### Summary

You searched for: inst=-3

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: 21.1 |  AESZ:  |  Superseeker: -3 -836/9  |  Hash: 0fe5589e355c32f4ff99894c93da5ebd

Degree: 21

$\theta^4-3 x\left(594\theta^4+388\theta^3+449\theta^2+255\theta+57\right)+3^{2} x^{2}\left(167949\theta^4+219736\theta^3+296165\theta^2+206058\theta+60327\right)-3^{3} x^{3}\left(30062564\theta^4+59082628\theta^3+90938680\theta^2+73390824\theta+25169787\right)+3^{4} x^{4}\left(3821918586\theta^4+10028695224\theta^3+17362063000\theta^2+15752079416\theta+6042025251\right)-3^{6} x^{5}\left(122323515588\theta^4+401741477192\theta^3+772934505898\theta^2+772767973606\theta+323443209951\right)+3^{7} x^{6}\left(9208285046694\theta^4+36335830001264\theta^3+76933908262582\theta^2+83605114571476\theta+37610075824851\right)-3^{8} x^{7}\left(556804111648224\theta^4+2566374206107640\theta^3+5931468185457740\theta^2+6936766968119084\theta+3319720514504883\right)+3^{9} x^{8}\left(27485425030131487\theta^4+144945187887393360\theta^3+363188370704177600\theta^2+453656002398028056\theta+229261144684401603\right)-3^{11} x^{9}\left(373144117026480050\theta^4+2216159730666735988\theta^3+5985131626117997505\theta^2+7937745663167991583\theta+4212346965321976686\right)+3^{12} x^{10}\left(12620773799957764793\theta^4+83371681116879474616\theta^3+241456176625052857369\theta^2+338390948699279517242\theta+187738474353413402628\right)-2^{2} 3^{13} x^{11}\left(88897318990506843163\theta^4+646615088663747698317\theta^3+1999372114801235907923\theta^2+2949327067455333140727\theta+1704572854502964047766\right)+2^{3} 3^{15} x^{12}\left(347739693458697250535\theta^4+2761194118785869833761\theta^3+9082378345988744152060\theta^2+14055373737057643782774\theta+8437449682549590949014\right)-2^{4} 3^{16} x^{13}\left(3388892533211296225843\theta^4+29186241106744032096123\theta^3+101718484183047761368709\theta^2+164675983283376235096123\theta+102422453838975446750766\right)+2^{5} 3^{17} x^{14}\left(27249665649734532251102\theta^4+252958456234974974975776421\theta^3+931464075137305276054819\theta^2+1573701956965471162096164\theta+1011951623372019370481502\right)-2^{6} 3^{19} x^{15}\left(59624661642978107387279\theta^4+593534732512385311078207\theta^3+2302778787973910263222855\theta^2+4051392721321863680953049\theta+2688523708721489677735446\right)+2^{7} 3^{21} x^{16}\left(104798156862907596826923\theta^4+1113675430740135170361867\theta^3+454112769317336457207052\theta^2+8304013490920595240792750\theta+5677660112851097019157260\right)-2^{8} 3^{23} x^{17}\left(144414331908091729604\theta^4+1631880922420590560058519\theta^3+6977539346859077115802728\theta^2+13239245712821134606222476\theta+9313169920208225411283528\right)+2^{8} 3^{25} x^{18}(\theta+2)(300609744176461608186257\theta^3+2998248186426335727135492\theta^2+10108382642002404275847711\theta+11441919541626435036478660)-2^{11} 3^{29} 5 13 x^{19}(\theta+2)(\theta+3)(94966488350134307817\theta^2+726354035060929832235\theta+1411592559746293379510)+2^{17} 3^{34} 5^{2} 13^{2} 277 x^{20}(\theta+2)(\theta+3)(\theta+4)(2857062816013\theta+12353662367364)-2^{21} 3^{37} 5^{3} 13^{3} 197 277^{2} 7477 x^{21}(\theta+2)(\theta+3)(\theta+4)(\theta+5)$

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Coefficients of the holomorphic solution: 1, 171, 21951, 2506887, 268618923, ...
--> OEIS
Normalized instanton numbers (n0=1): -3, -12, -836/9, -777, -7284, ... ; Common denominator:...

#### Discriminant

$1-1782z+1511541z^2-811689228z^3+309575405466z^4-89173842863652z^5+20138519397119778z^6-3653191776523997664z^7+540995620868078058621z^8-66101360898889861417350z^9+6707196649023354479356713z^10-566924161219607366848654596z^11+39917476173178841512659321960z^12-2334091382018078442915465772848z^13+112608840438470988852354214708032z^14-4435164589474967381812635371410752z^15+140316894183604724782276689879599232z^16-3480479814145334228077850084994048z^17+65204022304842271542325554911494361856z^18-867621039332733698991089432847107512320z^19+7309015082771056267093644376086154444800z^20-29309576848365568314888988820481245184000z^21$

No data for singularities

#### Note:

This is operator "21.1" from ...