This is the coarse moduli space of elliptic curves, a.k.a. the $j$-line.
Invariants
| Level: | $1$ | $\SL_2$-level: | $1$ | ||||
| Index: | $1$ | $\PSL_2$-index: | $1$ | ||||
| Genus: | $0 = 1 + \frac{ 1 }{12} - \frac{ 1 }{4} - \frac{ 1 }{3} - \frac{ 1 }{2}$ | ||||||
| Cusps: | $1$ (which is rational) | Cusp widths | $1$ | Cusp orbits | $1$ | ||
| Elliptic points: | $1$ of order $2$ and $1$ of order $3$ | ||||||
| $\Q$-gonality: | $1$ | ||||||
| $\overline{\Q}$-gonality: | $1$ | ||||||
| Rational cusps: | $1$ | ||||||
| Rational CM points: | yes $\quad(D =$ $-3,-4,-7,-8,-11,-12,-16,-19,-27,-28,-43,-67,-163$) |
Other labels
| Cummins and Pauli (CP) label: | 1A0 |
| Rouse and Zureick-Brown (RZB) label: | X1 |
| Rouse, Sutherland, and Zureick-Brown (RSZB) label: | 1.1.0.1 |
Models
This modular curve is isomorphic to $\mathbb{P}^1$.
Rational points
This modular curve has infinitely many rational points, corresponding to elliptic curves over $\Q$.
Modular covers
This modular curve is minimally covered by the modular curves in the database listed below.
| Covering curve | Level | Index | Degree | Genus |
|---|---|---|---|---|
| $X_{\mathrm{ns}}(2)$ | $2$ | $2$ | $2$ | $0$ |
| $X_0(2)$ | $2$ | $3$ | $3$ | $0$ |
| $X_{\mathrm{ns}}^+(3)$ | $3$ | $3$ | $3$ | $0$ |
| $X_0(3)$ | $3$ | $4$ | $4$ | $0$ |
| 4.2.0.a.1 | $4$ | $2$ | $2$ | $0$ |
| $X_{\mathrm{ns}}^+(4)$ | $4$ | $4$ | $4$ | $0$ |
| $X_{S_4}(5)$ | $5$ | $5$ | $5$ | $0$ |
| $X_0(5)$ | $5$ | $6$ | $6$ | $0$ |
| $X_{\mathrm{ns}}^+(5)$ | $5$ | $10$ | $10$ | $0$ |
| 6.2.0.a.1 | $6$ | $2$ | $2$ | $0$ |
| $X_0(7)$ | $7$ | $8$ | $8$ | $0$ |
| $X_{\mathrm{ns}}^+(7)$ | $7$ | $21$ | $21$ | $0$ |
| $X_{\mathrm{sp}}^+(7)$ | $7$ | $28$ | $28$ | $0$ |
| 8.2.0.a.1 | $8$ | $2$ | $2$ | $0$ |
| 8.2.0.b.1 | $8$ | $2$ | $2$ | $0$ |
| 9.27.0.a.1 | $9$ | $27$ | $27$ | $0$ |
| 10.2.0.a.1 | $10$ | $2$ | $2$ | $0$ |
| $X_0(11)$ | $11$ | $12$ | $12$ | $1$ |
| $X_{S_4}(11)$ | $11$ | $55$ | $55$ | $1$ |
| $X_{\mathrm{ns}}^+(11)$ | $11$ | $55$ | $55$ | $1$ |
| $X_{\mathrm{sp}}^+(11)$ | $11$ | $66$ | $66$ | $2$ |
| 12.2.0.a.1 | $12$ | $2$ | $2$ | $0$ |
| $X_0(13)$ | $13$ | $14$ | $14$ | $0$ |
| $X_{\mathrm{ns}}^+(13)$ | $13$ | $78$ | $78$ | $3$ |
| $X_{S_4}(13)$ | $13$ | $91$ | $91$ | $3$ |
| $X_{\mathrm{sp}}^+(13)$ | $13$ | $91$ | $91$ | $3$ |
| 14.2.0.a.1 | $14$ | $2$ | $2$ | $0$ |
| $X_0(17)$ | $17$ | $18$ | $18$ | $1$ |
| $X_{\mathrm{ns}}^+(17)$ | $17$ | $136$ | $136$ | $6$ |
| $X_{\mathrm{sp}}^+(17)$ | $17$ | $153$ | $153$ | $7$ |
| $X_0(19)$ | $19$ | $20$ | $20$ | $1$ |
| $X_{\mathrm{ns}}^+(19)$ | $19$ | $171$ | $171$ | $8$ |
| $X_{\mathrm{sp}}^+(19)$ | $19$ | $190$ | $190$ | $9$ |
| $X_{S_4}(19)$ | $19$ | $285$ | $285$ | $14$ |
| 20.2.0.a.1 | $20$ | $2$ | $2$ | $0$ |
| 22.2.0.a.1 | $22$ | $2$ | $2$ | $0$ |
| $X_0(23)$ | $23$ | $24$ | $24$ | $2$ |
| $X_{\mathrm{ns}}^+(23)$ | $23$ | $253$ | $253$ | $13$ |
| $X_{\mathrm{sp}}^+(23)$ | $23$ | $276$ | $276$ | $15$ |
| 24.2.0.a.1 | $24$ | $2$ | $2$ | $0$ |
| 24.2.0.b.1 | $24$ | $2$ | $2$ | $0$ |
| 26.2.0.a.1 | $26$ | $2$ | $2$ | $0$ |
| 28.2.0.a.1 | $28$ | $2$ | $2$ | $0$ |
| $X_0(29)$ | $29$ | $30$ | $30$ | $2$ |
| $X_{\mathrm{ns}}^+(29)$ | $29$ | $406$ | $406$ | $24$ |
| $X_{\mathrm{sp}}^+(29)$ | $29$ | $435$ | $435$ | $26$ |
| $X_{S_4}(29)$ | $29$ | $1015$ | $1015$ | $63$ |
| 30.2.0.a.1 | $30$ | $2$ | $2$ | $0$ |
| $X_0(31)$ | $31$ | $32$ | $32$ | $2$ |
| $X_{\mathrm{ns}}^+(31)$ | $31$ | $465$ | $465$ | $28$ |
| $X_{\mathrm{sp}}^+(31)$ | $31$ | $496$ | $496$ | $30$ |
| 34.2.0.a.1 | $34$ | $2$ | $2$ | $0$ |
| $X_0(37)$ | $37$ | $38$ | $38$ | $2$ |
| $X_{\mathrm{ns}}^+(37)$ | $37$ | $666$ | $666$ | $43$ |
| $X_{\mathrm{sp}}^+(37)$ | $37$ | $703$ | $703$ | $45$ |
| $X_{S_4}(37)$ | $37$ | $2109$ | $2109$ | $142$ |
| 38.2.0.a.1 | $38$ | $2$ | $2$ | $0$ |
| 40.2.0.a.1 | $40$ | $2$ | $2$ | $0$ |
| 40.2.0.b.1 | $40$ | $2$ | $2$ | $0$ |
| $X_0(41)$ | $41$ | $42$ | $42$ | $3$ |
| $X_{\mathrm{ns}}^+(41)$ | $41$ | $820$ | $820$ | $54$ |
| $X_{\mathrm{sp}}^+(41)$ | $41$ | $861$ | $861$ | $57$ |
| 42.2.0.a.1 | $42$ | $2$ | $2$ | $0$ |
| $X_0(43)$ | $43$ | $44$ | $44$ | $3$ |
| $X_{\mathrm{ns}}^+(43)$ | $43$ | $903$ | $903$ | $60$ |
| $X_{\mathrm{sp}}^+(43)$ | $43$ | $946$ | $946$ | $63$ |
| $X_{S_4}(43)$ | $43$ | $3311$ | $3311$ | $231$ |
| 44.2.0.a.1 | $44$ | $2$ | $2$ | $0$ |
| 46.2.0.a.1 | $46$ | $2$ | $2$ | $0$ |
| $X_0(47)$ | $47$ | $48$ | $48$ | $4$ |
| $X_{\mathrm{ns}}^+(47)$ | $47$ | $1081$ | $1081$ | $73$ |
| $X_{\mathrm{sp}}^+(47)$ | $47$ | $1128$ | $1128$ | $77$ |
| 52.2.0.a.1 | $52$ | $2$ | $2$ | $0$ |
| $X_0(53)$ | $53$ | $54$ | $54$ | $4$ |
| $X_{\mathrm{ns}}^+(53)$ | $53$ | $1378$ | $1378$ | $96$ |
| $X_{\mathrm{sp}}^+(53)$ | $53$ | $1431$ | $1431$ | $100$ |
| $X_{S_4}(53)$ | $53$ | $6201$ | $6201$ | $450$ |
| 56.2.0.a.1 | $56$ | $2$ | $2$ | $0$ |
| 56.2.0.b.1 | $56$ | $2$ | $2$ | $0$ |
| 58.2.0.a.1 | $58$ | $2$ | $2$ | $0$ |
| $X_0(59)$ | $59$ | $60$ | $60$ | $5$ |
| $X_{\mathrm{ns}}^+(59)$ | $59$ | $1711$ | $1711$ | $121$ |
| $X_{\mathrm{sp}}^+(59)$ | $59$ | $1770$ | $1770$ | $126$ |
| $X_{S_4}(59)$ | $59$ | $8555$ | $8555$ | $631$ |
| 60.2.0.a.1 | $60$ | $2$ | $2$ | $0$ |
| $X_0(61)$ | $61$ | $62$ | $62$ | $4$ |
| $X_{\mathrm{ns}}^+(61)$ | $61$ | $1830$ | $1830$ | $131$ |
| $X_{\mathrm{sp}}^+(61)$ | $61$ | $1891$ | $1891$ | $135$ |
| $X_{S_4}(61)$ | $61$ | $9455$ | $9455$ | $701$ |
| 62.2.0.a.1 | $62$ | $2$ | $2$ | $0$ |
| 66.2.0.a.1 | $66$ | $2$ | $2$ | $0$ |
| $X_0(67)$ | $67$ | $68$ | $68$ | $5$ |
| $X_{\mathrm{ns}}^+(67)$ | $67$ | $2211$ | $2211$ | $160$ |
| $X_{\mathrm{sp}}^+(67)$ | $67$ | $2278$ | $2278$ | $165$ |
| $X_{S_4}(67)$ | $67$ | $12529$ | $12529$ | $940$ |
| 68.2.0.a.1 | $68$ | $2$ | $2$ | $0$ |
| 70.2.0.a.1 | $70$ | $2$ | $2$ | $0$ |
| $X_0(71)$ | $71$ | $72$ | $72$ | $6$ |
| $X_{\mathrm{ns}}^+(71)$ | $71$ | $2485$ | $2485$ | $181$ |
| $X_{\mathrm{sp}}^+(71)$ | $71$ | $2556$ | $2556$ | $187$ |
| $X_0(73)$ | $73$ | $74$ | $74$ | $5$ |
| $X_{\mathrm{ns}}^+(73)$ | $73$ | $2628$ | $2628$ | $193$ |
| $X_{\mathrm{sp}}^+(73)$ | $73$ | $2701$ | $2701$ | $198$ |
| 74.2.0.a.1 | $74$ | $2$ | $2$ | $0$ |
| 76.2.0.a.1 | $76$ | $2$ | $2$ | $0$ |
| 78.2.0.a.1 | $78$ | $2$ | $2$ | $0$ |
| $X_0(79)$ | $79$ | $80$ | $80$ | $6$ |
| $X_{\mathrm{ns}}^+(79)$ | $79$ | $3081$ | $3081$ | $228$ |
| $X_{\mathrm{sp}}^+(79)$ | $79$ | $3160$ | $3160$ | $234$ |
| 82.2.0.a.1 | $82$ | $2$ | $2$ | $0$ |
| $X_0(83)$ | $83$ | $84$ | $84$ | $7$ |
| $X_{\mathrm{ns}}^+(83)$ | $83$ | $3403$ | $3403$ | $253$ |
| $X_{\mathrm{sp}}^+(83)$ | $83$ | $3486$ | $3486$ | $260$ |
| $X_{S_4}(83)$ | $83$ | $23821$ | $23821$ | $1828$ |
| 84.2.0.a.1 | $84$ | $2$ | $2$ | $0$ |
| 86.2.0.a.1 | $86$ | $2$ | $2$ | $0$ |
| 88.2.0.a.1 | $88$ | $2$ | $2$ | $0$ |
| 88.2.0.b.1 | $88$ | $2$ | $2$ | $0$ |
| $X_0(89)$ | $89$ | $90$ | $90$ | $7$ |
| $X_{\mathrm{ns}}^+(89)$ | $89$ | $3916$ | $3916$ | $294$ |
| $X_{\mathrm{sp}}^+(89)$ | $89$ | $4005$ | $4005$ | $301$ |
| 92.2.0.a.1 | $92$ | $2$ | $2$ | $0$ |
| 94.2.0.a.1 | $94$ | $2$ | $2$ | $0$ |
| $X_0(97)$ | $97$ | $98$ | $98$ | $7$ |
| $X_{\mathrm{ns}}^+(97)$ | $97$ | $4656$ | $4656$ | $353$ |
| $X_{\mathrm{sp}}^+(97)$ | $97$ | $4753$ | $4753$ | $360$ |
| $X_0(101)$ | $101$ | $102$ | $102$ | $8$ |
| $X_{\mathrm{ns}}^+(101)$ | $101$ | $5050$ | $5050$ | $384$ |
| $X_{\mathrm{sp}}^+(101)$ | $101$ | $5151$ | $5151$ | $392$ |
| $X_{S_4}(101)$ | $101$ | $42925$ | $42925$ | $3348$ |
| 102.2.0.a.1 | $102$ | $2$ | $2$ | $0$ |
| $X_0(103)$ | $103$ | $104$ | $104$ | $8$ |
| $X_{\mathrm{ns}}^+(103)$ | $103$ | $5253$ | $5253$ | $400$ |
| $X_{\mathrm{sp}}^+(103)$ | $103$ | $5356$ | $5356$ | $408$ |
| 104.2.0.a.1 | $104$ | $2$ | $2$ | $0$ |
| 104.2.0.b.1 | $104$ | $2$ | $2$ | $0$ |
| 106.2.0.a.1 | $106$ | $2$ | $2$ | $0$ |
| $X_0(107)$ | $107$ | $108$ | $108$ | $9$ |
| $X_{\mathrm{ns}}^+(107)$ | $107$ | $5671$ | $5671$ | $433$ |
| $X_{\mathrm{sp}}^+(107)$ | $107$ | $5778$ | $5778$ | $442$ |
| $X_{S_4}(107)$ | $107$ | $51039$ | $51039$ | $3997$ |
| $X_0(109)$ | $109$ | $110$ | $110$ | $8$ |
| $X_{\mathrm{ns}}^+(109)$ | $109$ | $5886$ | $5886$ | $451$ |
| $X_{\mathrm{sp}}^+(109)$ | $109$ | $5995$ | $5995$ | $459$ |
| $X_{S_4}(109)$ | $109$ | $53955$ | $53955$ | $4231$ |
| 110.2.0.a.1 | $110$ | $2$ | $2$ | $0$ |
| $X_0(113)$ | $113$ | $114$ | $114$ | $9$ |
| $X_{\mathrm{ns}}^+(113)$ | $113$ | $6328$ | $6328$ | $486$ |
| $X_{\mathrm{sp}}^+(113)$ | $113$ | $6441$ | $6441$ | $495$ |
| 114.2.0.a.1 | $114$ | $2$ | $2$ | $0$ |
| 116.2.0.a.1 | $116$ | $2$ | $2$ | $0$ |
| 118.2.0.a.1 | $118$ | $2$ | $2$ | $0$ |
| 120.2.0.a.1 | $120$ | $2$ | $2$ | $0$ |
| 120.2.0.b.1 | $120$ | $2$ | $2$ | $0$ |
| 122.2.0.a.1 | $122$ | $2$ | $2$ | $0$ |
| 124.2.0.a.1 | $124$ | $2$ | $2$ | $0$ |
| $X_0(127)$ | $127$ | $128$ | $128$ | $10$ |
| $X_{\mathrm{ns}}^+(127)$ | $127$ | $8001$ | $8001$ | $620$ |
| $X_{\mathrm{sp}}^+(127)$ | $127$ | $8128$ | $8128$ | $630$ |
| 130.2.0.a.1 | $130$ | $2$ | $2$ | $0$ |
| $X_0(131)$ | $131$ | $132$ | $132$ | $11$ |
| $X_{\mathrm{ns}}^+(131)$ | $131$ | $8515$ | $8515$ | $661$ |
| $X_{\mathrm{sp}}^+(131)$ | $131$ | $8646$ | $8646$ | $672$ |
| $X_{S_4}(131)$ | $131$ | $93665$ | $93665$ | $7426$ |
| 132.2.0.a.1 | $132$ | $2$ | $2$ | $0$ |
| 134.2.0.a.1 | $134$ | $2$ | $2$ | $0$ |
| 136.2.0.a.1 | $136$ | $2$ | $2$ | $0$ |
| 136.2.0.b.1 | $136$ | $2$ | $2$ | $0$ |
| $X_0(137)$ | $137$ | $138$ | $138$ | $11$ |
| $X_{\mathrm{ns}}^+(137)$ | $137$ | $9316$ | $9316$ | $726$ |
| $X_{\mathrm{sp}}^+(137)$ | $137$ | $9453$ | $9453$ | $737$ |
| 138.2.0.a.1 | $138$ | $2$ | $2$ | $0$ |
| $X_0(139)$ | $139$ | $140$ | $140$ | $11$ |
| $X_{\mathrm{ns}}^+(139)$ | $139$ | $9591$ | $9591$ | $748$ |
| $X_{\mathrm{sp}}^+(139)$ | $139$ | $9730$ | $9730$ | $759$ |
| $X_{S_4}(139)$ | $139$ | $111895$ | $111895$ | $8899$ |
| 140.2.0.a.1 | $140$ | $2$ | $2$ | $0$ |
| 142.2.0.a.1 | $142$ | $2$ | $2$ | $0$ |
| 146.2.0.a.1 | $146$ | $2$ | $2$ | $0$ |
| 148.2.0.a.1 | $148$ | $2$ | $2$ | $0$ |
| $X_0(149)$ | $149$ | $150$ | $150$ | $12$ |
| $X_{\mathrm{ns}}^+(149)$ | $149$ | $11026$ | $11026$ | $864$ |
| $X_{\mathrm{sp}}^+(149)$ | $149$ | $11175$ | $11175$ | $876$ |
| $X_{S_4}(149)$ | $149$ | $137825$ | $137825$ | $10998$ |
| $X_0(151)$ | $151$ | $152$ | $152$ | $12$ |
| $X_{\mathrm{ns}}^+(151)$ | $151$ | $11325$ | $11325$ | $888$ |
| $X_{\mathrm{sp}}^+(151)$ | $151$ | $11476$ | $11476$ | $900$ |
| 152.2.0.a.1 | $152$ | $2$ | $2$ | $0$ |
| 152.2.0.b.1 | $152$ | $2$ | $2$ | $0$ |
| 154.2.0.a.1 | $154$ | $2$ | $2$ | $0$ |
| 156.2.0.a.1 | $156$ | $2$ | $2$ | $0$ |
| $X_0(157)$ | $157$ | $158$ | $158$ | $12$ |
| $X_{\mathrm{ns}}^+(157)$ | $157$ | $12246$ | $12246$ | $963$ |
| $X_{\mathrm{sp}}^+(157)$ | $157$ | $12403$ | $12403$ | $975$ |
| $X_{S_4}(157)$ | $157$ | $161239$ | $161239$ | $12897$ |
| 158.2.0.a.1 | $158$ | $2$ | $2$ | $0$ |
| $X_0(163)$ | $163$ | $164$ | $164$ | $13$ |
| $X_{\mathrm{ns}}^+(163)$ | $163$ | $13203$ | $13203$ | $1040$ |
| $X_{\mathrm{sp}}^+(163)$ | $163$ | $13366$ | $13366$ | $1053$ |
| $X_{S_4}(163)$ | $163$ | $180441$ | $180441$ | $14456$ |
| 164.2.0.a.1 | $164$ | $2$ | $2$ | $0$ |
| 166.2.0.a.1 | $166$ | $2$ | $2$ | $0$ |
| $X_0(167)$ | $167$ | $168$ | $168$ | $14$ |
| $X_{\mathrm{ns}}^+(167)$ | $167$ | $13861$ | $13861$ | $1093$ |
| $X_{\mathrm{sp}}^+(167)$ | $167$ | $14028$ | $14028$ | $1107$ |
| 168.2.0.a.1 | $168$ | $2$ | $2$ | $0$ |
| 168.2.0.b.1 | $168$ | $2$ | $2$ | $0$ |
| 170.2.0.a.1 | $170$ | $2$ | $2$ | $0$ |
| 172.2.0.a.1 | $172$ | $2$ | $2$ | $0$ |
| $X_0(173)$ | $173$ | $174$ | $174$ | $14$ |
| $X_{\mathrm{ns}}^+(173)$ | $173$ | $14878$ | $14878$ | $1176$ |
| $X_{\mathrm{sp}}^+(173)$ | $173$ | $15051$ | $15051$ | $1190$ |
| $X_{S_4}(173)$ | $173$ | $215731$ | $215731$ | $17325$ |
| 174.2.0.a.1 | $174$ | $2$ | $2$ | $0$ |
| 178.2.0.a.1 | $178$ | $2$ | $2$ | $0$ |
| $X_0(179)$ | $179$ | $180$ | $180$ | $15$ |
| $X_{\mathrm{ns}}^+(179)$ | $179$ | $15931$ | $15931$ | $1261$ |
| $X_{\mathrm{sp}}^+(179)$ | $179$ | $16110$ | $16110$ | $1276$ |
| $X_{S_4}(179)$ | $179$ | $238965$ | $238965$ | $19216$ |
| $X_0(181)$ | $181$ | $182$ | $182$ | $14$ |
| $X_{\mathrm{ns}}^+(181)$ | $181$ | $16290$ | $16290$ | $1291$ |
| $X_{\mathrm{sp}}^+(181)$ | $181$ | $16471$ | $16471$ | $1305$ |
| $X_{S_4}(181)$ | $181$ | $247065$ | $247065$ | $19876$ |
| 182.2.0.a.1 | $182$ | $2$ | $2$ | $0$ |
| 184.2.0.a.1 | $184$ | $2$ | $2$ | $0$ |
| 184.2.0.b.1 | $184$ | $2$ | $2$ | $0$ |
| 186.2.0.a.1 | $186$ | $2$ | $2$ | $0$ |
| 188.2.0.a.1 | $188$ | $2$ | $2$ | $0$ |
| 190.2.0.a.1 | $190$ | $2$ | $2$ | $0$ |
| $X_0(191)$ | $191$ | $192$ | $192$ | $16$ |
| $X_{\mathrm{ns}}^+(191)$ | $191$ | $18145$ | $18145$ | $1441$ |
| $X_{\mathrm{sp}}^+(191)$ | $191$ | $18336$ | $18336$ | $1457$ |
| $X_0(193)$ | $193$ | $194$ | $194$ | $15$ |
| $X_{\mathrm{ns}}^+(193)$ | $193$ | $18528$ | $18528$ | $1473$ |
| $X_{\mathrm{sp}}^+(193)$ | $193$ | $18721$ | $18721$ | $1488$ |
| 194.2.0.a.1 | $194$ | $2$ | $2$ | $0$ |
| $X_0(197)$ | $197$ | $198$ | $198$ | $16$ |
| $X_{\mathrm{ns}}^+(197)$ | $197$ | $19306$ | $19306$ | $1536$ |
| $X_{\mathrm{sp}}^+(197)$ | $197$ | $19503$ | $19503$ | $1552$ |
| $X_{S_4}(197)$ | $197$ | $318549$ | $318549$ | $25704$ |
| $X_0(199)$ | $199$ | $200$ | $200$ | $16$ |
| $X_{\mathrm{ns}}^+(199)$ | $199$ | $19701$ | $19701$ | $1568$ |
| $X_{\mathrm{sp}}^+(199)$ | $199$ | $19900$ | $19900$ | $1584$ |
| 202.2.0.a.1 | $202$ | $2$ | $2$ | $0$ |
| 204.2.0.a.1 | $204$ | $2$ | $2$ | $0$ |
| 206.2.0.a.1 | $206$ | $2$ | $2$ | $0$ |
| 210.2.0.a.1 | $210$ | $2$ | $2$ | $0$ |
| $X_0(211)$ | $211$ | $212$ | $212$ | $17$ |
| $X_{\mathrm{ns}}^+(211)$ | $211$ | $22155$ | $22155$ | $1768$ |
| $X_{\mathrm{sp}}^+(211)$ | $211$ | $22366$ | $22366$ | $1785$ |
| $X_{S_4}(211)$ | $211$ | $391405$ | $391405$ | $31654$ |
| 212.2.0.a.1 | $212$ | $2$ | $2$ | $0$ |
| 214.2.0.a.1 | $214$ | $2$ | $2$ | $0$ |
| 218.2.0.a.1 | $218$ | $2$ | $2$ | $0$ |
| 220.2.0.a.1 | $220$ | $2$ | $2$ | $0$ |
| 222.2.0.a.1 | $222$ | $2$ | $2$ | $0$ |
| $X_0(223)$ | $223$ | $224$ | $224$ | $18$ |
| $X_{\mathrm{ns}}^+(223)$ | $223$ | $24753$ | $24753$ | $1980$ |
| $X_{\mathrm{sp}}^+(223)$ | $223$ | $24976$ | $24976$ | $1998$ |
| 226.2.0.a.1 | $226$ | $2$ | $2$ | $0$ |
| $X_0(227)$ | $227$ | $228$ | $228$ | $19$ |
| $X_{\mathrm{ns}}^+(227)$ | $227$ | $25651$ | $25651$ | $2053$ |
| $X_{\mathrm{sp}}^+(227)$ | $227$ | $25878$ | $25878$ | $2072$ |
| $X_{S_4}(227)$ | $227$ | $487369$ | $487369$ | $39502$ |
| 228.2.0.a.1 | $228$ | $2$ | $2$ | $0$ |
| $X_0(229)$ | $229$ | $230$ | $230$ | $18$ |
| $X_{\mathrm{ns}}^+(229)$ | $229$ | $26106$ | $26106$ | $2091$ |
| $X_{\mathrm{sp}}^+(229)$ | $229$ | $26335$ | $26335$ | $2109$ |
| $X_{S_4}(229)$ | $229$ | $500365$ | $500365$ | $40566$ |
| 230.2.0.a.1 | $230$ | $2$ | $2$ | $0$ |
| 232.2.0.a.1 | $232$ | $2$ | $2$ | $0$ |
| 232.2.0.b.1 | $232$ | $2$ | $2$ | $0$ |
| $X_0(233)$ | $233$ | $234$ | $234$ | $19$ |
| $X_{\mathrm{ns}}^+(233)$ | $233$ | $27028$ | $27028$ | $2166$ |
| $X_{\mathrm{sp}}^+(233)$ | $233$ | $27261$ | $27261$ | $2185$ |
| 236.2.0.a.1 | $236$ | $2$ | $2$ | $0$ |
| 238.2.0.a.1 | $238$ | $2$ | $2$ | $0$ |
| $X_0(239)$ | $239$ | $240$ | $240$ | $20$ |
| $X_{\mathrm{ns}}^+(239)$ | $239$ | $28441$ | $28441$ | $2281$ |
| $X_{\mathrm{sp}}^+(239)$ | $239$ | $28680$ | $28680$ | $2301$ |
| $X_0(241)$ | $241$ | $242$ | $242$ | $19$ |
| $X_{\mathrm{ns}}^+(241)$ | $241$ | $28920$ | $28920$ | $2321$ |
| $X_{\mathrm{sp}}^+(241)$ | $241$ | $29161$ | $29161$ | $2340$ |
| 244.2.0.a.1 | $244$ | $2$ | $2$ | $0$ |
| 246.2.0.a.1 | $246$ | $2$ | $2$ | $0$ |
| 248.2.0.a.1 | $248$ | $2$ | $2$ | $0$ |
| 248.2.0.b.1 | $248$ | $2$ | $2$ | $0$ |
| $X_0(251)$ | $251$ | $252$ | $252$ | $21$ |
| $X_{\mathrm{ns}}^+(251)$ | $251$ | $31375$ | $31375$ | $2521$ |
| $X_{\mathrm{sp}}^+(251)$ | $251$ | $31626$ | $31626$ | $2542$ |
| $X_{S_4}(251)$ | $251$ | $658875$ | $658875$ | $53551$ |
| 254.2.0.a.1 | $254$ | $2$ | $2$ | $0$ |
| $X_0(257)$ | $257$ | $258$ | $258$ | $21$ |
| $X_{\mathrm{ns}}^+(257)$ | $257$ | $32896$ | $32896$ | $2646$ |
| $X_{\mathrm{sp}}^+(257)$ | $257$ | $33153$ | $33153$ | $2667$ |
| 258.2.0.a.1 | $258$ | $2$ | $2$ | $0$ |
| 260.2.0.a.1 | $260$ | $2$ | $2$ | $0$ |
| 262.2.0.a.1 | $262$ | $2$ | $2$ | $0$ |
| $X_0(263)$ | $263$ | $264$ | $264$ | $22$ |
| $X_{\mathrm{ns}}^+(263)$ | $263$ | $34453$ | $34453$ | $2773$ |
| $X_{\mathrm{sp}}^+(263)$ | $263$ | $34716$ | $34716$ | $2795$ |
| 264.2.0.a.1 | $264$ | $2$ | $2$ | $0$ |
| 264.2.0.b.1 | $264$ | $2$ | $2$ | $0$ |
| 266.2.0.a.1 | $266$ | $2$ | $2$ | $0$ |
| 268.2.0.a.1 | $268$ | $2$ | $2$ | $0$ |
| $X_0(269)$ | $269$ | $270$ | $270$ | $22$ |
| $X_{\mathrm{ns}}^+(269)$ | $269$ | $36046$ | $36046$ | $2904$ |
| $X_{\mathrm{sp}}^+(269)$ | $269$ | $36315$ | $36315$ | $2926$ |
| $X_{S_4}(269)$ | $269$ | $811035$ | $811035$ | $66033$ |
| $X_0(271)$ | $271$ | $272$ | $272$ | $22$ |
| $X_{\mathrm{ns}}^+(271)$ | $271$ | $36585$ | $36585$ | $2948$ |
| $X_{\mathrm{sp}}^+(271)$ | $271$ | $36856$ | $36856$ | $2970$ |
| 274.2.0.a.1 | $274$ | $2$ | $2$ | $0$ |
| 276.2.0.a.1 | $276$ | $2$ | $2$ | $0$ |
| $X_0(277)$ | $277$ | $278$ | $278$ | $22$ |
| $X_{\mathrm{ns}}^+(277)$ | $277$ | $38226$ | $38226$ | $3083$ |
| $X_{\mathrm{sp}}^+(277)$ | $277$ | $38503$ | $38503$ | $3105$ |
| $X_{S_4}(277)$ | $277$ | $885569$ | $885569$ | $72152$ |
| 278.2.0.a.1 | $278$ | $2$ | $2$ | $0$ |
| 280.2.0.a.1 | $280$ | $2$ | $2$ | $0$ |
| 280.2.0.b.1 | $280$ | $2$ | $2$ | $0$ |
| $X_0(281)$ | $281$ | $282$ | $282$ | $23$ |
| $X_{\mathrm{ns}}^+(281)$ | $281$ | $39340$ | $39340$ | $3174$ |
| $X_{\mathrm{sp}}^+(281)$ | $281$ | $39621$ | $39621$ | $3197$ |
| 282.2.0.a.1 | $282$ | $2$ | $2$ | $0$ |
| $X_0(283)$ | $283$ | $284$ | $284$ | $23$ |
| $X_{\mathrm{ns}}^+(283)$ | $283$ | $39903$ | $39903$ | $3220$ |
| $X_{\mathrm{sp}}^+(283)$ | $283$ | $40186$ | $40186$ | $3243$ |
| $X_{S_4}(283)$ | $283$ | $944371$ | $944371$ | $76981$ |
| 284.2.0.a.1 | $284$ | $2$ | $2$ | $0$ |
| 286.2.0.a.1 | $286$ | $2$ | $2$ | $0$ |
| 290.2.0.a.1 | $290$ | $2$ | $2$ | $0$ |
| 292.2.0.a.1 | $292$ | $2$ | $2$ | $0$ |
| $X_0(293)$ | $293$ | $294$ | $294$ | $24$ |
| $X_{\mathrm{ns}}^+(293)$ | $293$ | $42778$ | $42778$ | $3456$ |
| $X_{\mathrm{sp}}^+(293)$ | $293$ | $43071$ | $43071$ | $3480$ |
| $X_{S_4}(293)$ | $293$ | $1048061$ | $1048061$ | $85500$ |
| 296.2.0.a.1 | $296$ | $2$ | $2$ | $0$ |
| 296.2.0.b.1 | $296$ | $2$ | $2$ | $0$ |
| 298.2.0.a.1 | $298$ | $2$ | $2$ | $0$ |
| 302.2.0.a.1 | $302$ | $2$ | $2$ | $0$ |
| $X_0(307)$ | $307$ | $308$ | $308$ | $25$ |
| $X_{\mathrm{ns}}^+(307)$ | $307$ | $46971$ | $46971$ | $3800$ |
| $X_{\mathrm{sp}}^+(307)$ | $307$ | $47278$ | $47278$ | $3825$ |
| $X_{S_4}(307)$ | $307$ | $1205589$ | $1205589$ | $98450$ |
| 308.2.0.a.1 | $308$ | $2$ | $2$ | $0$ |
| 310.2.0.a.1 | $310$ | $2$ | $2$ | $0$ |
| $X_0(311)$ | $311$ | $312$ | $312$ | $26$ |
| $X_{\mathrm{ns}}^+(311)$ | $311$ | $48205$ | $48205$ | $3901$ |
| $X_{\mathrm{sp}}^+(311)$ | $311$ | $48516$ | $48516$ | $3927$ |
| 312.2.0.a.1 | $312$ | $2$ | $2$ | $0$ |
| 312.2.0.b.1 | $312$ | $2$ | $2$ | $0$ |
| $X_0(313)$ | $313$ | $314$ | $314$ | $25$ |
| $X_{\mathrm{ns}}^+(313)$ | $313$ | $48828$ | $48828$ | $3953$ |
| $X_{\mathrm{sp}}^+(313)$ | $313$ | $49141$ | $49141$ | $3978$ |
| 314.2.0.a.1 | $314$ | $2$ | $2$ | $0$ |
| 316.2.0.a.1 | $316$ | $2$ | $2$ | $0$ |
| $X_0(317)$ | $317$ | $318$ | $318$ | $26$ |
| $X_{\mathrm{ns}}^+(317)$ | $317$ | $50086$ | $50086$ | $4056$ |
| $X_{\mathrm{sp}}^+(317)$ | $317$ | $50403$ | $50403$ | $4082$ |
| $X_{S_4}(317)$ | $317$ | $1327279$ | $1327279$ | $108459$ |
| 318.2.0.a.1 | $318$ | $2$ | $2$ | $0$ |
| 322.2.0.a.1 | $322$ | $2$ | $2$ | $0$ |
| 326.2.0.a.1 | $326$ | $2$ | $2$ | $0$ |
| 328.2.0.a.1 | $328$ | $2$ | $2$ | $0$ |
| 328.2.0.b.1 | $328$ | $2$ | $2$ | $0$ |
| 330.2.0.a.1 | $330$ | $2$ | $2$ | $0$ |
| $X_0(331)$ | $331$ | $332$ | $332$ | $27$ |
| $X_{\mathrm{ns}}^+(331)$ | $331$ | $54615$ | $54615$ | $4428$ |
| $X_{\mathrm{sp}}^+(331)$ | $331$ | $54946$ | $54946$ | $4455$ |
| $X_{S_4}(331)$ | $331$ | $1511015$ | $1511015$ | $123579$ |
| 332.2.0.a.1 | $332$ | $2$ | $2$ | $0$ |
| 334.2.0.a.1 | $334$ | $2$ | $2$ | $0$ |