beta _{4}+\beta _{5})q^{4}+\cdots$
29.4.d.a	$29$	$4$	29.d	29.d	$7$	$42$	$7$	$1.711$		None		✓	✓	✓	29.4.d.a	$2$	$0$	$-5$	$-5$	$-7$	$-31$			$\mathrm{SU}(2)[C_{7}]$
29.4.e.a	$29$	$4$	29.e	29.e	$14$	$36$	$6$	$1.711$		None		✓	✓	✓	29.4.e.a	$2$	$0$	$-7$	$-7$	$-29$	$21$			$\mathrm{SU}(2)[C_{14}]$
29.5.c.a	$29$	$5$	29.c	29.c	$4$	$18$	$9$	$2.998$	$\mathbb{Q}[x]/(x^{18} - \cdots)$	None		✓	✓	✓	29.5.c.a	$2$	$0$	$-8$	$-2$	$0$	$-4$		$2^{8}$	$\mathrm{SU}(2)[C_{4}]$	$q-\beta _{1}q^{2}+\beta _{6}q^{3}+(\beta _{1}-\beta _{2}+6\beta _{4}+\cdots)q^{4}+\cdots$
29.5.f.a	$29$	$5$	29.f	29.f	$28$	$108$	$9$	$2.998$		None		✓	✓	✓	29.5.f.a	$2$	$0$	$-6$	$-12$	$-14$	$-10$			$\mathrm{SU}(2)[C_{28}]$
29.6.a.a	$29$	$6$	29.a	1.a	$1$	$4$	$4$	$4.651$	4.4.3257317.1	None	✓	✓	✓	✓	29.6.a.a	$1$	$1$	$0$	$-28$	$-68$	$-208$	$+$	$2^{2}$	$\mathrm{SU}(2)$	$q-\beta _{2}q^{2}+(-7+\beta _{1}+\beta _{2})q^{3}+(2-3\beta _{1}+\cdots)q^{4}+\cdots$
29.6.a.b	$29$	$6$	29.a	1.a	$1$	$7$	$7$	$4.651$	$\mathbb{Q}[x]/(x^{7} - \cdots)$	None	✓	✓	✓	✓	29.6.a.b	$1$	$0$	$4$	$26$	$32$	$184$	$-$	$2^{5}$	$\mathrm{SU}(2)$	$q+(1-\beta _{1})q^{2}+(4+\beta _{5})q^{3}+(23-3\beta _{1}+\cdots)q^{4}+\cdots$
29.6.b.a	$29$	$6$	29.b	29.b	$2$	$12$	$12$	$4.651$	$\mathbb{Q}[x]/(x^{12} + \cdots)$	None		✓	✓	✓	29.6.b.a	$2$	$0$	$0$	$0$	$46$	$20$		$2^{14}\cdot 5$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{2}-\beta _{4}q^{3}+(-14+\beta _{2})q^{4}+\cdots$
29.6.d.a	$29$	$6$	29.d	29.d	$7$	$66$	$11$	$4.651$		None		✓	✓	✓	29.6.d.a	$2$	$0$	$-11$	$-5$	$29$	$17$			$\mathrm{SU}(2)[C_{7}]$
29.6.e.a	$29$	$6$	29.e	29.e	$14$	$72$	$12$	$4.651$		None		✓	✓	✓	29.6.e.a	$2$	$0$	$-7$	$-7$	$-53$	$-27$			$\mathrm{SU}(2)[C_{14}]$
29.7.c.a	$29$	$7$	29.c	29.c	$4$	$28$	$14$	$6.672$		None		✓	✓	✓	29.7.c.a	$2$	$0$	$0$	$-2$	$0$	$-4$			$\mathrm{SU}(2)[C_{4}]$
29.7.f.a	$29$	$7$	29.f	29.f	$28$	$168$	$14$	$6.672$		None		✓	✓	✓	29.7.f.a	$2$	$0$	$-14$	$-12$	$-14$	$-10$			$\mathrm{SU}(2)[C_{28}]$
29.8.a.a	$29$	$8$	29.a	1.a	$1$	$7$	$7$	$9.059$	$\mathbb{Q}[x]/(x^{7} - \cdots)$	None	✓	✓	✓	✓	29.8.a.a	$1$	$1$	$-8$	$-82$	$-320$	$-1704$	$-$	$2^{4}\cdot 7$	$\mathrm{SU}(2)$	$q+(-1-\beta _{1})q^{2}+(-12+\beta _{1}-\beta _{2}+\cdots)q^{3}+\cdots$
29.8.a.b	$29$	$8$	29.a	1.a	$1$	$10$	$10$	$9.059$	$\mathbb{Q}[x]/(x^{10} - \cdots)$	None	✓	✓	✓	✓	29.8.a.b	$1$	$0$	$0$	$80$	$180$	$1040$	$+$	$2^{11}$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+(8+\beta _{2})q^{3}+(92+2\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots$
29.8.b.a	$29$	$8$	29.b	29.b	$2$	$16$	$16$	$9.059$	$\mathbb{Q}[x]/(x^{16} + \cdots)$	None		✓	✓	✓	29.8.b.a	$2$	$0$	$0$	$0$	$-198$	$660$		$2^{17}\cdot 3^{2}\cdot 5$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{2}+(-\beta _{1}-\beta _{6})q^{3}+(-45+\beta _{2}+\cdots)q^{4}+\cdots$
29.8.d.a	$29$	$8$	29.d	29.d	$7$	$102$	$17$	$9.059$		None		✓	✓	✓	29.8.d.a	$2$	$0$	$1$	$-5$	$133$	$657$			$\mathrm{SU}(2)[C_{7}]$
29.8.e.a	$29$	$8$	29.e	29.e	$14$	$96$	$16$	$9.059$		None		✓	✓	✓	29.8.e.a	$2$	$0$	$-7$	$-7$	$191$	$-667$			$\mathrm{SU}(2)[C_{14}]$
29.9.c.a	$29$	$9$	29.c	29.c	$4$	$38$	$19$	$11.814$		None		✓	✓	✓	29.9.c.a	$2$	$0$	$-8$	$-2$	$0$	$-4$			$\mathrm{SU}(2)[C_{4}]$
29.9.f.a	$29$	$9$	29.f	29.f	$28$	$228$	$19$	$11.814$		None		✓	✓	✓	29.9.f.a	$2$	$0$	$-6$	$-12$	$-14$	$-10$			$\mathrm{SU}(2)[C_{28}]$
29.10.a.a	$29$	$10$	29.a	1.a	$1$	$9$	$9$	$14.936$	$\mathbb{Q}[x]/(x^{9} - \cdots)$	None	✓	✓	✓	✓	29.10.a.a	$1$	$1$	$0$	$-244$	$-738$	$-7128$	$+$	$2^{9}\cdot 3^{2}\cdot 7$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+(-3^{3}-\beta _{4})q^{3}+(133+2\beta _{1}+\cdots)q^{4}+\cdots$
29.10.a.b	$29$	$10$	29.a	1.a	$1$	$12$	$12$	$14.936$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	None	✓	✓	✓	✓	29.10.a.b	$1$	$0$	$16$	$242$	$1762$	$12080$	$-$	$2^{14}\cdot 3^{2}$	$\mathrm{SU}(2)$	$q+(1+\beta _{1})q^{2}+(20+\beta _{1}-\beta _{3})q^{3}+(291+\cdots)q^{4}+\cdots$
29.10.b.a	$29$	$10$	29.b	29.b	$2$	$22$	$22$	$14.936$		None		✓	✓	✓	29.10.b.a	$2$	$0$	$0$	$0$	$-1374$	$-4956$			$\mathrm{SU}(2)[C_{2}]$
29.10.d.a	$29$	$10$	29.d	29.d	$7$	$126$	$21$	$14.936$		None		✓	✓	✓	29.10.d.a	$2$	$0$	$-23$	$-5$	$-1031$	$-4959$			$\mathrm{SU}(2)[C_{7}]$
29.10.e.a	$29$	$10$	29.e	29.e	$14$	$132$	$22$	$14.936$		None		✓	✓	✓	29.10.e.a	$2$	$0$	$-7$	$-7$	$1367$	$4949$			$\mathrm{SU}(2)[C_{14}]$
29.11.c.a	$29$	$11$	29.c	29.c	$4$	$48$	$24$	$18.425$		None		✓	✓	✓	29.11.c.a	$2$	$0$	$8$	$-2$	$0$	$-4$			$\mathrm{SU}(2)[C_{4}]$
29.11.f.a	$29$	$11$	29.f	29.f	$28$	$288$	$24$	$18.425$		None		✓	✓	✓	29.11.f.a	$2$	$0$	$-22$	$-12$	$-14$	$-10$			$\mathrm{SU}(2)[C_{28}]$
29.12.a.a	$29$	$12$	29.a	1.a	$1$	$11$	$11$	$22.282$	$\mathbb{Q}[x]/(x^{11} - \cdots)$	None	✓	✓	✓	✓	29.12.a.a	$1$	$1$	$-32$	$-982$	$-2740$	$-49432$	$-$	$2^{13}\cdot 3^{2}$	$\mathrm{SU}(2)$	$q+(-3+\beta _{1})q^{2}+(-89-\beta _{1}-\beta _{3}+\cdots)q^{3}+\cdots$
29.12.a.b	$29$	$12$	29.a	1.a	$1$	$14$	$14$	$22.282$	$\mathbb{Q}[x]/(x^{14} - \cdots)$	None	✓	✓	✓	✓	29.12.a.b	$1$	$0$	$0$	$476$	$9760$	$85024$	$+$	$2^{20}\cdot 3^{2}$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+(34-\beta _{3})q^{3}+(1312+3\beta _{1}+\cdots)q^{4}+\cdots$
29.12.b.a	$29$	$12$	29.b	29.b	$2$	$26$	$26$	$22.282$		None		✓	✓	✓	29.12.b.a	$2$	$0$	$0$	$0$	$3742$	$-2108$			$\mathrm{SU}(2)[C_{2}]$
29.12.d.a	$29$	$12$	29.d	29.d	$7$	$162$	$27$	$22.282$		None		✓	✓	✓	29.12.d.a	$2$	$0$	$73$	$-5$	$-16687$	$-2111$			$\mathrm{SU}(2)[C_{7}]$
29.12.e.a	$29$	$12$	29.e	29.e	$14$	$156$	$26$	$22.282$		None		✓	✓	✓	29.12.e.a	$2$	$0$	$-7$	$-7$	$-3749$	$2101$			$\mathrm{SU}(2)[C_{14}]$
29.13.c.a	$29$	$13$	29.c	29.c	$4$	$58$	$29$	$26.506$		None		✓	✓	✓	29.13.c.a	$2$	$0$	$88$	$-2$	$0$	$-4$			$\mathrm{SU}(2)[C_{4}]$
29.14.a.a	$29$	$14$	29.a	1.a	$1$	$14$	$14$	$31.097$	$\mathbb{Q}[x]/(x^{14} - \cdots)$	None	✓	✓	✓	✓	29.14.a.a	$1$	$1$	$0$	$-2188$	$-67808$	$-669728$	$+$	$2^{24}\cdot 3^{4}$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+(-156-\beta _{1}+\beta _{3})q^{3}+(2912+\cdots)q^{4}+\cdots$
29.14.a.b	$29$	$14$	29.a	1.a	$1$	$17$	$17$	$31.097$	$\mathbb{Q}[x]/(x^{17} - \cdots)$	None	✓	✓	✓	✓	29.14.a.b	$1$	$0$	$64$	$2186$	$-5308$	$271464$	$-$	$2^{29}\cdot 3^{4}\cdot 7$	$\mathrm{SU}(2)$	$q+(4-\beta _{1})q^{2}+(129-\beta _{1}+\beta _{3})q^{3}+\cdots$
29.14.b.a	$29$	$14$	29.b	29.b	$2$	$32$	$32$	$31.097$		None		✓	✓	✓	29.14.b.a	$2$	$0$	$0$	$0$	$-90794$	$398260$			$\mathrm{SU}(2)[C_{2}]$
29.15.c.a	$29$	$15$	29.c	29.c	$4$	$68$	$34$	$36.055$		None		✓	✓	✓	29.15.c.a	$2$	$0$	$-312$	$-2$	$0$	$-4$			$\mathrm{SU}(2)[C_{4}]$
29.16.a.a	$29$	$16$	29.a	1.a	$1$	$16$	$16$	$41.381$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	None	✓	✓	✓	✓	29.16.a.a	$1$	$1$	$-128$	$-3214$	$-82010$	$-3706320$	$-$	$2^{33}\cdot 3^{7}\cdot 5^{4}\cdot 7^{2}$	$\mathrm{SU}(2)$	$q+(-8-\beta _{1})q^{2}+(-201+\beta _{2})q^{3}+\cdots$
29.16.a.b	$29$	$16$	29.a	1.a	$1$	$19$	$19$	$41.381$	$\mathbb{Q}[x]/(x^{19} - \cdots)$	None	✓	✓	✓	✓	29.16.a.b	$1$	$0$	$0$	$9908$	$230490$	$2882024$	$+$	$2^{43}\cdot 3^{6}\cdot 5^{5}\cdot 7$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+(521+2\beta _{1}+\beta _{2})q^{3}+(20389+\cdots)q^{4}+\cdots$
29.16.b.a	$29$	$16$	29.b	29.b	$2$	$36$	$36$	$41.381$		None		✓	✓	✓	29.16.b.a	$2$	$0$	$0$	$0$	$470082$	$-4820620$			$\mathrm{SU}(2)[C_{2}]$
29.17.c.a	$29$	$17$	29.c	29.c	$4$	$78$	$39$	$47.074$		None		✓	✓	✓	29.17.c.a	$2$	$0$	$184$	$-2$	$0$	$-4$			$\mathrm{SU}(2)[C_{4}]$
29.18.a.a	$29$	$18$	29.a	1.a	$1$	$18$	$18$	$53.134$	$\mathbb{Q}[x]/(x^{18} - \cdots)$	None	✓	✓	✓	✓	29.18.a.a	$1$	$1$	$0$	$-15400$	$-564228$	$-43925040$	$+$	$2^{42}\cdot 3^{14}\cdot 17$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+(-856-2\beta _{1}+\beta _{2})q^{3}+\cdots$
29.18.a.b	$29$	$18$	29.a	1.a	$1$	$21$	$21$	$53.134$		None	✓	✓	✓	✓	29.18.a.b	$1$	$0$	$256$	$23966$	$998272$	$2193368$	$-$		$\mathrm{SU}(2)$

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Elliptic curves over $\Q$
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