Modular curve search results

Results (1-50 of 126 matches)

 

Label	RSZB label	RZB label	CP label	SZ label	S label	Name	Level	Index	Genus	Rank	$\Q$-gonality	Cusps	$\Q$-cusps	CM points	Conductor	Simple	Squarefree	Contains -1	Decomposition	Models	$j$-points	Local obstruction	$\operatorname{GL}_2(\mathbb{Z}/N\mathbb{Z})$-generators
1.1.0.a.1	1.1.0.1	X1	1A0			$X(1)$	$1$	$1$	$0$	$0$	$1$	$1$	$1$	✓	$?$	?	?	✓	not computed	$1$	$0$		trivial subgroup
2.6.0.a.1	2.6.0.1	X8	2C0	2C0-2a	2Cs	$X(2)$	$2$	$6$	$0$	$0$	$1$	$3$	$3$	✓	$?$	?	?	✓	not computed	$1$	$31721$		trivial subgroup
3.12.0.a.1	3.12.0.1		3D0	3D0-3a	3Cs	$X_{\mathrm{sp}}(3)$	$3$	$12$	$0$	$0$	$1$	$4$	$2$	✓	$?$	?	?	✓	not computed	$1$	$1551$		$\begin{bmatrix}1&0\\0&2\end{bmatrix}$, $\begin{bmatrix}2&0\\0&2\end{bmatrix}$
4.24.0.b.1	4.24.0.8	X58	4G0	4G0-4a		$X_{\mathrm{sp}}(4)$	$4$	$24$	$0$	$0$	$1$	$6$	$4$		$?$	?	?	✓	not computed	$1$	$62$		$\begin{bmatrix}1&0\\0&3\end{bmatrix}$, $\begin{bmatrix}3&0\\0&3\end{bmatrix}$
5.30.0.a.1	5.30.0.1		5G0	5G0-5a	5Cs	$X_{\mathrm{sp}}(5)$	$5$	$30$	$0$	$0$	$1$	$6$	$2$		$?$	?	?	✓	not computed	$1$	$14$		$\begin{bmatrix}1&0\\0&2\end{bmatrix}$, $\begin{bmatrix}3&0\\0&3\end{bmatrix}$
6.72.1.a.1	6.72.1.1		6F1			$X_{\mathrm{sp}}(6)$	$6$	$72$	$1$	$0$	$2$	$12$	$6$		$2^{2}\cdot3^{2}$	✓	✓	✓	$1$	$1$	$1$		$\begin{bmatrix}5&0\\0&1\end{bmatrix}$, $\begin{bmatrix}5&0\\0&5\end{bmatrix}$
7.56.1.a.1	7.56.1.1		7B1		7Cs	$X_{\mathrm{sp}}(7)$	$7$	$56$	$1$	$0$	$2$	$8$	$2$		$7^{2}$	✓	✓	✓	$1$	$1$	$1$		$\begin{bmatrix}3&0\\0&2\end{bmatrix}$, $\begin{bmatrix}3&0\\0&3\end{bmatrix}$
8.96.3.g.1	8.96.3.16	X536	8A3			$X_{\mathrm{sp}}(8)$	$8$	$96$	$3$	$0$	$3$	$12$	$4$		$2^{16}$			✓	$1^{3}$	$1$	$1$		$\begin{bmatrix}1&0\\0&5\end{bmatrix}$, $\begin{bmatrix}3&0\\0&3\end{bmatrix}$, $\begin{bmatrix}5&0\\0&5\end{bmatrix}$, $\begin{bmatrix}7&0\\0&5\end{bmatrix}$
9.108.4.c.1	9.108.4.4		9B4			$X_{\mathrm{sp}}(9)$	$9$	$108$	$4$	$0$	$3$	$12$	$2$		$3^{14}$			✓	$1^{2}\cdot2$	$2$	$1$		$\begin{bmatrix}2&0\\0&1\end{bmatrix}$, $\begin{bmatrix}2&0\\0&2\end{bmatrix}$
10.180.7.a.1	10.180.7.1		10A7			$X_{\mathrm{sp}}(10)$	$10$	$180$	$7$	$0$	$4$	$18$	$6$		$2^{10}\cdot5^{12}$			✓	$1^{7}$	$2$	$1$		$\begin{bmatrix}7&0\\0&1\end{bmatrix}$, $\begin{bmatrix}7&0\\0&7\end{bmatrix}$
11.132.6.a.1	11.132.6.1		11A6		11Cs	$X_{\mathrm{sp}}(11)$	$11$	$132$	$6$	$1$	$4$	$12$	$2$		$11^{10}$			✓	$1^{6}$	$1$	$1$		$\begin{bmatrix}1&0\\0&2\end{bmatrix}$, $\begin{bmatrix}2&0\\0&6\end{bmatrix}$
12.288.13.c.1	12.288.13.3		12A13			$X_{\mathrm{sp}}(12)$	$12$	$288$	$13$	$0$	$5 \le \gamma \le 6$	$24$	$8$		$2^{40}\cdot3^{20}$			✓	$1^{13}$	$1$	$1$		$\begin{bmatrix}1&0\\0&5\end{bmatrix}$, $\begin{bmatrix}1&0\\0&7\end{bmatrix}$, $\begin{bmatrix}5&0\\0&5\end{bmatrix}$, $\begin{bmatrix}7&0\\0&7\end{bmatrix}$
13.182.8.a.1	13.182.8.1		13B8		13Cs	$X_{\mathrm{sp}}(13)$	$13$	$182$	$8$	$3$	$4 \le \gamma \le 6$	$14$	$2$		$13^{16}$		✓	✓	$2\cdot3^{2}$	$2$	$1$		$\begin{bmatrix}10&0\\0&11\end{bmatrix}$, $\begin{bmatrix}11&0\\0&6\end{bmatrix}$
14.336.17.a.1	14.336.17.5		14B17			$X_{\mathrm{sp}}(14)$	$14$	$336$	$17$	$1$	$7 \le \gamma \le 12$	$24$	$6$		$2^{18}\cdot7^{30}$			✓	$1^{11}\cdot2^{3}$	$1$	$1$		$\begin{bmatrix}5&0\\0&1\end{bmatrix}$, $\begin{bmatrix}5&0\\0&3\end{bmatrix}$
15.360.19.a.1	15.360.19.1		15B19			$X_{\mathrm{sp}}(15)$	$15$	$360$	$19$	$2$	$8 \le \gamma \le 12$	$24$	$4$		$3^{28}\cdot5^{32}$			✓	$1^{17}\cdot2$	$1$	$1$		$\begin{bmatrix}7&0\\0&1\end{bmatrix}$, $\begin{bmatrix}11&0\\0&1\end{bmatrix}$, $\begin{bmatrix}11&0\\0&11\end{bmatrix}$, $\begin{bmatrix}13&0\\0&13\end{bmatrix}$
16.384.21.j.1	16.384.21.47		16C21			$X_{\mathrm{sp}}(16)$	$16$	$384$	$21$	$4$	$8$	$24$	$4$		$2^{142}$			✓	$1^{19}\cdot2$	$2$	$1$		$\begin{bmatrix}3&0\\0&7\end{bmatrix}$, $\begin{bmatrix}5&0\\0&13\end{bmatrix}$, $\begin{bmatrix}7&0\\0&9\end{bmatrix}$, $\begin{bmatrix}15&0\\0&15\end{bmatrix}$
17.306.17.a.1	17.306.17.1		17A17		17Cs	$X_{\mathrm{sp}}(17)$	$17$	$306$	$17$	$6$	$7 \le \gamma \le 14$	$18$	$2$		$17^{32}$			✓	$1^{3}\cdot2^{2}\cdot3^{2}\cdot4$	$1$	$1$		$\begin{bmatrix}3&0\\0&3\end{bmatrix}$, $\begin{bmatrix}12&0\\0&9\end{bmatrix}$
18.648.37.c.1	18.648.37.11					$X_{\mathrm{sp}}(18)$	$18$	$648$	$37$	$3$	$9 \le \gamma \le 12$	$36$	$6$		$2^{34}\cdot3^{126}$			✓	$1^{31}\cdot2^{3}$		$0$		$\begin{bmatrix}5&0\\0&1\end{bmatrix}$, $\begin{bmatrix}5&0\\0&5\end{bmatrix}$
19.380.22.a.1	19.380.22.1		19A22		19Cs	$X_{\mathrm{sp}}(19)$	$19$	$380$	$22$	$8$	$8 \le \gamma \le 18$	$20$	$2$		$19^{42}$			✓	$1^{4}\cdot2^{4}\cdot3^{2}\cdot4$	$1$	$1$		$\begin{bmatrix}1&0\\0&14\end{bmatrix}$, $\begin{bmatrix}14&0\\0&15\end{bmatrix}$
20.720.43.e.1	20.720.43.5					$X_{\mathrm{sp}}(20)$	$20$	$720$	$43$	$5$	$14 \le \gamma \le 16$	$36$	$8$		$2^{116}\cdot5^{72}$			✓	$1^{43}$		$0$		$\begin{bmatrix}11&0\\0&1\end{bmatrix}$, $\begin{bmatrix}11&0\\0&11\end{bmatrix}$, $\begin{bmatrix}13&0\\0&1\end{bmatrix}$, $\begin{bmatrix}17&0\\0&17\end{bmatrix}$
21.672.41.a.1	21.672.41.1					$X_{\mathrm{sp}}(21)$	$21$	$672$	$41$	$8$	$13 \le \gamma \le 24$	$32$	$4$		$3^{58}\cdot7^{72}$			✓	$1^{21}\cdot2^{10}$		$0$		$\begin{bmatrix}2&0\\0&1\end{bmatrix}$, $\begin{bmatrix}8&0\\0&8\end{bmatrix}$, $\begin{bmatrix}13&0\\0&1\end{bmatrix}$, $\begin{bmatrix}19&0\\0&10\end{bmatrix}$
22.792.49.a.1	22.792.49.1					$X_{\mathrm{sp}}(22)$	$22$	$792$	$49$	$12$	$15 \le \gamma \le 24$	$36$	$6$		$2^{42}\cdot11^{90}$			✓	$1^{25}\cdot2^{12}$		$0$		$\begin{bmatrix}7&0\\0&15\end{bmatrix}$, $\begin{bmatrix}7&0\\0&19\end{bmatrix}$
23.552.35.a.1	23.552.35.1				23Cs	$X_{\mathrm{sp}}(23)$	$23$	$552$	$35$	$13$	$11 \le \gamma \le 30$	$24$	$2$		$23^{66}$			✓	$2^{7}\cdot3\cdot4^{2}\cdot5^{2}$		$0$		$\begin{bmatrix}5&0\\0&14\end{bmatrix}$, $\begin{bmatrix}14&0\\0&9\end{bmatrix}$
24.1152.73.cg.1	24.1152.73.20					$X_{\mathrm{sp}}(24)$	$24$	$1152$	$73$	$9$	$17 \le \gamma \le 24$	$48$	$8$		$2^{334}\cdot3^{98}$			✓	$1^{73}$		$0$		$\begin{bmatrix}1&0\\0&17\end{bmatrix}$, $\begin{bmatrix}7&0\\0&13\end{bmatrix}$, $\begin{bmatrix}13&0\\0&1\end{bmatrix}$, $\begin{bmatrix}13&0\\0&13\end{bmatrix}$, $\begin{bmatrix}17&0\\0&17\end{bmatrix}$, $\begin{bmatrix}19&0\\0&19\end{bmatrix}$
25.750.48.a.1	25.750.48.1					$X_{\mathrm{sp}}(25)$	$25$	$750$	$48$	$18$	$13 \le \gamma \le 20$	$30$	$2$		$5^{176}$			✓	$2^{8}\cdot4^{2}\cdot8^{3}$		$0$		$\begin{bmatrix}2&0\\0&1\end{bmatrix}$, $\begin{bmatrix}3&0\\0&3\end{bmatrix}$
26.1092.71.a.1	26.1092.71.7					$X_{\mathrm{sp}}(26)$	$26$	$1092$	$71$	$20$	$19 \le \gamma \le 36$	$42$	$6$		$2^{62}\cdot13^{132}$			✓	$1^{27}\cdot2^{4}\cdot3^{12}$		$0$		$\begin{bmatrix}15&0\\0&3\end{bmatrix}$, $\begin{bmatrix}15&0\\0&7\end{bmatrix}$
27.972.64.d.1	27.972.64.5					$X_{\mathrm{sp}}(27)$	$27$	$972$	$64$	$20$	$18 \le \gamma \le 27$	$36$	$2$		$3^{336}$			✓	$1^{8}\cdot2^{7}\cdot3^{4}\cdot6^{5}$		$0$		$\begin{bmatrix}2&0\\0&1\end{bmatrix}$, $\begin{bmatrix}25&0\\0&14\end{bmatrix}$
28.1344.89.e.1	28.1344.89.9					$X_{\mathrm{sp}}(28)$	$28$	$1344$	$89$	$18$	$24 \le \gamma \le 48$	$48$	$8$		$2^{224}\cdot7^{156}$			✓	$1^{59}\cdot2^{15}$		$0$		$\begin{bmatrix}5&0\\0&17\end{bmatrix}$, $\begin{bmatrix}11&0\\0&17\end{bmatrix}$, $\begin{bmatrix}15&0\\0&1\end{bmatrix}$, $\begin{bmatrix}15&0\\0&15\end{bmatrix}$
29.870.58.a.1	29.870.58.1				29Cs	$X_{\mathrm{sp}}(29)$	$29$	$870$	$58$	$24$	$16 \le \gamma \le 52$	$30$	$2$		$29^{112}$			✓	$2^{6}\cdot3^{2}\cdot6^{2}\cdot8^{2}\cdot12$		$0$		$\begin{bmatrix}1&0\\0&10\end{bmatrix}$, $\begin{bmatrix}3&0\\0&10\end{bmatrix}$
30.2160.145.a.1	30.2160.145.1					$X_{\mathrm{sp}}(30)$	$30$	$2160$	$145$	$15$	$23 \le \gamma \le 48$	$72$	$12$		$2^{118}\cdot3^{190}\cdot5^{238}$			✓	$1^{139}\cdot2^{3}$		$0$		$\begin{bmatrix}7&0\\0&7\end{bmatrix}$, $\begin{bmatrix}11&0\\0&1\end{bmatrix}$, $\begin{bmatrix}11&0\\0&11\end{bmatrix}$, $\begin{bmatrix}13&0\\0&1\end{bmatrix}$
31.992.67.a.1	31.992.67.1				31Cs	$X_{\mathrm{sp}}(31)$	$31$	$992$	$67$	$28$	$18 \le \gamma \le 60$	$32$	$2$		$31^{130}$			✓	$2^{8}\cdot3\cdot4\cdot8^{2}\cdot12\cdot16$		$0$		$\begin{bmatrix}14&0\\0&17\end{bmatrix}$, $\begin{bmatrix}17&0\\0&11\end{bmatrix}$
32.1536.105.bv.1	32.1536.105.101					$X_{\mathrm{sp}}(32)$	$32$	$1536$	$105$	$34$	$28 \le \gamma \le 32$	$48$	$4$		$2^{884}$			✓	$1^{39}\cdot2^{21}\cdot4^{6}$		$0$		$\begin{bmatrix}1&0\\0&31\end{bmatrix}$, $\begin{bmatrix}3&0\\0&11\end{bmatrix}$, $\begin{bmatrix}15&0\\0&15\end{bmatrix}$, $\begin{bmatrix}17&0\\0&21\end{bmatrix}$
33.1584.109.a.1	33.1584.109.1					$X_{\mathrm{sp}}(33)$	$33$	$1584$	$109$	$33$	$28 \le \gamma \le 48$	$48$	$4$		$3^{140}\cdot11^{200}$			✓	$1^{47}\cdot2^{21}\cdot4^{5}$		$0$		$\begin{bmatrix}1&0\\0&23\end{bmatrix}$, $\begin{bmatrix}7&0\\0&4\end{bmatrix}$, $\begin{bmatrix}7&0\\0&19\end{bmatrix}$, $\begin{bmatrix}23&0\\0&23\end{bmatrix}$
34.1836.127.a.1	34.1836.127.1					$X_{\mathrm{sp}}(34)$	$34$	$1836$	$127$	$43$	$33 \le \gamma \le 68$	$54$	$6$		$2^{102}\cdot17^{240}$			✓	$1^{15}\cdot2^{18}\cdot3^{16}\cdot4^{7}$		$0$		$\begin{bmatrix}3&0\\0&23\end{bmatrix}$, $\begin{bmatrix}31&0\\0&1\end{bmatrix}$
35.1680.117.q.1	35.1680.117.9					$X_{\mathrm{sp}}(35)$	$35$	$1680$	$117$	$38$	$29 \le \gamma \le 56$	$48$	$4$		$5^{190}\cdot7^{204}$			✓	$1^{29}\cdot2^{32}\cdot3^{4}\cdot4^{3}$		$0$		$\begin{bmatrix}17&0\\0&26\end{bmatrix}$, $\begin{bmatrix}22&0\\0&3\end{bmatrix}$, $\begin{bmatrix}29&0\\0&34\end{bmatrix}$, $\begin{bmatrix}34&0\\0&6\end{bmatrix}$
36.2592.181.l.1	36.2592.181.58					$X_{\mathrm{sp}}(36)$	$36$	$2592$	$181$	$36$	$35 \le \gamma \le 48$	$72$	$8$		$2^{440}\cdot3^{582}$			✓	$1^{145}\cdot2^{18}$		$0$		$\begin{bmatrix}1&0\\0&5\end{bmatrix}$, $\begin{bmatrix}17&0\\0&19\end{bmatrix}$, $\begin{bmatrix}19&0\\0&19\end{bmatrix}$, $\begin{bmatrix}25&0\\0&19\end{bmatrix}$
37.1406.98.a.1	37.1406.98.1				37Cs	$X_{\mathrm{sp}}(37)$	$37$	$1406$	$98$	$45$	$25 \le \gamma \le 74$	$38$	$2$		$37^{192}$			✓	$1^{10}\cdot2^{2}\cdot3^{4}\cdot18\cdot27^{2}$		$0$		$\begin{bmatrix}13&0\\0&20\end{bmatrix}$, $\begin{bmatrix}17&0\\0&28\end{bmatrix}$
38.2280.161.a.1	38.2280.161.1					$X_{\mathrm{sp}}(38)$	$38$	$2280$	$161$	$56$	$40 \le \gamma \le 108$	$60$	$6$		$2^{126}\cdot19^{306}$			✓	$1^{37}\cdot2^{23}\cdot3^{10}\cdot4^{7}\cdot6^{2}\cdot8$		$0$		$\begin{bmatrix}15&0\\0&1\end{bmatrix}$, $\begin{bmatrix}15&0\\0&13\end{bmatrix}$
39.2184.155.a.1	39.2184.155.1					$X_{\mathrm{sp}}(39)$	$39$	$2184$	$155$	$54$	$38 \le \gamma \le 72$	$56$	$4$		$3^{200}\cdot13^{288}$			✓	$1^{17}\cdot2^{29}\cdot3^{20}\cdot4^{2}\cdot6^{2}$		$0$		$\begin{bmatrix}1&0\\0&20\end{bmatrix}$, $\begin{bmatrix}1&0\\0&38\end{bmatrix}$, $\begin{bmatrix}2&0\\0&20\end{bmatrix}$, $\begin{bmatrix}38&0\\0&38\end{bmatrix}$
40.2880.205.gm.2	40.2880.205.42					$X_{\mathrm{sp}}(40)$	$40$	$2880$	$205$	$51$	$51 \le \gamma \le 64$	$72$	$8$		$2^{894}\cdot5^{330}$			✓	$1^{163}\cdot2^{21}$		$0$		$\begin{bmatrix}9&0\\0&19\end{bmatrix}$, $\begin{bmatrix}11&0\\0&1\end{bmatrix}$, $\begin{bmatrix}23&0\\0&1\end{bmatrix}$, $\begin{bmatrix}29&0\\0&29\end{bmatrix}$, $\begin{bmatrix}31&0\\0&1\end{bmatrix}$, $\begin{bmatrix}33&0\\0&33\end{bmatrix}$
41.1722.123.a.1	41.1722.123.1				41Cs	$X_{\mathrm{sp}}(41)$	$41$	$1722$	$123$	$54$	$30 \le \gamma \le 82$	$42$	$2$		$41^{240}$			✓	$2\cdot3^{5}\cdot4^{2}\cdot6\cdot8\cdot12^{2}\cdot18^{2}\cdot24$		$0$		$\begin{bmatrix}28&0\\0&28\end{bmatrix}$, $\begin{bmatrix}30&0\\0&4\end{bmatrix}$
42.4032.289.a.1	42.4032.289.28					$X_{\mathrm{sp}}(42)$	$42$	$4032$	$289$	$57$	$53 \le \gamma \le 96$	$96$	$12$		$2^{222}\cdot3^{366}\cdot7^{502}$			✓	$1^{193}\cdot2^{46}\cdot4$		$0$		$\begin{bmatrix}1&0\\0&29\end{bmatrix}$, $\begin{bmatrix}19&0\\0&19\end{bmatrix}$, $\begin{bmatrix}25&0\\0&19\end{bmatrix}$, $\begin{bmatrix}29&0\\0&29\end{bmatrix}$
43.1892.136.a.1	43.1892.136.1				43Cs	$X_{\mathrm{sp}}(43)$	$43$	$1892$	$136$	$62$	$33 \le \gamma \le 126$	$44$	$2$		$43^{266}$			✓	$1^{6}\cdot2^{6}\cdot3^{4}\cdot10\cdot18^{2}\cdot20^{3}$		$0$		$\begin{bmatrix}30&0\\0&26\end{bmatrix}$, $\begin{bmatrix}38&0\\0&30\end{bmatrix}$
44.3168.229.e.1	44.3168.229.3					$X_{\mathrm{sp}}(44)$	$44$	$3168$	$229$	$76$	$54 \le \gamma \le 88$	$72$	$8$		$2^{544}\cdot11^{420}$			✓	$1^{79}\cdot2^{63}\cdot4^{6}$		$0$		$\begin{bmatrix}9&0\\0&13\end{bmatrix}$, $\begin{bmatrix}21&0\\0&21\end{bmatrix}$, $\begin{bmatrix}23&0\\0&23\end{bmatrix}$, $\begin{bmatrix}37&0\\0&3\end{bmatrix}$
45.3240.235.j.1	45.3240.235.43					$X_{\mathrm{sp}}(45)$	$45$	$3240$	$235$	$72$	$57 \le \gamma \le 90$	$72$	$4$		$3^{746}\cdot5^{376}$			✓	$1^{91}\cdot2^{41}\cdot3^{6}\cdot4^{11}$		$0$		$\begin{bmatrix}7&0\\0&1\end{bmatrix}$, $\begin{bmatrix}13&0\\0&7\end{bmatrix}$, $\begin{bmatrix}44&0\\0&1\end{bmatrix}$, $\begin{bmatrix}44&0\\0&44\end{bmatrix}$
46.3312.241.a.1	46.3312.241.1					$X_{\mathrm{sp}}(46)$	$46$	$3312$	$241$	$95$	$56 \le \gamma \le 92$	$72$	$6$		$2^{182}\cdot23^{462}$			✓	$1^{22}\cdot2^{29}\cdot3^{3}\cdot4^{8}\cdot5^{14}\cdot6\cdot8^{3}\cdot10^{2}$		$0$		$\begin{bmatrix}21&0\\0&21\end{bmatrix}$, $\begin{bmatrix}37&0\\0&1\end{bmatrix}$
47.2256.165.a.1	47.2256.165.1				47Cs	$X_{\mathrm{sp}}(47)$	$47$	$2256$	$165$	$73$	$39 \le \gamma \le 154$	$48$	$2$		$47^{322}$			✓	$1^{2}\cdot3^{2}\cdot4^{3}\cdot5\cdot8\cdot10\cdot16^{2}\cdot24\cdot33^{2}$		$0$		$\begin{bmatrix}1&0\\0&39\end{bmatrix}$, $\begin{bmatrix}30&0\\0&11\end{bmatrix}$
48.4608.337.wu.1	48.4608.337.299					$X_{\mathrm{sp}}(48)$	$48$	$4608$	$337$	$89$	$62 \le \gamma \le 64$	$96$	$8$		$2^{2124}\cdot3^{422}$			✓	$1^{293}\cdot2^{20}\cdot4$		$0$		$\begin{bmatrix}1&0\\0&7\end{bmatrix}$, $\begin{bmatrix}1&0\\0&17\end{bmatrix}$, $\begin{bmatrix}17&0\\0&17\end{bmatrix}$, $\begin{bmatrix}19&0\\0&43\end{bmatrix}$, $\begin{bmatrix}31&0\\0&31\end{bmatrix}$, $\begin{bmatrix}31&0\\0&37\end{bmatrix}$
49.2744.201.a.1	49.2744.201.2					$X_{\mathrm{sp}}(49)$	$49$	$2744$	$201$	$87$	$47 \le \gamma \le 98$	$56$	$2$		$7^{750}$			✓	$1^{3}\cdot3^{6}\cdot6^{8}\cdot9^{2}\cdot18\cdot24^{2}\cdot48$		$0$		$\begin{bmatrix}5&0\\0&10\end{bmatrix}$, $\begin{bmatrix}16&0\\0&6\end{bmatrix}$
50.4500.331.a.1	50.4500.331.3					$X_{\mathrm{sp}}(50)$	$50$	$4500$	$331$	$112$	$76 \le \gamma \le 100$	$90$	$6$		$2^{250}\cdot5^{1186}$			✓	$1^{19}\cdot2^{54}\cdot4^{24}\cdot6^{2}\cdot8^{12}$		$0$		$\begin{bmatrix}3&0\\0&1\end{bmatrix}$, $\begin{bmatrix}3&0\\0&17\end{bmatrix}$