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Label Class Base field Conductor norm Rank Torsion CM Regulator Period Leading coeff j-invariant Weierstrass coefficients Weierstrass equation
3.1-a1 3.1-a 5.5.65657.1 \( 3 \) $0$ $\Z/5\Z$ $1$ $813.6852207$ 1.270211094 \( \frac{747179612}{59049} a^{4} - \frac{4155930605}{19683} a^{3} - \frac{9128857582}{59049} a^{2} + \frac{3220249090}{6561} a + \frac{7149149617}{59049} \) \( \bigl[a^{2} - a - 2\) , \( 3 a^{4} - 4 a^{3} - 13 a^{2} + 12 a + 8\) , \( -a^{4} + 2 a^{3} + 5 a^{2} - 7 a - 4\) , \( 2 a^{3} - 2 a^{2} - 8 a + 8\) , \( 4 a^{4} - 5 a^{3} - 19 a^{2} + 16 a + 11\bigr] \) ${y}^2+\left(a^{2}-a-2\right){x}{y}+\left(-a^{4}+2a^{3}+5a^{2}-7a-4\right){y}={x}^{3}+\left(3a^{4}-4a^{3}-13a^{2}+12a+8\right){x}^{2}+\left(2a^{3}-2a^{2}-8a+8\right){x}+4a^{4}-5a^{3}-19a^{2}+16a+11$
3.1-a2 3.1-a 5.5.65657.1 \( 3 \) $0$ $\mathsf{trivial}$ $1$ $0.260379270$ 1.270211094 \( \frac{2521498274075249905348265612}{9} a^{4} - \frac{1488610650200171884252903124}{3} a^{3} - \frac{9163877093686100970416615593}{9} a^{2} + 1345476142192101801059271874 a + \frac{3269990960361707860438009855}{9} \) \( \bigl[a^{3} - 3 a\) , \( 2 a^{4} - 3 a^{3} - 9 a^{2} + 9 a + 7\) , \( 1\) , \( 91 a^{4} + 186 a^{3} - 421 a^{2} - 905 a - 395\) , \( 2034 a^{4} + 1729 a^{3} - 9273 a^{2} - 12289 a - 3889\bigr] \) ${y}^2+\left(a^{3}-3a\right){x}{y}+{y}={x}^{3}+\left(2a^{4}-3a^{3}-9a^{2}+9a+7\right){x}^{2}+\left(91a^{4}+186a^{3}-421a^{2}-905a-395\right){x}+2034a^{4}+1729a^{3}-9273a^{2}-12289a-3889$
3.1-b1 3.1-b 5.5.65657.1 \( 3 \) $1$ $\mathsf{trivial}$ $0.003012214$ $9008.072607$ 1.058954300 \( -\frac{346538649913}{729} a^{4} + \frac{304213159354}{243} a^{3} + \frac{131211798509}{729} a^{2} - \frac{95505911702}{81} a - \frac{199860865145}{729} \) \( \bigl[-a^{4} + a^{3} + 5 a^{2} - 2 a - 3\) , \( -a^{2} + a + 2\) , \( -a^{4} + 2 a^{3} + 4 a^{2} - 6 a - 2\) , \( -7 a^{4} + 6 a^{3} + 24 a^{2} - 14 a - 3\) , \( -7 a^{4} + 15 a^{3} + 32 a^{2} - 29 a - 8\bigr] \) ${y}^2+\left(-a^{4}+a^{3}+5a^{2}-2a-3\right){x}{y}+\left(-a^{4}+2a^{3}+4a^{2}-6a-2\right){y}={x}^{3}+\left(-a^{2}+a+2\right){x}^{2}+\left(-7a^{4}+6a^{3}+24a^{2}-14a-3\right){x}-7a^{4}+15a^{3}+32a^{2}-29a-8$
3.1-b2 3.1-b 5.5.65657.1 \( 3 \) $1$ $\mathsf{trivial}$ $0.001004071$ $27024.21782$ 1.058954300 \( \frac{463637}{9} a^{4} - \frac{90008}{3} a^{3} - \frac{1905559}{9} a^{2} - 8065 a + \frac{82504}{9} \) \( \bigl[-a^{4} + a^{3} + 5 a^{2} - 2 a - 4\) , \( -2 a^{4} + 3 a^{3} + 8 a^{2} - 7 a - 4\) , \( a^{4} - a^{3} - 4 a^{2} + 3 a + 3\) , \( 14 a^{4} - 25 a^{3} - 52 a^{2} + 68 a + 22\) , \( -22 a^{4} + 38 a^{3} + 80 a^{2} - 103 a - 29\bigr] \) ${y}^2+\left(-a^{4}+a^{3}+5a^{2}-2a-4\right){x}{y}+\left(a^{4}-a^{3}-4a^{2}+3a+3\right){y}={x}^{3}+\left(-2a^{4}+3a^{3}+8a^{2}-7a-4\right){x}^{2}+\left(14a^{4}-25a^{3}-52a^{2}+68a+22\right){x}-22a^{4}+38a^{3}+80a^{2}-103a-29$
5.1-a1 5.1-a 5.5.65657.1 \( 5 \) $0$ $\mathsf{trivial}$ $1$ $526.9651791$ 2.056560079 \( \frac{144184611}{5} a^{4} - \frac{255843129}{5} a^{3} - \frac{524006273}{5} a^{2} + \frac{693618211}{5} a + \frac{186593617}{5} \) \( \bigl[-a^{4} + 2 a^{3} + 4 a^{2} - 5 a - 3\) , \( -a^{4} + a^{3} + 4 a^{2} - 3 a - 1\) , \( a^{4} - a^{3} - 4 a^{2} + 3 a + 2\) , \( -3 a^{4} + 2 a^{3} + 10 a^{2} - 7 a - 3\) , \( a^{4} + 3 a^{3} - 6 a - 3\bigr] \) ${y}^2+\left(-a^{4}+2a^{3}+4a^{2}-5a-3\right){x}{y}+\left(a^{4}-a^{3}-4a^{2}+3a+2\right){y}={x}^{3}+\left(-a^{4}+a^{3}+4a^{2}-3a-1\right){x}^{2}+\left(-3a^{4}+2a^{3}+10a^{2}-7a-3\right){x}+a^{4}+3a^{3}-6a-3$
5.1-b1 5.1-b 5.5.65657.1 \( 5 \) $0$ $\mathsf{trivial}$ $1$ $0.111196110$ 0.813673831 \( \frac{9227278873526453906244312610219036327836}{125} a^{4} + \frac{3459009377990835094505717267240191015816}{125} a^{3} - \frac{41380713886380859304809564621687978514293}{125} a^{2} - \frac{38438451731868504360194666541225269140904}{125} a - \frac{6711393728551335750914883813930912798473}{125} \) \( \bigl[a^{2} - a - 1\) , \( -3 a^{4} + 4 a^{3} + 13 a^{2} - 10 a - 9\) , \( 0\) , \( 846 a^{4} - 1524 a^{3} - 3297 a^{2} + 4382 a + 1145\) , \( 20454 a^{4} - 36469 a^{3} - 77364 a^{2} + 102303 a + 27278\bigr] \) ${y}^2+\left(a^{2}-a-1\right){x}{y}={x}^{3}+\left(-3a^{4}+4a^{3}+13a^{2}-10a-9\right){x}^{2}+\left(846a^{4}-1524a^{3}-3297a^{2}+4382a+1145\right){x}+20454a^{4}-36469a^{3}-77364a^{2}+102303a+27278$
5.1-b2 5.1-b 5.5.65657.1 \( 5 \) $0$ $\mathsf{trivial}$ $1$ $0.333588330$ 0.813673831 \( -\frac{660212871515640604}{5} a^{4} + \frac{1794053534107468711}{5} a^{3} + \frac{220022592976562427}{5} a^{2} - \frac{1698345910262749894}{5} a - \frac{384439131601574358}{5} \) \( \bigl[-a^{4} + 2 a^{3} + 4 a^{2} - 5 a - 2\) , \( -2 a^{4} + 3 a^{3} + 9 a^{2} - 10 a - 8\) , \( a^{4} - a^{3} - 4 a^{2} + 2 a + 3\) , \( 86 a^{4} + 73 a^{3} - 426 a^{2} - 515 a - 104\) , \( 1231 a^{4} + 500 a^{3} - 5653 a^{2} - 5184 a - 905\bigr] \) ${y}^2+\left(-a^{4}+2a^{3}+4a^{2}-5a-2\right){x}{y}+\left(a^{4}-a^{3}-4a^{2}+2a+3\right){y}={x}^{3}+\left(-2a^{4}+3a^{3}+9a^{2}-10a-8\right){x}^{2}+\left(86a^{4}+73a^{3}-426a^{2}-515a-104\right){x}+1231a^{4}+500a^{3}-5653a^{2}-5184a-905$
5.1-b3 5.1-b 5.5.65657.1 \( 5 \) $0$ $\Z/5\Z$ $1$ $347.4878438$ 0.813673831 \( \frac{175802229236840746}{30517578125} a^{4} + \frac{65933855205252401}{30517578125} a^{3} - \frac{788398234528339998}{30517578125} a^{2} - \frac{732499454042744644}{30517578125} a - \frac{127944679222457853}{30517578125} \) \( \bigl[-2 a^{4} + 3 a^{3} + 9 a^{2} - 9 a - 7\) , \( a^{4} - 5 a^{2} - a + 4\) , \( a^{4} - a^{3} - 4 a^{2} + 3 a + 2\) , \( 5 a^{4} - 2 a^{3} - 25 a^{2} - 4 a + 29\) , \( a^{4} + 3 a^{3} - 10 a^{2} - 16 a + 22\bigr] \) ${y}^2+\left(-2a^{4}+3a^{3}+9a^{2}-9a-7\right){x}{y}+\left(a^{4}-a^{3}-4a^{2}+3a+2\right){y}={x}^{3}+\left(a^{4}-5a^{2}-a+4\right){x}^{2}+\left(5a^{4}-2a^{3}-25a^{2}-4a+29\right){x}+a^{4}+3a^{3}-10a^{2}-16a+22$
5.1-b4 5.1-b 5.5.65657.1 \( 5 \) $0$ $\Z/5\Z$ $1$ $1042.463531$ 0.813673831 \( \frac{81829946}{3125} a^{4} - \frac{143808649}{3125} a^{3} - \frac{300612723}{3125} a^{2} + \frac{393132181}{3125} a + \frac{109010922}{3125} \) \( \bigl[-a^{4} + 2 a^{3} + 4 a^{2} - 5 a - 2\) , \( -2 a^{4} + 3 a^{3} + 9 a^{2} - 10 a - 8\) , \( a^{4} - a^{3} - 4 a^{2} + 2 a + 3\) , \( a^{4} - 2 a^{3} - 6 a^{2} + 5 a + 11\) , \( -2 a^{4} + 3 a^{3} + 9 a^{2} - 9 a - 9\bigr] \) ${y}^2+\left(-a^{4}+2a^{3}+4a^{2}-5a-2\right){x}{y}+\left(a^{4}-a^{3}-4a^{2}+2a+3\right){y}={x}^{3}+\left(-2a^{4}+3a^{3}+9a^{2}-10a-8\right){x}^{2}+\left(a^{4}-2a^{3}-6a^{2}+5a+11\right){x}-2a^{4}+3a^{3}+9a^{2}-9a-9$
9.1-a1 9.1-a 5.5.65657.1 \( 3^{2} \) $0$ $\mathsf{trivial}$ $1$ $23.24954646$ 1.633226706 \( -\frac{346538649913}{729} a^{4} + \frac{304213159354}{243} a^{3} + \frac{131211798509}{729} a^{2} - \frac{95505911702}{81} a - \frac{199860865145}{729} \) \( \bigl[-a^{4} + 2 a^{3} + 4 a^{2} - 6 a - 2\) , \( -2 a^{4} + 2 a^{3} + 9 a^{2} - 6 a - 6\) , \( -a^{4} + 2 a^{3} + 4 a^{2} - 5 a - 3\) , \( -45 a^{4} + 79 a^{3} + 158 a^{2} - 211 a - 53\) , \( -242 a^{4} + 430 a^{3} + 867 a^{2} - 1149 a - 312\bigr] \) ${y}^2+\left(-a^{4}+2a^{3}+4a^{2}-6a-2\right){x}{y}+\left(-a^{4}+2a^{3}+4a^{2}-5a-3\right){y}={x}^{3}+\left(-2a^{4}+2a^{3}+9a^{2}-6a-6\right){x}^{2}+\left(-45a^{4}+79a^{3}+158a^{2}-211a-53\right){x}-242a^{4}+430a^{3}+867a^{2}-1149a-312$
9.1-a2 9.1-a 5.5.65657.1 \( 3^{2} \) $0$ $\Z/3\Z$ $1$ $1883.213263$ 1.633226706 \( \frac{463637}{9} a^{4} - \frac{90008}{3} a^{3} - \frac{1905559}{9} a^{2} - 8065 a + \frac{82504}{9} \) \( \bigl[a^{4} - a^{3} - 4 a^{2} + 3 a + 3\) , \( -a^{4} + 5 a^{2} + 2 a - 4\) , \( -2 a^{4} + 3 a^{3} + 9 a^{2} - 8 a - 6\) , \( 2 a^{4} - 2 a^{3} - 13 a^{2} + 9 a + 17\) , \( -58 a^{4} + 72 a^{3} + 271 a^{2} - 176 a - 247\bigr] \) ${y}^2+\left(a^{4}-a^{3}-4a^{2}+3a+3\right){x}{y}+\left(-2a^{4}+3a^{3}+9a^{2}-8a-6\right){y}={x}^{3}+\left(-a^{4}+5a^{2}+2a-4\right){x}^{2}+\left(2a^{4}-2a^{3}-13a^{2}+9a+17\right){x}-58a^{4}+72a^{3}+271a^{2}-176a-247$
9.1-b1 9.1-b 5.5.65657.1 \( 3^{2} \) $0$ $\mathsf{trivial}$ $1$ $134.1493644$ 1.047075740 \( \frac{747179612}{59049} a^{4} - \frac{4155930605}{19683} a^{3} - \frac{9128857582}{59049} a^{2} + \frac{3220249090}{6561} a + \frac{7149149617}{59049} \) \( \bigl[a^{4} - a^{3} - 4 a^{2} + 2 a + 3\) , \( -a^{4} + 2 a^{3} + 3 a^{2} - 6 a - 2\) , \( a^{3} - 3 a\) , \( -a^{3} - a^{2} + 2 a + 4\) , \( 2 a^{4} - 3 a^{3} - 10 a^{2} + 7 a + 8\bigr] \) ${y}^2+\left(a^{4}-a^{3}-4a^{2}+2a+3\right){x}{y}+\left(a^{3}-3a\right){y}={x}^{3}+\left(-a^{4}+2a^{3}+3a^{2}-6a-2\right){x}^{2}+\left(-a^{3}-a^{2}+2a+4\right){x}+2a^{4}-3a^{3}-10a^{2}+7a+8$
9.1-b2 9.1-b 5.5.65657.1 \( 3^{2} \) $0$ $\mathsf{trivial}$ $1$ $5.365974579$ 1.047075740 \( \frac{2521498274075249905348265612}{9} a^{4} - \frac{1488610650200171884252903124}{3} a^{3} - \frac{9163877093686100970416615593}{9} a^{2} + 1345476142192101801059271874 a + \frac{3269990960361707860438009855}{9} \) \( \bigl[a^{3} - 4 a - 1\) , \( -3 a^{4} + 4 a^{3} + 13 a^{2} - 11 a - 10\) , \( a^{2} - 2\) , \( 17 a^{4} + 247 a^{3} - 506 a^{2} - 251 a - 16\) , \( 3325 a^{4} - 6557 a^{3} - 5396 a^{2} + 5378 a + 1457\bigr] \) ${y}^2+\left(a^{3}-4a-1\right){x}{y}+\left(a^{2}-2\right){y}={x}^{3}+\left(-3a^{4}+4a^{3}+13a^{2}-11a-10\right){x}^{2}+\left(17a^{4}+247a^{3}-506a^{2}-251a-16\right){x}+3325a^{4}-6557a^{3}-5396a^{2}+5378a+1457$
15.1-a1 15.1-a 5.5.65657.1 \( 3 \cdot 5 \) $0$ $\Z/2\Z$ $1$ $396.8489402$ 1.548762082 \( \frac{43762711342084459813388}{6328125} a^{4} + \frac{19657683179991310734076}{2109375} a^{3} - \frac{80370595538065362656194}{6328125} a^{2} - \frac{11238856761605347645073}{703125} a - \frac{18641764309297167053009}{6328125} \) \( \bigl[-2 a^{4} + 3 a^{3} + 9 a^{2} - 9 a - 6\) , \( -2 a^{4} + 3 a^{3} + 8 a^{2} - 7 a - 5\) , \( -a^{4} + a^{3} + 5 a^{2} - 2 a - 4\) , \( -46 a^{4} + 109 a^{3} + 43 a^{2} - 117 a - 48\) , \( 463 a^{4} - 1139 a^{3} - 594 a^{2} + 1290 a + 662\bigr] \) ${y}^2+\left(-2a^{4}+3a^{3}+9a^{2}-9a-6\right){x}{y}+\left(-a^{4}+a^{3}+5a^{2}-2a-4\right){y}={x}^{3}+\left(-2a^{4}+3a^{3}+8a^{2}-7a-5\right){x}^{2}+\left(-46a^{4}+109a^{3}+43a^{2}-117a-48\right){x}+463a^{4}-1139a^{3}-594a^{2}+1290a+662$
15.1-a2 15.1-a 5.5.65657.1 \( 3 \cdot 5 \) $0$ $\Z/2\Z\oplus\Z/2\Z$ $1$ $1587.395761$ 1.548762082 \( \frac{810387038438023516}{54931640625} a^{4} + \frac{363395431073753132}{18310546875} a^{3} - \frac{1491237718490098883}{54931640625} a^{2} - \frac{207634903981355686}{6103515625} a - \frac{338342690307372463}{54931640625} \) \( \bigl[a^{2} - 2\) , \( a^{4} - a^{3} - 4 a^{2} + 2 a + 2\) , \( a^{2} - 2\) , \( 10 a^{4} - 10 a^{3} - 40 a^{2} + 16 a + 5\) , \( -25 a^{4} + 18 a^{3} + 100 a^{2} - 13 a - 9\bigr] \) ${y}^2+\left(a^{2}-2\right){x}{y}+\left(a^{2}-2\right){y}={x}^{3}+\left(a^{4}-a^{3}-4a^{2}+2a+2\right){x}^{2}+\left(10a^{4}-10a^{3}-40a^{2}+16a+5\right){x}-25a^{4}+18a^{3}+100a^{2}-13a-9$
15.1-a3 15.1-a 5.5.65657.1 \( 3 \cdot 5 \) $0$ $\Z/2\Z$ $1$ $1587.395761$ 1.548762082 \( \frac{1404373231}{234375} a^{4} - \frac{1413777188}{78125} a^{3} - \frac{830144678}{234375} a^{2} + \frac{1478965772}{78125} a + \frac{1473768167}{234375} \) \( \bigl[a^{2} - 2\) , \( a^{4} - a^{3} - 4 a^{2} + 2 a + 2\) , \( a^{2} - 2\) , \( a\) , \( -a^{4} + a^{3} + 4 a^{2} - a - 1\bigr] \) ${y}^2+\left(a^{2}-2\right){x}{y}+\left(a^{2}-2\right){y}={x}^{3}+\left(a^{4}-a^{3}-4a^{2}+2a+2\right){x}^{2}+a{x}-a^{4}+a^{3}+4a^{2}-a-1$
15.1-a4 15.1-a 5.5.65657.1 \( 3 \cdot 5 \) $0$ $\Z/2\Z$ $1$ $198.4244701$ 1.548762082 \( \frac{359045212142585076290656747468}{111758708953857421875} a^{4} - \frac{147682742439513102209920029764}{37252902984619140625} a^{3} - \frac{1691569060032060442379194043234}{111758708953857421875} a^{2} + \frac{371284744650378795256836683741}{37252902984619140625} a + \frac{1534625546447161055611719609551}{111758708953857421875} \) \( \bigl[a^{2} - 2\) , \( a^{4} - a^{3} - 4 a^{2} + 2 a + 2\) , \( a^{2} - 2\) , \( 20 a^{4} - 20 a^{3} - 75 a^{2} + 26 a\) , \( 30 a^{4} - 29 a^{3} - 120 a^{2} + 39 a + 19\bigr] \) ${y}^2+\left(a^{2}-2\right){x}{y}+\left(a^{2}-2\right){y}={x}^{3}+\left(a^{4}-a^{3}-4a^{2}+2a+2\right){x}^{2}+\left(20a^{4}-20a^{3}-75a^{2}+26a\right){x}+30a^{4}-29a^{3}-120a^{2}+39a+19$
19.1-a1 19.1-a 5.5.65657.1 \( 19 \) $1$ $\mathsf{trivial}$ $0.019623793$ $2766.708886$ 2.118877814 \( \frac{218695}{361} a^{4} - \frac{376550}{361} a^{3} - \frac{959505}{361} a^{2} + \frac{1058864}{361} a + \frac{910976}{361} \) \( \bigl[a^{4} - a^{3} - 4 a^{2} + 2 a + 2\) , \( a^{4} - a^{3} - 5 a^{2} + 4 a + 4\) , \( -a^{4} + a^{3} + 5 a^{2} - 3 a - 4\) , \( 4 a^{4} - 5 a^{3} - 17 a^{2} + 12 a + 16\) , \( 2 a^{4} - 2 a^{3} - 10 a^{2} + 6 a + 9\bigr] \) ${y}^2+\left(a^{4}-a^{3}-4a^{2}+2a+2\right){x}{y}+\left(-a^{4}+a^{3}+5a^{2}-3a-4\right){y}={x}^{3}+\left(a^{4}-a^{3}-5a^{2}+4a+4\right){x}^{2}+\left(4a^{4}-5a^{3}-17a^{2}+12a+16\right){x}+2a^{4}-2a^{3}-10a^{2}+6a+9$
25.1-a1 25.1-a 5.5.65657.1 \( 5^{2} \) $0$ $\mathsf{trivial}$ $1$ $311.5669663$ 1.215936480 \( -23437386 a^{4} + 63684350 a^{3} + 7819892 a^{2} - 60287715 a - 13652392 \) \( \bigl[-2 a^{4} + 3 a^{3} + 9 a^{2} - 9 a - 6\) , \( -a^{2} + 3\) , \( a^{3} - 3 a - 1\) , \( a^{4} + 3 a^{3} - 8 a^{2} - 15 a + 8\) , \( -2 a^{4} + 3 a^{3} + 6 a^{2} - 5 a + 6\bigr] \) ${y}^2+\left(-2a^{4}+3a^{3}+9a^{2}-9a-6\right){x}{y}+\left(a^{3}-3a-1\right){y}={x}^{3}+\left(-a^{2}+3\right){x}^{2}+\left(a^{4}+3a^{3}-8a^{2}-15a+8\right){x}-2a^{4}+3a^{3}+6a^{2}-5a+6$
25.1-b1 25.1-b 5.5.65657.1 \( 5^{2} \) $1$ $\mathsf{trivial}$ $0.002247456$ $8560.393133$ 1.501670153 \( \frac{144184611}{5} a^{4} - \frac{255843129}{5} a^{3} - \frac{524006273}{5} a^{2} + \frac{693618211}{5} a + \frac{186593617}{5} \) \( \bigl[a^{4} - a^{3} - 4 a^{2} + 3 a + 3\) , \( -a^{4} + 5 a^{2} - 2\) , \( -a^{4} + a^{3} + 5 a^{2} - 2 a - 3\) , \( 18 a^{4} - 34 a^{3} - 65 a^{2} + 92 a + 27\) , \( -50 a^{4} + 87 a^{3} + 183 a^{2} - 235 a - 65\bigr] \) ${y}^2+\left(a^{4}-a^{3}-4a^{2}+3a+3\right){x}{y}+\left(-a^{4}+a^{3}+5a^{2}-2a-3\right){y}={x}^{3}+\left(-a^{4}+5a^{2}-2\right){x}^{2}+\left(18a^{4}-34a^{3}-65a^{2}+92a+27\right){x}-50a^{4}+87a^{3}+183a^{2}-235a-65$
25.1-c1 25.1-c 5.5.65657.1 \( 5^{2} \) $1$ $\mathsf{trivial}$ $0.670481688$ $54.38783543$ 2.846283625 \( \frac{9227278873526453906244312610219036327836}{125} a^{4} + \frac{3459009377990835094505717267240191015816}{125} a^{3} - \frac{41380713886380859304809564621687978514293}{125} a^{2} - \frac{38438451731868504360194666541225269140904}{125} a - \frac{6711393728551335750914883813930912798473}{125} \) \( \bigl[-a^{4} + 2 a^{3} + 4 a^{2} - 5 a - 3\) , \( -a^{4} + 2 a^{3} + 3 a^{2} - 4 a - 2\) , \( a^{3} - 4 a - 1\) , \( 1015 a^{4} - 1849 a^{3} - 3633 a^{2} + 4940 a + 991\) , \( -23261 a^{4} + 41576 a^{3} + 81774 a^{2} - 113086 a - 22399\bigr] \) ${y}^2+\left(-a^{4}+2a^{3}+4a^{2}-5a-3\right){x}{y}+\left(a^{3}-4a-1\right){y}={x}^{3}+\left(-a^{4}+2a^{3}+3a^{2}-4a-2\right){x}^{2}+\left(1015a^{4}-1849a^{3}-3633a^{2}+4940a+991\right){x}-23261a^{4}+41576a^{3}+81774a^{2}-113086a-22399$
25.1-c2 25.1-c 5.5.65657.1 \( 5^{2} \) $1$ $\mathsf{trivial}$ $0.223493896$ $163.1635062$ 2.846283625 \( -\frac{660212871515640604}{5} a^{4} + \frac{1794053534107468711}{5} a^{3} + \frac{220022592976562427}{5} a^{2} - \frac{1698345910262749894}{5} a - \frac{384439131601574358}{5} \) \( \bigl[-a^{4} + a^{3} + 5 a^{2} - 3 a - 4\) , \( a - 1\) , \( a^{4} - a^{3} - 4 a^{2} + 3 a + 2\) , \( -125 a^{4} + 373 a^{3} + 183 a^{2} - 759 a - 265\) , \( 241 a^{4} - 2229 a^{3} + 3233 a^{2} + 1399 a + 390\bigr] \) ${y}^2+\left(-a^{4}+a^{3}+5a^{2}-3a-4\right){x}{y}+\left(a^{4}-a^{3}-4a^{2}+3a+2\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-125a^{4}+373a^{3}+183a^{2}-759a-265\right){x}+241a^{4}-2229a^{3}+3233a^{2}+1399a+390$
25.1-c3 25.1-c 5.5.65657.1 \( 5^{2} \) $1$ $\mathsf{trivial}$ $0.134096337$ $271.9391771$ 2.846283625 \( \frac{175802229236840746}{30517578125} a^{4} + \frac{65933855205252401}{30517578125} a^{3} - \frac{788398234528339998}{30517578125} a^{2} - \frac{732499454042744644}{30517578125} a - \frac{127944679222457853}{30517578125} \) \( \bigl[-a^{4} + a^{3} + 5 a^{2} - 2 a - 3\) , \( -a^{4} + a^{3} + 5 a^{2} - 4 a - 3\) , \( a\) , \( -6 a^{4} + 5 a^{3} + 21 a^{2} - 20 a - 6\) , \( 148 a^{4} + 191 a^{3} - 275 a^{2} - 325 a - 59\bigr] \) ${y}^2+\left(-a^{4}+a^{3}+5a^{2}-2a-3\right){x}{y}+a{y}={x}^{3}+\left(-a^{4}+a^{3}+5a^{2}-4a-3\right){x}^{2}+\left(-6a^{4}+5a^{3}+21a^{2}-20a-6\right){x}+148a^{4}+191a^{3}-275a^{2}-325a-59$
25.1-c4 25.1-c 5.5.65657.1 \( 5^{2} \) $1$ $\mathsf{trivial}$ $0.044698779$ $815.8175314$ 2.846283625 \( \frac{81829946}{3125} a^{4} - \frac{143808649}{3125} a^{3} - \frac{300612723}{3125} a^{2} + \frac{393132181}{3125} a + \frac{109010922}{3125} \) \( \bigl[a^{4} - a^{3} - 4 a^{2} + 2 a + 3\) , \( -3 a^{4} + 4 a^{3} + 13 a^{2} - 10 a - 10\) , \( a^{2} - a - 2\) , \( 4 a^{4} - 3 a^{3} - 20 a^{2} + 5 a + 15\) , \( -11 a^{4} + 49 a^{2} + 27 a - 4\bigr] \) ${y}^2+\left(a^{4}-a^{3}-4a^{2}+2a+3\right){x}{y}+\left(a^{2}-a-2\right){y}={x}^{3}+\left(-3a^{4}+4a^{3}+13a^{2}-10a-10\right){x}^{2}+\left(4a^{4}-3a^{3}-20a^{2}+5a+15\right){x}-11a^{4}+49a^{2}+27a-4$
25.1-d1 25.1-d 5.5.65657.1 \( 5^{2} \) $1$ $\mathsf{trivial}$ $0.007778396$ $15969.78087$ 2.423921236 \( -23437386 a^{4} + 63684350 a^{3} + 7819892 a^{2} - 60287715 a - 13652392 \) \( \bigl[a + 1\) , \( a^{4} - a^{3} - 4 a^{2} + 2 a + 1\) , \( a^{3} - 4 a\) , \( -a^{4} + a^{3} + 4 a^{2} - 2 a - 1\) , \( -32 a^{4} + 57 a^{3} + 116 a^{2} - 155 a - 42\bigr] \) ${y}^2+\left(a+1\right){x}{y}+\left(a^{3}-4a\right){y}={x}^{3}+\left(a^{4}-a^{3}-4a^{2}+2a+1\right){x}^{2}+\left(-a^{4}+a^{3}+4a^{2}-2a-1\right){x}-32a^{4}+57a^{3}+116a^{2}-155a-42$
27.1-a1 27.1-a 5.5.65657.1 \( 3^{3} \) $0$ $\mathsf{trivial}$ $1$ $503.6602642$ 1.965609178 \( -169969542 a^{4} + 461869972 a^{3} + 56647563 a^{2} - 437225155 a - 98969253 \) \( \bigl[a^{3} - 4 a\) , \( 2 a^{4} - 3 a^{3} - 9 a^{2} + 10 a + 6\) , \( -2 a^{4} + 3 a^{3} + 9 a^{2} - 8 a - 7\) , \( 2 a^{4} - a^{3} - 15 a^{2} + 10 a + 16\) , \( a^{3} - 4 a^{2} + 4 a + 3\bigr] \) ${y}^2+\left(a^{3}-4a\right){x}{y}+\left(-2a^{4}+3a^{3}+9a^{2}-8a-7\right){y}={x}^{3}+\left(2a^{4}-3a^{3}-9a^{2}+10a+6\right){x}^{2}+\left(2a^{4}-a^{3}-15a^{2}+10a+16\right){x}+a^{3}-4a^{2}+4a+3$
27.1-b1 27.1-b 5.5.65657.1 \( 3^{3} \) $0$ $\mathsf{trivial}$ $1$ $410.8582841$ 1.603435632 \( 124002 a^{4} - 33919 a^{3} - 523999 a^{2} - 180889 a - 13950 \) \( \bigl[a + 1\) , \( a^{4} - 2 a^{3} - 3 a^{2} + 6 a\) , \( a^{4} - a^{3} - 4 a^{2} + 2 a + 3\) , \( 3 a^{3} + a^{2} - 16 a - 4\) , \( 5 a^{4} + a^{3} - 22 a^{2} - 16 a - 4\bigr] \) ${y}^2+\left(a+1\right){x}{y}+\left(a^{4}-a^{3}-4a^{2}+2a+3\right){y}={x}^{3}+\left(a^{4}-2a^{3}-3a^{2}+6a\right){x}^{2}+\left(3a^{3}+a^{2}-16a-4\right){x}+5a^{4}+a^{3}-22a^{2}-16a-4$
27.1-c1 27.1-c 5.5.65657.1 \( 3^{3} \) $1$ $\mathsf{trivial}$ $0.210572102$ $635.6217671$ 2.611734837 \( -24302019083166184075 a^{4} + 29987786156907253441 a^{3} + 114494070674765766206 a^{2} - 75391385133403896914 a - 103871320062709432359 \) \( \bigl[a^{2} - a - 1\) , \( 2 a^{4} - 2 a^{3} - 9 a^{2} + 4 a + 7\) , \( a + 1\) , \( 6 a^{4} - 15 a^{3} - 24 a^{2} + 36 a + 16\) , \( 18 a^{4} - 27 a^{3} - 60 a^{2} + 70 a + 21\bigr] \) ${y}^2+\left(a^{2}-a-1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(2a^{4}-2a^{3}-9a^{2}+4a+7\right){x}^{2}+\left(6a^{4}-15a^{3}-24a^{2}+36a+16\right){x}+18a^{4}-27a^{3}-60a^{2}+70a+21$
27.1-c2 27.1-c 5.5.65657.1 \( 3^{3} \) $1$ $\mathsf{trivial}$ $0.070190700$ $1906.865301$ 2.611734837 \( -1283318 a^{4} + 1637833 a^{3} + 6106189 a^{2} - 4095058 a - 5583206 \) \( \bigl[a^{2} - 2\) , \( -2 a^{4} + 2 a^{3} + 9 a^{2} - 5 a - 5\) , \( -a^{4} + a^{3} + 5 a^{2} - 3 a - 4\) , \( -3 a^{4} + 2 a^{3} + 13 a^{2} - a - 3\) , \( -18 a^{4} - 5 a^{3} + 80 a^{2} + 68 a + 10\bigr] \) ${y}^2+\left(a^{2}-2\right){x}{y}+\left(-a^{4}+a^{3}+5a^{2}-3a-4\right){y}={x}^{3}+\left(-2a^{4}+2a^{3}+9a^{2}-5a-5\right){x}^{2}+\left(-3a^{4}+2a^{3}+13a^{2}-a-3\right){x}-18a^{4}-5a^{3}+80a^{2}+68a+10$
27.1-d1 27.1-d 5.5.65657.1 \( 3^{3} \) $0$ $\mathsf{trivial}$ $1$ $36.77387620$ 1.291639749 \( -24302019083166184075 a^{4} + 29987786156907253441 a^{3} + 114494070674765766206 a^{2} - 75391385133403896914 a - 103871320062709432359 \) \( \bigl[a^{2} - 2\) , \( -a^{4} + 5 a^{2} - 2\) , \( a^{2} - a - 1\) , \( 3 a^{4} - 9 a^{3} - 7 a^{2} + 21 a + 2\) , \( 9 a^{4} - 15 a^{3} - 40 a^{2} + 52 a + 13\bigr] \) ${y}^2+\left(a^{2}-2\right){x}{y}+\left(a^{2}-a-1\right){y}={x}^{3}+\left(-a^{4}+5a^{2}-2\right){x}^{2}+\left(3a^{4}-9a^{3}-7a^{2}+21a+2\right){x}+9a^{4}-15a^{3}-40a^{2}+52a+13$
27.1-d2 27.1-d 5.5.65657.1 \( 3^{3} \) $0$ $\Z/3\Z$ $1$ $2978.683972$ 1.291639749 \( -1283318 a^{4} + 1637833 a^{3} + 6106189 a^{2} - 4095058 a - 5583206 \) \( \bigl[-a^{4} + a^{3} + 5 a^{2} - 3 a - 3\) , \( a^{4} - a^{3} - 5 a^{2} + 3 a + 4\) , \( a^{2} - a - 2\) , \( -2 a^{2} + 3 a + 4\) , \( -2 a^{4} - 2 a^{3} + 10 a^{2} + 12 a + 3\bigr] \) ${y}^2+\left(-a^{4}+a^{3}+5a^{2}-3a-3\right){x}{y}+\left(a^{2}-a-2\right){y}={x}^{3}+\left(a^{4}-a^{3}-5a^{2}+3a+4\right){x}^{2}+\left(-2a^{2}+3a+4\right){x}-2a^{4}-2a^{3}+10a^{2}+12a+3$
27.1-e1 27.1-e 5.5.65657.1 \( 3^{3} \) $0$ $\mathsf{trivial}$ $1$ $265.8551399$ 1.037539270 \( 124002 a^{4} - 33919 a^{3} - 523999 a^{2} - 180889 a - 13950 \) \( \bigl[-a^{4} + a^{3} + 5 a^{2} - 2 a - 3\) , \( -a^{4} + 2 a^{3} + 3 a^{2} - 4 a\) , \( -a^{4} + 2 a^{3} + 5 a^{2} - 6 a - 4\) , \( 2 a^{4} - 8 a^{3} + 5 a^{2} + 6 a + 1\) , \( -2 a^{4} + 5 a^{3} + a^{2} - 5 a - 1\bigr] \) ${y}^2+\left(-a^{4}+a^{3}+5a^{2}-2a-3\right){x}{y}+\left(-a^{4}+2a^{3}+5a^{2}-6a-4\right){y}={x}^{3}+\left(-a^{4}+2a^{3}+3a^{2}-4a\right){x}^{2}+\left(2a^{4}-8a^{3}+5a^{2}+6a+1\right){x}-2a^{4}+5a^{3}+a^{2}-5a-1$
27.1-f1 27.1-f 5.5.65657.1 \( 3^{3} \) $1$ $\mathsf{trivial}$ $0.006570846$ $5293.284853$ 2.036091728 \( -169969542 a^{4} + 461869972 a^{3} + 56647563 a^{2} - 437225155 a - 98969253 \) \( \bigl[a^{3} - 3 a - 1\) , \( -3 a^{4} + 4 a^{3} + 13 a^{2} - 10 a - 10\) , \( -2 a^{4} + 3 a^{3} + 9 a^{2} - 8 a - 7\) , \( 2 a^{4} - 3 a^{3} - 12 a^{2} + 12 a + 19\) , \( -8 a^{4} + 9 a^{3} + 37 a^{2} - 21 a - 25\bigr] \) ${y}^2+\left(a^{3}-3a-1\right){x}{y}+\left(-2a^{4}+3a^{3}+9a^{2}-8a-7\right){y}={x}^{3}+\left(-3a^{4}+4a^{3}+13a^{2}-10a-10\right){x}^{2}+\left(2a^{4}-3a^{3}-12a^{2}+12a+19\right){x}-8a^{4}+9a^{3}+37a^{2}-21a-25$
29.1-a1 29.1-a 5.5.65657.1 \( 29 \) $1$ $\mathsf{trivial}$ $0.012463742$ $6352.309501$ 1.544932797 \( \frac{12183}{29} a^{4} - \frac{19048}{29} a^{3} - \frac{55150}{29} a^{2} + \frac{66157}{29} a + \frac{70545}{29} \) \( \bigl[-a^{4} + 2 a^{3} + 5 a^{2} - 6 a - 5\) , \( 3 a^{4} - 4 a^{3} - 13 a^{2} + 10 a + 8\) , \( a^{2} - a - 1\) , \( 4 a^{4} - 4 a^{3} - 21 a^{2} + 10 a + 22\) , \( 5 a^{4} - 6 a^{3} - 24 a^{2} + 16 a + 21\bigr] \) ${y}^2+\left(-a^{4}+2a^{3}+5a^{2}-6a-5\right){x}{y}+\left(a^{2}-a-1\right){y}={x}^{3}+\left(3a^{4}-4a^{3}-13a^{2}+10a+8\right){x}^{2}+\left(4a^{4}-4a^{3}-21a^{2}+10a+22\right){x}+5a^{4}-6a^{3}-24a^{2}+16a+21$
29.1-a2 29.1-a 5.5.65657.1 \( 29 \) $1$ $\mathsf{trivial}$ $0.037391226$ $2117.436500$ 1.544932797 \( \frac{3112416550238}{24389} a^{4} - \frac{4117133380738}{24389} a^{3} - \frac{14702539245891}{24389} a^{2} + \frac{10904653871054}{24389} a + \frac{14162641194095}{24389} \) \( \bigl[-a^{4} + 2 a^{3} + 4 a^{2} - 6 a - 2\) , \( -a^{2} + 3\) , \( a^{3} - 3 a - 1\) , \( -6 a^{4} + 9 a^{3} + 25 a^{2} - 25 a - 16\) , \( 3 a^{4} - 5 a^{3} - 12 a^{2} + 11 a + 8\bigr] \) ${y}^2+\left(-a^{4}+2a^{3}+4a^{2}-6a-2\right){x}{y}+\left(a^{3}-3a-1\right){y}={x}^{3}+\left(-a^{2}+3\right){x}^{2}+\left(-6a^{4}+9a^{3}+25a^{2}-25a-16\right){x}+3a^{4}-5a^{3}-12a^{2}+11a+8$
32.1-a1 32.1-a 5.5.65657.1 \( 2^{5} \) $0$ $\mathsf{trivial}$ $1$ $126.7141884$ 0.989041977 \( 26869605 a^{4} - 40011890 a^{3} - \frac{497646017}{4} a^{2} + \frac{294534937}{2} a + \frac{162685211}{4} \) \( \bigl[-a^{4} + a^{3} + 5 a^{2} - 3 a - 3\) , \( -a^{4} + a^{3} + 5 a^{2} - 3 a - 3\) , \( -2 a^{4} + 3 a^{3} + 9 a^{2} - 8 a - 7\) , \( -3 a^{4} + 4 a^{3} + 8 a^{2} - 5 a - 7\) , \( -a^{4} - 2 a^{3} + 7 a^{2} + a - 6\bigr] \) ${y}^2+\left(-a^{4}+a^{3}+5a^{2}-3a-3\right){x}{y}+\left(-2a^{4}+3a^{3}+9a^{2}-8a-7\right){y}={x}^{3}+\left(-a^{4}+a^{3}+5a^{2}-3a-3\right){x}^{2}+\left(-3a^{4}+4a^{3}+8a^{2}-5a-7\right){x}-a^{4}-2a^{3}+7a^{2}+a-6$
37.1-a1 37.1-a 5.5.65657.1 \( 37 \) $0$ $\mathsf{trivial}$ $1$ $0.516065317$ 1.258763590 \( -\frac{1682103188678259782838444650496}{37} a^{4} + \frac{4570890135767342003193598513152}{37} a^{3} + \frac{560624301911253507213468364800}{37} a^{2} - \frac{4327003532745719478147674701824}{37} a - \frac{979466879795506810202756071424}{37} \) \( \bigl[0\) , \( -3 a^{4} + 4 a^{3} + 13 a^{2} - 11 a - 10\) , \( a^{2} - a - 2\) , \( 345 a^{4} - 549 a^{3} - 1365 a^{2} + 1487 a + 783\) , \( 3135 a^{4} - 5551 a^{3} - 12034 a^{2} + 14521 a + 5015\bigr] \) ${y}^2+\left(a^{2}-a-2\right){y}={x}^{3}+\left(-3a^{4}+4a^{3}+13a^{2}-11a-10\right){x}^{2}+\left(345a^{4}-549a^{3}-1365a^{2}+1487a+783\right){x}+3135a^{4}-5551a^{3}-12034a^{2}+14521a+5015$
37.1-a2 37.1-a 5.5.65657.1 \( 37 \) $0$ $\Z/5\Z$ $1$ $1612.704115$ 1.258763590 \( -\frac{2507214671425536}{69343957} a^{4} + \frac{3099587870568448}{69343957} a^{3} + \frac{11795529019346944}{69343957} a^{2} - \frac{7777196659007488}{69343957} a - \frac{10702583291781120}{69343957} \) \( \bigl[0\) , \( a^{4} - 2 a^{3} - 4 a^{2} + 7 a + 3\) , \( -a^{4} + a^{3} + 5 a^{2} - 3 a - 4\) , \( 49 a^{4} - 88 a^{3} - 178 a^{2} + 239 a + 64\) , \( 162 a^{4} - 287 a^{3} - 588 a^{2} + 779 a + 208\bigr] \) ${y}^2+\left(-a^{4}+a^{3}+5a^{2}-3a-4\right){y}={x}^{3}+\left(a^{4}-2a^{3}-4a^{2}+7a+3\right){x}^{2}+\left(49a^{4}-88a^{3}-178a^{2}+239a+64\right){x}+162a^{4}-287a^{3}-588a^{2}+779a+208$
37.1-b1 37.1-b 5.5.65657.1 \( 37 \) $1$ $\mathsf{trivial}$ $0.020206397$ $4207.941219$ 1.659159130 \( -\frac{18254600376320}{50653} a^{4} + \frac{49539534499840}{50653} a^{3} + \frac{6263292940288}{50653} a^{2} - \frac{47056864038912}{50653} a - \frac{10663276101632}{50653} \) \( \bigl[0\) , \( -a^{3} + 4 a + 2\) , \( -2 a^{4} + 3 a^{3} + 9 a^{2} - 8 a - 7\) , \( -20 a^{4} + 24 a^{3} + 92 a^{2} - 55 a - 81\) , \( 136 a^{4} - 170 a^{3} - 637 a^{2} + 426 a + 579\bigr] \) ${y}^2+\left(-2a^{4}+3a^{3}+9a^{2}-8a-7\right){y}={x}^{3}+\left(-a^{3}+4a+2\right){x}^{2}+\left(-20a^{4}+24a^{3}+92a^{2}-55a-81\right){x}+136a^{4}-170a^{3}-637a^{2}+426a+579$
37.1-b2 37.1-b 5.5.65657.1 \( 37 \) $1$ $\mathsf{trivial}$ $0.006735465$ $12623.82365$ 1.659159130 \( \frac{2371584}{37} a^{4} + \frac{970752}{37} a^{3} - \frac{10678272}{37} a^{2} - \frac{10203136}{37} a - \frac{1785856}{37} \) \( \bigl[0\) , \( a^{4} - 2 a^{3} - 5 a^{2} + 6 a + 5\) , \( -a^{4} + 2 a^{3} + 5 a^{2} - 7 a - 4\) , \( 5 a^{4} - 8 a^{3} - 19 a^{2} + 22 a + 10\) , \( -5 a^{4} + 9 a^{3} + 17 a^{2} - 24 a - 6\bigr] \) ${y}^2+\left(-a^{4}+2a^{3}+5a^{2}-7a-4\right){y}={x}^{3}+\left(a^{4}-2a^{3}-5a^{2}+6a+5\right){x}^{2}+\left(5a^{4}-8a^{3}-19a^{2}+22a+10\right){x}-5a^{4}+9a^{3}+17a^{2}-24a-6$
43.1-a1 43.1-a 5.5.65657.1 \( 43 \) $1$ $\mathsf{trivial}$ $0.078230725$ $1874.332834$ 2.861235187 \( -\frac{12952}{43} a^{4} + \frac{5048}{43} a^{3} + \frac{43307}{43} a^{2} + \frac{10999}{43} a + \frac{393}{43} \) \( \bigl[1\) , \( -2 a^{4} + 3 a^{3} + 9 a^{2} - 10 a - 8\) , \( a^{4} - a^{3} - 4 a^{2} + 3 a + 2\) , \( -a^{4} - 2 a^{3} + 4 a^{2} + 11 a + 10\) , \( 2 a^{4} + 3 a^{3} - 9 a^{2} - 20 a - 9\bigr] \) ${y}^2+{x}{y}+\left(a^{4}-a^{3}-4a^{2}+3a+2\right){y}={x}^{3}+\left(-2a^{4}+3a^{3}+9a^{2}-10a-8\right){x}^{2}+\left(-a^{4}-2a^{3}+4a^{2}+11a+10\right){x}+2a^{4}+3a^{3}-9a^{2}-20a-9$
43.1-a2 43.1-a 5.5.65657.1 \( 43 \) $1$ $\mathsf{trivial}$ $0.234692176$ $624.7776116$ 2.861235187 \( -\frac{23968185390845}{79507} a^{4} - \frac{32340604970044}{79507} a^{3} + \frac{43993086493009}{79507} a^{2} + \frac{55492835852009}{79507} a + \frac{10232774495362}{79507} \) \( \bigl[-2 a^{4} + 3 a^{3} + 9 a^{2} - 8 a - 6\) , \( a^{4} - 2 a^{3} - 4 a^{2} + 7 a + 2\) , \( a + 1\) , \( 5 a^{4} - 3 a^{3} - 21 a^{2} - 3 a + 6\) , \( 9 a^{4} + 2 a^{3} - 40 a^{2} - 33 a - 4\bigr] \) ${y}^2+\left(-2a^{4}+3a^{3}+9a^{2}-8a-6\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a^{4}-2a^{3}-4a^{2}+7a+2\right){x}^{2}+\left(5a^{4}-3a^{3}-21a^{2}-3a+6\right){x}+9a^{4}+2a^{3}-40a^{2}-33a-4$
45.1-a1 45.1-a 5.5.65657.1 \( 3^{2} \cdot 5 \) $1$ $\Z/2\Z$ $0.149447375$ $1827.780293$ 2.665089355 \( \frac{34992}{5} a^{4} - \frac{81598}{5} a^{3} - \frac{54171}{5} a^{2} + \frac{89407}{5} a + \frac{46644}{5} \) \( \bigl[-a^{4} + a^{3} + 5 a^{2} - 2 a - 4\) , \( 2 a^{4} - 3 a^{3} - 8 a^{2} + 9 a + 5\) , \( -2 a^{4} + 3 a^{3} + 9 a^{2} - 9 a - 6\) , \( -2 a^{4} + 5 a^{3} + 4 a^{2} - 9 a + 1\) , \( 2 a^{4} - 2 a^{3} - 11 a^{2} + 10 a + 5\bigr] \) ${y}^2+\left(-a^{4}+a^{3}+5a^{2}-2a-4\right){x}{y}+\left(-2a^{4}+3a^{3}+9a^{2}-9a-6\right){y}={x}^{3}+\left(2a^{4}-3a^{3}-8a^{2}+9a+5\right){x}^{2}+\left(-2a^{4}+5a^{3}+4a^{2}-9a+1\right){x}+2a^{4}-2a^{3}-11a^{2}+10a+5$
45.1-a2 45.1-a 5.5.65657.1 \( 3^{2} \cdot 5 \) $1$ $\Z/2\Z$ $0.298894751$ $456.9450733$ 2.665089355 \( \frac{11314724189}{25} a^{4} - \frac{30736776391}{25} a^{3} - \frac{3562664832}{25} a^{2} + \frac{29192288229}{25} a + \frac{6597394298}{25} \) \( \bigl[-2 a^{4} + 3 a^{3} + 9 a^{2} - 9 a - 6\) , \( a^{4} - a^{3} - 5 a^{2} + 4 a + 3\) , \( -a^{4} + 2 a^{3} + 5 a^{2} - 6 a - 5\) , \( 16 a^{4} - 20 a^{3} - 76 a^{2} + 58 a + 56\) , \( -11 a^{4} + 10 a^{3} + 56 a^{2} - 13 a - 77\bigr] \) ${y}^2+\left(-2a^{4}+3a^{3}+9a^{2}-9a-6\right){x}{y}+\left(-a^{4}+2a^{3}+5a^{2}-6a-5\right){y}={x}^{3}+\left(a^{4}-a^{3}-5a^{2}+4a+3\right){x}^{2}+\left(16a^{4}-20a^{3}-76a^{2}+58a+56\right){x}-11a^{4}+10a^{3}+56a^{2}-13a-77$
45.1-b1 45.1-b 5.5.65657.1 \( 3^{2} \cdot 5 \) $0$ $\mathsf{trivial}$ $1$ $1.656052230$ 1.454172845 \( \frac{9227278873526453906244312610219036327836}{125} a^{4} + \frac{3459009377990835094505717267240191015816}{125} a^{3} - \frac{41380713886380859304809564621687978514293}{125} a^{2} - \frac{38438451731868504360194666541225269140904}{125} a - \frac{6711393728551335750914883813930912798473}{125} \) \( \bigl[-a^{4} + a^{3} + 5 a^{2} - 3 a - 3\) , \( -a^{4} + 5 a^{2} - 2\) , \( a^{3} - 4 a - 1\) , \( -527 a^{4} + 1330 a^{3} + 662 a^{2} - 1670 a - 937\) , \( 18278 a^{4} - 41440 a^{3} - 28524 a^{2} + 47105 a + 27660\bigr] \) ${y}^2+\left(-a^{4}+a^{3}+5a^{2}-3a-3\right){x}{y}+\left(a^{3}-4a-1\right){y}={x}^{3}+\left(-a^{4}+5a^{2}-2\right){x}^{2}+\left(-527a^{4}+1330a^{3}+662a^{2}-1670a-937\right){x}+18278a^{4}-41440a^{3}-28524a^{2}+47105a+27660$
45.1-b2 45.1-b 5.5.65657.1 \( 3^{2} \cdot 5 \) $0$ $\Z/3\Z$ $1$ $134.1402306$ 1.454172845 \( -\frac{660212871515640604}{5} a^{4} + \frac{1794053534107468711}{5} a^{3} + \frac{220022592976562427}{5} a^{2} - \frac{1698345910262749894}{5} a - \frac{384439131601574358}{5} \) \( \bigl[a\) , \( a^{4} - 2 a^{3} - 4 a^{2} + 7 a + 3\) , \( -a^{4} + 2 a^{3} + 5 a^{2} - 7 a - 4\) , \( 330 a^{4} + 154 a^{3} - 1529 a^{2} - 1577 a - 314\) , \( 9329 a^{4} + 3425 a^{3} - 41530 a^{2} - 38029 a - 6558\bigr] \) ${y}^2+a{x}{y}+\left(-a^{4}+2a^{3}+5a^{2}-7a-4\right){y}={x}^{3}+\left(a^{4}-2a^{3}-4a^{2}+7a+3\right){x}^{2}+\left(330a^{4}+154a^{3}-1529a^{2}-1577a-314\right){x}+9329a^{4}+3425a^{3}-41530a^{2}-38029a-6558$
45.1-b3 45.1-b 5.5.65657.1 \( 3^{2} \cdot 5 \) $0$ $\mathsf{trivial}$ $1$ $41.40130575$ 1.454172845 \( \frac{175802229236840746}{30517578125} a^{4} + \frac{65933855205252401}{30517578125} a^{3} - \frac{788398234528339998}{30517578125} a^{2} - \frac{732499454042744644}{30517578125} a - \frac{127944679222457853}{30517578125} \) \( \bigl[a^{4} - a^{3} - 4 a^{2} + 2 a + 2\) , \( a^{4} - 2 a^{3} - 3 a^{2} + 4 a\) , \( -a^{4} + 2 a^{3} + 5 a^{2} - 7 a - 4\) , \( 9 a^{3} - 3 a^{2} - 40 a - 8\) , \( 10 a^{4} + 2 a^{3} - 44 a^{2} - 35 a - 7\bigr] \) ${y}^2+\left(a^{4}-a^{3}-4a^{2}+2a+2\right){x}{y}+\left(-a^{4}+2a^{3}+5a^{2}-7a-4\right){y}={x}^{3}+\left(a^{4}-2a^{3}-3a^{2}+4a\right){x}^{2}+\left(9a^{3}-3a^{2}-40a-8\right){x}+10a^{4}+2a^{3}-44a^{2}-35a-7$
45.1-b4 45.1-b 5.5.65657.1 \( 3^{2} \cdot 5 \) $0$ $\Z/3\Z$ $1$ $3353.505766$ 1.454172845 \( \frac{81829946}{3125} a^{4} - \frac{143808649}{3125} a^{3} - \frac{300612723}{3125} a^{2} + \frac{393132181}{3125} a + \frac{109010922}{3125} \) \( \bigl[a^{2} - a - 1\) , \( -a^{2} + a + 2\) , \( -a^{4} + 2 a^{3} + 4 a^{2} - 6 a - 3\) , \( 4 a^{4} - 5 a^{3} - 19 a^{2} + 13 a + 17\) , \( 8 a^{4} - 10 a^{3} - 37 a^{2} + 25 a + 32\bigr] \) ${y}^2+\left(a^{2}-a-1\right){x}{y}+\left(-a^{4}+2a^{3}+4a^{2}-6a-3\right){y}={x}^{3}+\left(-a^{2}+a+2\right){x}^{2}+\left(4a^{4}-5a^{3}-19a^{2}+13a+17\right){x}+8a^{4}-10a^{3}-37a^{2}+25a+32$
45.1-c1 45.1-c 5.5.65657.1 \( 3^{2} \cdot 5 \) $0$ $\Z/2\Z$ $1$ $887.0117130$ 1.730847645 \( \frac{34992}{5} a^{4} - \frac{81598}{5} a^{3} - \frac{54171}{5} a^{2} + \frac{89407}{5} a + \frac{46644}{5} \) \( \bigl[-a^{4} + 2 a^{3} + 5 a^{2} - 6 a - 5\) , \( a^{4} - 5 a^{2} - 2 a + 2\) , \( a^{3} - 3 a\) , \( 2 a^{4} - 4 a^{3} - 11 a^{2} + 13 a + 13\) , \( 2 a^{4} - 3 a^{3} - 9 a^{2} + 5 a + 6\bigr] \) ${y}^2+\left(-a^{4}+2a^{3}+5a^{2}-6a-5\right){x}{y}+\left(a^{3}-3a\right){y}={x}^{3}+\left(a^{4}-5a^{2}-2a+2\right){x}^{2}+\left(2a^{4}-4a^{3}-11a^{2}+13a+13\right){x}+2a^{4}-3a^{3}-9a^{2}+5a+6$
45.1-c2 45.1-c 5.5.65657.1 \( 3^{2} \cdot 5 \) $0$ $\Z/2\Z$ $1$ $443.5058565$ 1.730847645 \( \frac{11314724189}{25} a^{4} - \frac{30736776391}{25} a^{3} - \frac{3562664832}{25} a^{2} + \frac{29192288229}{25} a + \frac{6597394298}{25} \) \( \bigl[-a^{4} + 2 a^{3} + 5 a^{2} - 7 a - 5\) , \( -3 a^{4} + 4 a^{3} + 13 a^{2} - 11 a - 9\) , \( -a^{4} + 2 a^{3} + 5 a^{2} - 6 a - 4\) , \( 24 a^{4} - 31 a^{3} - 110 a^{2} + 79 a + 89\) , \( 93 a^{4} - 125 a^{3} - 415 a^{2} + 318 a + 327\bigr] \) ${y}^2+\left(-a^{4}+2a^{3}+5a^{2}-7a-5\right){x}{y}+\left(-a^{4}+2a^{3}+5a^{2}-6a-4\right){y}={x}^{3}+\left(-3a^{4}+4a^{3}+13a^{2}-11a-9\right){x}^{2}+\left(24a^{4}-31a^{3}-110a^{2}+79a+89\right){x}+93a^{4}-125a^{3}-415a^{2}+318a+327$
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  *The rank, regulator and analytic order of Ш are not known for all curves in the database; curves for which these are unknown will not appear in searches specifying one of these quantities.