### Summary

You searched for: sol=42

1

New Number: 7.9 |  AESZ:  |  Superseeker: -3 -245/3  |  Hash: 5641c09b76662b0741e41b41b0c6f105

Degree: 7

$\theta^4-3 x\left(96\theta^4+120\theta^3+127\theta^2+67\theta+14\right)+3^{2} x^{2}\left(3897\theta^4+9540\theta^3+13209\theta^2+9246\theta+2608\right)-2 3^{4} x^{3}\left(14445\theta^4+52002\theta^3+88179\theta^2+73278\theta+23920\right)+2^{2} 3^{6} x^{4}\left(31671\theta^4+149364\theta^3+298089\theta^2+280512\theta+100780\right)-2^{3} 3^{12} x^{5}(\theta+1)(507\theta^3+2439\theta^2+4306\theta+2704)+2^{6} 3^{14} x^{6}(\theta+1)(\theta+2)(90\theta^2+351\theta+370)-2^{7} 3^{19} x^{7}(\theta+1)(\theta+2)^2(\theta+3)$

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Coefficients of the holomorphic solution: 1, 42, 1872, 86712, 4126716, ...
--> OEIS
Normalized instanton numbers (n0=1): -3, 69/4, -245/3, 879, -11829, ... ; Common denominator:...

#### Discriminant

$-(36z-1)^2(27z-1)^2(54z-1)^3$

#### Local exponents

$0$$\frac{ 1}{ 54}$$\frac{ 1}{ 36}$$\frac{ 1}{ 27}$$\infty$
$0$$0$$0$$0$$1$
$0$$0$$1$$\frac{ 1}{ 3}$$2$
$0$$-\frac{ 1}{ 3}$$3$$\frac{ 2}{ 3}$$2$
$0$$\frac{ 1}{ 3}$$4$$1$$3$

#### Note:

This is operator "7.9" from ...

2

New Number: 24.2 |  AESZ:  |  Superseeker: 14/3 13813/81  |  Hash: 41744bc2b21cfd322eaaeeef9708f32d

Degree: 24

$3^{3} \theta^4-3^{2} x\left(51\theta^4+166\theta^3+126\theta^2+43\theta+6\right)-3 x^{2}\left(8565\theta^4-5068\theta^3-4379\theta^2+5314\theta+3696\right)+2^{3} x^{3}\left(97217\theta^4+85594\theta^3+1042\theta^2+126065\theta+85260\right)+2^{4} x^{4}\left(169515\theta^4-51450\theta^3+3610310\theta^2+2229139\theta+376554\right)-2^{6} x^{5}\left(54033673\theta^4+3817434\theta^3+23026430\theta^2+18524325\theta+5269236\right)+2^{6} x^{6}\left(56745577\theta^4-58947232\theta^3-9100317\theta^2-107018560\theta-95196876\right)+2^{9} x^{7}\left(65530931\theta^4+428839238\theta^3+747632002\theta^2+855490591\theta+415787350\right)-2^{12} x^{8}\left(224356709\theta^4+564772296\theta^3+806751290\theta^2+577253730\theta+163219723\right)+2^{15} x^{9}\left(114705522\theta^4-402572832\theta^3-1600120000\theta^2-2391161140\theta-1263777229\right)+2^{18} x^{10}\left(221581518\theta^4+1753790880\theta^3+4463022454\theta^2+5290385822\theta+2416009977\right)-2^{21} x^{11}\left(297104050\theta^4+1400293560\theta^3+2545523552\theta^2+1898196336\theta+390414885\right)+2^{24} x^{12}\left(10381942\theta^4-638906128\theta^3-3420395594\theta^2-6131585970\theta-3713844291\right)+2^{27} x^{13}\left(169708186\theta^4+1632741184\theta^3+5661963400\theta^2+8312515476\theta+4455840251\right)-2^{30} x^{14}\left(77350272\theta^4+671060736\theta^3+196015614\theta^2+2227548066\theta+858195311\right)-2^{33} x^{15}\left(17292844\theta^4+225530588\theta^3+1196571252\theta^2+2510894402\theta+1734945305\right)+2^{36} x^{16}\left(12130172\theta^4+177960128\theta^3+899828890\theta^2+1740569194\theta+1131946327\right)+2^{39} x^{17}\left(2418550\theta^4-1367904\theta^3-97574768\theta^2-250801932\theta-179706127\right)-2^{42} x^{18}\left(425070\theta^4+769632\theta^3-7412666\theta^2-16056554\theta-8835779\right)-2^{45} x^{19}\left(740094\theta^4+721836\theta^3+20106464\theta^2+17226568\theta+1351671\right)+2^{48} x^{20}\left(107306\theta^4+1324272\theta^3+3588658\theta^2+3406170\theta+914247\right)+2^{51} x^{21}\left(18758\theta^4+64528\theta^3+62232\theta^2+29908\theta+36609\right)+2^{54} x^{22}\left(7159\theta^4+51040\theta^3+122273\theta^2+126170\theta+49919\right)-2^{57} 5 x^{23}\left(491\theta^4+2994\theta^3+6902\theta^2+7137\theta+2797\right)+2^{60} 5^{2} x^{24}\left((\theta+2)^4\right)$

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Coefficients of the holomorphic solution: 1, 2, 42, 184, 2282, ...
--> OEIS
Normalized instanton numbers (n0=1): 14/3, -337/18, 13813/81, -928499/486, 16107365/729, ... ; Common denominator:...

#### Discriminant

$27-459z+128965078929381523456z^22-353802786726226165760z^23+28823037615171174400z^24+3631716928z^6+33551836672z^7-918965080064z^8+3758670544896z^9+58086265454592z^10+833579072557678592z^16+1329611923678822400z^17-25695z^2+777736z^3+2712240z^4-3458155072z^5-1869477630474977280z^18-623072352665600z^11+174180083433472z^12+22777847147921408z^13-83054222144176128z^14-148544398869659648z^15-26039742676712030208z^19+30203953850913652736z^20+42239260905107881984z^21$

No data for singularities

#### Note:

This is operator "24.2" from ...