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Label Class Base field Conductor norm Rank Torsion CM Regulator Period Leading coeff j-invariant Weierstrass coefficients Weierstrass equation
8.1-a1 8.1-a 3.3.148.1 \( 2^{3} \) $0$ $\Z/8\Z$ $1$ $223.1882642$ 0.573311322 \( -2624 a^{2} + 1536 a + 9024 \) \( \bigl[a^{2} - 1\) , \( -1\) , \( a^{2} - a - 2\) , \( 1727261180779898112178031 a^{2} + 2021044966504285468600887 a - 795941171665179475905777\) , \( 279884457042981407569057081184688558284 a^{2} + 327489021002657174715208924802606509852 a - 128973872132688546804017272390232511682\bigr] \) ${y}^2+\left(a^{2}-1\right){x}{y}+\left(a^{2}-a-2\right){y}={x}^{3}-{x}^{2}+\left(1727261180779898112178031a^{2}+2021044966504285468600887a-795941171665179475905777\right){x}+279884457042981407569057081184688558284a^{2}+327489021002657174715208924802606509852a-128973872132688546804017272390232511682$
8.1-a2 8.1-a 3.3.148.1 \( 2^{3} \) $0$ $\Z/2\Z\oplus\Z/4\Z$ $1$ $223.1882642$ 0.573311322 \( 5088 a^{2} + 8224 a + 3904 \) \( \bigl[a^{2} - 1\) , \( -a^{2} + a + 1\) , \( 0\) , \( -122876240093597390564 a^{2} - 143775828060934351842 a + 56622738702290433353\) , \( 1339806177584198660985008156380 a^{2} + 1567689103089350829411708766103 a - 617397594907508652287429548778\bigr] \) ${y}^2+\left(a^{2}-1\right){x}{y}={x}^{3}+\left(-a^{2}+a+1\right){x}^{2}+\left(-122876240093597390564a^{2}-143775828060934351842a+56622738702290433353\right){x}+1339806177584198660985008156380a^{2}+1567689103089350829411708766103a-617397594907508652287429548778$
8.1-a3 8.1-a 3.3.148.1 \( 2^{3} \) $0$ $\Z/2\Z$ $1$ $6.974633256$ 0.573311322 \( -437389120487750 a^{2} + 301313945830146 a + 1405908485521968 \) \( \bigl[a + 1\) , \( a^{2} - a - 3\) , \( a^{2} - a - 2\) , \( 4 a^{2} + 15 a - 2\) , \( -14 a^{2} + 6 a - 2\bigr] \) ${y}^2+\left(a+1\right){x}{y}+\left(a^{2}-a-2\right){y}={x}^{3}+\left(a^{2}-a-3\right){x}^{2}+\left(4a^{2}+15a-2\right){x}-14a^{2}+6a-2$
8.1-a4 8.1-a 3.3.148.1 \( 2^{3} \) $0$ $\Z/2\Z\oplus\Z/2\Z$ $1$ $55.79706605$ 0.573311322 \( -10821604 a^{2} + 6316064 a + 37257972 \) \( \bigl[a + 1\) , \( a^{2} - 2 a - 1\) , \( a^{2} - a - 2\) , \( -83347907948 a^{2} - 97524260781 a + 38407643413\) , \( -13188165606368355 a^{2} - 15431294359397846 a + 6077253458627265\bigr] \) ${y}^2+\left(a+1\right){x}{y}+\left(a^{2}-a-2\right){y}={x}^{3}+\left(a^{2}-2a-1\right){x}^{2}+\left(-83347907948a^{2}-97524260781a+38407643413\right){x}-13188165606368355a^{2}-15431294359397846a+6077253458627265$
8.1-a5 8.1-a 3.3.148.1 \( 2^{3} \) $0$ $\Z/2\Z$ $1$ $6.974633256$ 0.573311322 \( 2644415465286 a^{2} - 6561307231490 a + 1785326087072 \) \( \bigl[a + 1\) , \( a^{2} - 2 a - 1\) , \( a^{2} - a - 2\) , \( -1157658655878 a^{2} - 1354560749371 a + 533461990118\) , \( -1248619261868812725 a^{2} - 1460992525253670641 a + 575377649491803209\bigr] \) ${y}^2+\left(a+1\right){x}{y}+\left(a^{2}-a-2\right){y}={x}^{3}+\left(a^{2}-2a-1\right){x}^{2}+\left(-1157658655878a^{2}-1354560749371a+533461990118\right){x}-1248619261868812725a^{2}-1460992525253670641a+575377649491803209$
8.1-a6 8.1-a 3.3.148.1 \( 2^{3} \) $0$ $\Z/8\Z$ $1$ $223.1882642$ 0.573311322 \( 297852964 a^{2} + 348495840 a - 137248100 \) \( \bigl[a + 1\) , \( -a^{2} + a + 1\) , \( a^{2} - 1\) , \( -23137255028952366700772 a^{2} - 27072589446997404913200 a + 10661904569953464468393\) , \( 3529193720251159834920437017851122 a^{2} + 4129461880751340931496180433614334 a - 1626291736297668628974848142500566\bigr] \) ${y}^2+\left(a+1\right){x}{y}+\left(a^{2}-1\right){y}={x}^{3}+\left(-a^{2}+a+1\right){x}^{2}+\left(-23137255028952366700772a^{2}-27072589446997404913200a+10661904569953464468393\right){x}+3529193720251159834920437017851122a^{2}+4129461880751340931496180433614334a-1626291736297668628974848142500566$
16.1-a1 16.1-a 3.3.148.1 \( 2^{4} \) $0$ $\Z/2\Z$ $1$ $19.84404198$ 0.815585101 \( -437389120487750 a^{2} + 301313945830146 a + 1405908485521968 \) \( \bigl[a^{2} - a - 2\) , \( a^{2} - 2 a - 3\) , \( a^{2} - 1\) , \( 54 a^{2} + 61 a - 27\) , \( 214 a^{2} + 250 a - 99\bigr] \) ${y}^2+\left(a^{2}-a-2\right){x}{y}+\left(a^{2}-1\right){y}={x}^{3}+\left(a^{2}-2a-3\right){x}^{2}+\left(54a^{2}+61a-27\right){x}+214a^{2}+250a-99$
16.1-a2 16.1-a 3.3.148.1 \( 2^{4} \) $0$ $\Z/2\Z\oplus\Z/2\Z$ $1$ $158.7523358$ 0.815585101 \( -10821604 a^{2} + 6316064 a + 37257972 \) \( \bigl[a^{2} - a - 2\) , \( a^{2} - 2 a - 3\) , \( a^{2} - 1\) , \( -16 a^{2} - 19 a + 8\) , \( 49 a^{2} + 57 a - 23\bigr] \) ${y}^2+\left(a^{2}-a-2\right){x}{y}+\left(a^{2}-1\right){y}={x}^{3}+\left(a^{2}-2a-3\right){x}^{2}+\left(-16a^{2}-19a+8\right){x}+49a^{2}+57a-23$
16.1-a3 16.1-a 3.3.148.1 \( 2^{4} \) $0$ $\Z/4\Z$ $1$ $79.37616793$ 0.815585101 \( 2644415465286 a^{2} - 6561307231490 a + 1785326087072 \) \( \bigl[a^{2} - a - 2\) , \( a^{2} - 2 a - 3\) , \( a^{2} - 1\) , \( -226 a^{2} - 259 a + 103\) , \( 3566 a^{2} + 4170 a - 1643\bigr] \) ${y}^2+\left(a^{2}-a-2\right){x}{y}+\left(a^{2}-1\right){y}={x}^{3}+\left(a^{2}-2a-3\right){x}^{2}+\left(-226a^{2}-259a+103\right){x}+3566a^{2}+4170a-1643$
16.1-a4 16.1-a 3.3.148.1 \( 2^{4} \) $0$ $\Z/2\Z$ $1$ $39.68808396$ 0.815585101 \( 297852964 a^{2} + 348495840 a - 137248100 \) \( \bigl[a^{2} - a - 2\) , \( a^{2} - 2 a - 3\) , \( a + 1\) , \( -119 a^{2} - 139 a + 58\) , \( -1195 a^{2} - 1399 a + 550\bigr] \) ${y}^2+\left(a^{2}-a-2\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a^{2}-2a-3\right){x}^{2}+\left(-119a^{2}-139a+58\right){x}-1195a^{2}-1399a+550$
16.1-a5 16.1-a 3.3.148.1 \( 2^{4} \) $0$ $\Z/2\Z\oplus\Z/2\Z$ $1$ $158.7523358$ 0.815585101 \( 5088 a^{2} + 8224 a + 3904 \) \( \bigl[a^{2} - 1\) , \( a^{2} - 1\) , \( 0\) , \( 2 a^{2} + 2 a - 1\) , \( 0\bigr] \) ${y}^2+\left(a^{2}-1\right){x}{y}={x}^{3}+\left(a^{2}-1\right){x}^{2}+\left(2a^{2}+2a-1\right){x}$
16.1-a6 16.1-a 3.3.148.1 \( 2^{4} \) $0$ $\Z/4\Z$ $1$ $158.7523358$ 0.815585101 \( -2624 a^{2} + 1536 a + 9024 \) \( \bigl[a^{2} - 1\) , \( -a^{2} + a + 1\) , \( a^{2} - a - 2\) , \( 8858 a^{2} + 10364 a - 4082\) , \( -102778712 a^{2} - 120259982 a + 47361573\bigr] \) ${y}^2+\left(a^{2}-1\right){x}{y}+\left(a^{2}-a-2\right){y}={x}^{3}+\left(-a^{2}+a+1\right){x}^{2}+\left(8858a^{2}+10364a-4082\right){x}-102778712a^{2}-120259982a+47361573$
17.1-a1 17.1-a 3.3.148.1 \( 17 \) $0$ $\Z/2\Z$ $1$ $27.09027313$ 0.556701683 \( \frac{1166385842037470}{17} a^{2} - \frac{2894050974029619}{17} a + \frac{787508804920048}{17} \) \( \bigl[a^{2} - 2\) , \( -a^{2} + a + 3\) , \( a\) , \( 238 a^{2} - 154 a - 789\) , \( -2388 a^{2} + 1668 a + 7624\bigr] \) ${y}^2+\left(a^{2}-2\right){x}{y}+a{y}={x}^{3}+\left(-a^{2}+a+3\right){x}^{2}+\left(238a^{2}-154a-789\right){x}-2388a^{2}+1668a+7624$
17.1-a2 17.1-a 3.3.148.1 \( 17 \) $0$ $\Z/2\Z$ $1$ $6.772568284$ 0.556701683 \( \frac{2039354031507687810}{83521} a^{2} + \frac{2386220594007153091}{83521} a - \frac{939757029887526432}{83521} \) \( \bigl[a^{2} - 2\) , \( -a^{2} + a + 3\) , \( a\) , \( 28 a^{2} - 24 a - 99\) , \( 108 a^{2} - 86 a - 366\bigr] \) ${y}^2+\left(a^{2}-2\right){x}{y}+a{y}={x}^{3}+\left(-a^{2}+a+3\right){x}^{2}+\left(28a^{2}-24a-99\right){x}+108a^{2}-86a-366$
17.1-a3 17.1-a 3.3.148.1 \( 17 \) $0$ $\Z/2\Z\oplus\Z/2\Z$ $1$ $54.18054627$ 0.556701683 \( \frac{1479738789}{289} a^{2} - \frac{1677591684}{289} a + \frac{392777968}{289} \) \( \bigl[a^{2} - 2\) , \( -a^{2} + a + 3\) , \( a\) , \( 13 a^{2} - 9 a - 44\) , \( -22 a^{2} + 15 a + 69\bigr] \) ${y}^2+\left(a^{2}-2\right){x}{y}+a{y}={x}^{3}+\left(-a^{2}+a+3\right){x}^{2}+\left(13a^{2}-9a-44\right){x}-22a^{2}+15a+69$
17.1-a4 17.1-a 3.3.148.1 \( 17 \) $0$ $\Z/4\Z$ $1$ $108.3610925$ 0.556701683 \( \frac{6748}{17} a^{2} - \frac{43238}{17} a + \frac{12799}{17} \) \( \bigl[a^{2} - 2\) , \( -a^{2} + a + 3\) , \( a\) , \( -2 a^{2} + a + 6\) , \( -3 a^{2} + 2 a + 9\bigr] \) ${y}^2+\left(a^{2}-2\right){x}{y}+a{y}={x}^{3}+\left(-a^{2}+a+3\right){x}^{2}+\left(-2a^{2}+a+6\right){x}-3a^{2}+2a+9$
19.1-a1 19.1-a 3.3.148.1 \( 19 \) $0$ $\Z/6\Z$ $1$ $148.1410998$ 0.676506855 \( \frac{309847904}{361} a^{2} + \frac{362105728}{361} a - \frac{142642480}{361} \) \( \bigl[a^{2} - a - 2\) , \( -1\) , \( a\) , \( -10233 a^{2} - 11974 a + 4716\) , \( 1041051 a^{2} + 1218120 a - 479728\bigr] \) ${y}^2+\left(a^{2}-a-2\right){x}{y}+a{y}={x}^{3}-{x}^{2}+\left(-10233a^{2}-11974a+4716\right){x}+1041051a^{2}+1218120a-479728$
19.1-a2 19.1-a 3.3.148.1 \( 19 \) $0$ $\Z/2\Z$ $1$ $5.486707401$ 0.676506855 \( \frac{15636831814539296}{47045881} a^{2} - \frac{38648046941482112}{47045881} a + \frac{10231591814174352}{47045881} \) \( \bigl[a^{2} - a - 2\) , \( -1\) , \( a\) , \( -24578 a^{2} - 28759 a + 11326\) , \( -2418130 a^{2} - 2829421 a + 1114301\bigr] \) ${y}^2+\left(a^{2}-a-2\right){x}{y}+a{y}={x}^{3}-{x}^{2}+\left(-24578a^{2}-28759a+11326\right){x}-2418130a^{2}-2829421a+1114301$
19.1-a3 19.1-a 3.3.148.1 \( 19 \) $0$ $\Z/2\Z$ $1$ $10.97341480$ 0.676506855 \( -\frac{72241514230136832}{6859} a^{2} + \frac{49766614320668672}{6859} a + \frac{232207325676879872}{6859} \) \( \bigl[0\) , \( -a^{2} + 2\) , \( a^{2} - a - 1\) , \( 20 a^{2} - 9 a - 70\) , \( 81 a^{2} - 52 a - 273\bigr] \) ${y}^2+\left(a^{2}-a-1\right){y}={x}^{3}+\left(-a^{2}+2\right){x}^{2}+\left(20a^{2}-9a-70\right){x}+81a^{2}-52a-273$
19.1-a4 19.1-a 3.3.148.1 \( 19 \) $0$ $\Z/6\Z$ $1$ $296.2821996$ 0.676506855 \( -\frac{16384}{19} a^{2} - \frac{319488}{19} a + \frac{737280}{19} \) \( \bigl[0\) , \( -a^{2} + 2\) , \( a^{2} - a - 1\) , \( a\) , \( -1\bigr] \) ${y}^2+\left(a^{2}-a-1\right){y}={x}^{3}+\left(-a^{2}+2\right){x}^{2}+a{x}-1$
19.1-b1 19.1-b 3.3.148.1 \( 19 \) $1$ $\Z/2\Z$ $1.264840851$ $2.907033256$ 0.453363221 \( \frac{34600248516351310880}{6131066257801} a^{2} + \frac{14707001073639931296}{6131066257801} a - \frac{7931450838072839760}{6131066257801} \) \( \bigl[a^{2} - a - 2\) , \( a^{2} - a - 2\) , \( a^{2} - 2\) , \( -75390 a^{2} - 88214 a + 34739\) , \( -20772669 a^{2} - 24305819 a + 9572276\bigr] \) ${y}^2+\left(a^{2}-a-2\right){x}{y}+\left(a^{2}-2\right){y}={x}^{3}+\left(a^{2}-a-2\right){x}^{2}+\left(-75390a^{2}-88214a+34739\right){x}-20772669a^{2}-24305819a+9572276$
19.1-b2 19.1-b 3.3.148.1 \( 19 \) $1$ $\Z/10\Z$ $0.252968170$ $363.3791571$ 0.453363221 \( \frac{19422176}{361} a^{2} - \frac{29688224}{361} a + \frac{7279536}{361} \) \( \bigl[a^{2} - a - 2\) , \( -a^{2} + a + 2\) , \( a^{2} - 2\) , \( -1\) , \( -a^{2} + 3\bigr] \) ${y}^2+\left(a^{2}-a-2\right){x}{y}+\left(a^{2}-2\right){y}={x}^{3}+\left(-a^{2}+a+2\right){x}^{2}-{x}-a^{2}+3$
19.1-b3 19.1-b 3.3.148.1 \( 19 \) $1$ $\Z/10\Z$ $0.505936340$ $363.3791571$ 0.453363221 \( -\frac{2985984}{19} a^{2} + \frac{2048000}{19} a + \frac{9617408}{19} \) \( \bigl[0\) , \( -a\) , \( 1\) , \( -2423600 a^{2} - 2835822 a + 1116822\) , \( 78861696894 a^{2} + 92275005848 a - 36340347438\bigr] \) ${y}^2+{y}={x}^{3}-a{x}^{2}+\left(-2423600a^{2}-2835822a+1116822\right){x}+78861696894a^{2}+92275005848a-36340347438$
19.1-b4 19.1-b 3.3.148.1 \( 19 \) $1$ $\Z/2\Z$ $2.529681702$ $2.907033256$ 0.453363221 \( \frac{21475865428001583104}{2476099} a^{2} - \frac{53285799291084800000}{2476099} a + \frac{14499029076062806016}{2476099} \) \( \bigl[0\) , \( -a^{2} + 2 a + 3\) , \( 1\) , \( -14413186731445 a^{2} - 16864675023680 a + 6641756824108\) , \( -63968762883395881049 a^{2} - 74848985016046516967 a + 29477517729190614798\bigr] \) ${y}^2+{y}={x}^{3}+\left(-a^{2}+2a+3\right){x}^{2}+\left(-14413186731445a^{2}-16864675023680a+6641756824108\right){x}-63968762883395881049a^{2}-74848985016046516967a+29477517729190614798$
20.1-a1 20.1-a 3.3.148.1 \( 2^{2} \cdot 5 \) $0$ $\Z/6\Z$ $1$ $56.24286296$ 0.770522476 \( \frac{13838352792668}{25} a^{2} - \frac{34335804621874}{25} a + \frac{9343051795654}{25} \) \( \bigl[a^{2} - a - 2\) , \( 0\) , \( a^{2} - 1\) , \( 1292 a^{2} + 1512 a - 596\) , \( 38980968 a^{2} + 45611104 a - 17962864\bigr] \) ${y}^2+\left(a^{2}-a-2\right){x}{y}+\left(a^{2}-1\right){y}={x}^{3}+\left(1292a^{2}+1512a-596\right){x}+38980968a^{2}+45611104a-17962864$
20.1-a2 20.1-a 3.3.148.1 \( 2^{2} \cdot 5 \) $0$ $\Z/2\Z$ $1$ $2.083068998$ 0.770522476 \( -\frac{8271321267405818624506172}{15625} a^{2} + \frac{5698048560343235071057746}{15625} a + \frac{26586671253641020172342134}{15625} \) \( \bigl[a^{2} - a - 2\) , \( 0\) , \( a^{2} - 1\) , \( -11628 a^{2} - 13608 a + 5354\) , \( -1052486900 a^{2} - 1231500702 a + 484997670\bigr] \) ${y}^2+\left(a^{2}-a-2\right){x}{y}+\left(a^{2}-1\right){y}={x}^{3}+\left(-11628a^{2}-13608a+5354\right){x}-1052486900a^{2}-1231500702a+484997670$
20.1-a3 20.1-a 3.3.148.1 \( 2^{2} \cdot 5 \) $0$ $\Z/2\Z\oplus\Z/6\Z$ $1$ $224.9714518$ 0.770522476 \( \frac{185785252}{625} a^{2} - \frac{445080936}{625} a + \frac{123160356}{625} \) \( \bigl[a^{2} - a - 2\) , \( 0\) , \( a^{2} - 1\) , \( -56443 a^{2} - 66043 a + 26009\) , \( 13218157 a^{2} + 15466387 a - 6091074\bigr] \) ${y}^2+\left(a^{2}-a-2\right){x}{y}+\left(a^{2}-1\right){y}={x}^{3}+\left(-56443a^{2}-66043a+26009\right){x}+13218157a^{2}+15466387a-6091074$
20.1-a4 20.1-a 3.3.148.1 \( 2^{2} \cdot 5 \) $0$ $\Z/2\Z\oplus\Z/2\Z$ $1$ $8.332275994$ 0.770522476 \( -\frac{3077332109418143868}{244140625} a^{2} + \frac{2119953522630977224}{244140625} a + \frac{9891535601060896996}{244140625} \) \( \bigl[a^{2} - a - 2\) , \( 0\) , \( a^{2} - 1\) , \( -516708 a^{2} - 604593 a + 238104\) , \( -366738953 a^{2} - 429116293 a + 168997390\bigr] \) ${y}^2+\left(a^{2}-a-2\right){x}{y}+\left(a^{2}-1\right){y}={x}^{3}+\left(-516708a^{2}-604593a+238104\right){x}-366738953a^{2}-429116293a+168997390$
20.1-a5 20.1-a 3.3.148.1 \( 2^{2} \cdot 5 \) $0$ $\Z/6\Z$ $1$ $56.24286296$ 0.770522476 \( \frac{148445904580292}{390625} a^{2} + \frac{173694846086594}{390625} a - \frac{68405381268774}{390625} \) \( \bigl[a^{2} - a - 2\) , \( 0\) , \( a^{2} - 1\) , \( -898838 a^{2} - 1051718 a + 414194\) , \( 854513176 a^{2} + 999854320 a - 393769180\bigr] \) ${y}^2+\left(a^{2}-a-2\right){x}{y}+\left(a^{2}-1\right){y}={x}^{3}+\left(-898838a^{2}-1051718a+414194\right){x}+854513176a^{2}+999854320a-393769180$
20.1-a6 20.1-a 3.3.148.1 \( 2^{2} \cdot 5 \) $0$ $\Z/2\Z$ $1$ $2.083068998$ 0.770522476 \( \frac{3678043576600698623452}{59604644775390625} a^{2} - \frac{2506193844958703814786}{59604644775390625} a - \frac{11746914365786968746294}{59604644775390625} \) \( \bigl[a^{2} - a - 2\) , \( 0\) , \( a^{2} - 1\) , \( -1057168 a^{2} - 1236978 a + 487154\) , \( 532872492 a^{2} + 623506902 a - 245553574\bigr] \) ${y}^2+\left(a^{2}-a-2\right){x}{y}+\left(a^{2}-1\right){y}={x}^{3}+\left(-1057168a^{2}-1236978a+487154\right){x}+532872492a^{2}+623506902a-245553574$
20.1-a7 20.1-a 3.3.148.1 \( 2^{2} \cdot 5 \) $0$ $\Z/6\Z$ $1$ $112.4857259$ 0.770522476 \( -\frac{385146932}{5} a^{2} + \frac{268247176}{5} a + \frac{1242320604}{5} \) \( \bigl[a^{2} - a - 2\) , \( 0\) , \( a + 1\) , \( -101641 a^{2} - 118928 a + 46839\) , \( -32483626 a^{2} - 38008652 a + 14968816\bigr] \) ${y}^2+\left(a^{2}-a-2\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-101641a^{2}-118928a+46839\right){x}-32483626a^{2}-38008652a+14968816$
20.1-a8 20.1-a 3.3.148.1 \( 2^{2} \cdot 5 \) $0$ $\Z/2\Z$ $1$ $4.166137997$ 0.770522476 \( \frac{179143376765057962508}{125} a^{2} + \frac{209613244321350839256}{125} a - \frac{82551261375569819076}{125} \) \( \bigl[a^{2} - a - 2\) , \( 0\) , \( a + 1\) , \( -8231946 a^{2} - 9632088 a + 3793374\) , \( -23684559407 a^{2} - 27712982904 a + 10914108517\bigr] \) ${y}^2+\left(a^{2}-a-2\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-8231946a^{2}-9632088a+3793374\right){x}-23684559407a^{2}-27712982904a+10914108517$
20.1-a9 20.1-a 3.3.148.1 \( 2^{2} \cdot 5 \) $0$ $\Z/2\Z\oplus\Z/6\Z$ $1$ $224.9714518$ 0.770522476 \( -\frac{108768}{25} a^{2} + \frac{75424}{25} a + \frac{407296}{25} \) \( \bigl[a^{2} - 1\) , \( a^{2} - 3\) , \( 0\) , \( -625 a^{2} - 730 a + 290\) , \( -9146 a^{2} - 10702 a + 4214\bigr] \) ${y}^2+\left(a^{2}-1\right){x}{y}={x}^{3}+\left(a^{2}-3\right){x}^{2}+\left(-625a^{2}-730a+290\right){x}-9146a^{2}-10702a+4214$
20.1-a10 20.1-a 3.3.148.1 \( 2^{2} \cdot 5 \) $0$ $\Z/2\Z\oplus\Z/2\Z$ $1$ $8.332275994$ 0.770522476 \( \frac{7209817568672}{15625} a^{2} + \frac{8324376473504}{15625} a - \frac{3284389248384}{15625} \) \( \bigl[a^{2} - 1\) , \( a^{2} - 3\) , \( 0\) , \( -43485 a^{2} - 50880 a + 20040\) , \( -9168052 a^{2} - 10727414 a + 4224740\bigr] \) ${y}^2+\left(a^{2}-1\right){x}{y}={x}^{3}+\left(a^{2}-3\right){x}^{2}+\left(-43485a^{2}-50880a+20040\right){x}-9168052a^{2}-10727414a+4224740$
20.1-a11 20.1-a 3.3.148.1 \( 2^{2} \cdot 5 \) $0$ $\Z/2\Z$ $1$ $4.166137997$ 0.770522476 \( \frac{3238786394956992}{125} a^{2} - \frac{8036058359040256}{125} a + \frac{2186604679552576}{125} \) \( \bigl[a^{2} - 1\) , \( a^{2} - a - 2\) , \( a^{2} - a - 2\) , \( -40 a^{2} + 102 a - 30\) , \( -285 a^{2} + 712 a - 203\bigr] \) ${y}^2+\left(a^{2}-1\right){x}{y}+\left(a^{2}-a-2\right){y}={x}^{3}+\left(a^{2}-a-2\right){x}^{2}+\left(-40a^{2}+102a-30\right){x}-285a^{2}+712a-203$
20.1-a12 20.1-a 3.3.148.1 \( 2^{2} \cdot 5 \) $0$ $\Z/6\Z$ $1$ $112.4857259$ 0.770522476 \( \frac{43712}{5} a^{2} - \frac{105216}{5} a + \frac{28736}{5} \) \( \bigl[a^{2} - 1\) , \( a^{2} - a - 2\) , \( a^{2} - a - 2\) , \( 2 a\) , \( 2 a - 2\bigr] \) ${y}^2+\left(a^{2}-1\right){x}{y}+\left(a^{2}-a-2\right){y}={x}^{3}+\left(a^{2}-a-2\right){x}^{2}+2a{x}+2a-2$
25.1-a1 25.1-a 3.3.148.1 \( 5^{2} \) $0$ $\Z/2\Z$ $1$ $27.32435168$ 1.123023936 \( \frac{344767070183}{25} a^{2} - \frac{855434265001}{25} a + \frac{232763312321}{25} \) \( \bigl[1\) , \( -a - 1\) , \( 1\) , \( 6 a - 10\) , \( -4 a^{2} + 12 a - 9\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(6a-10\right){x}-4a^{2}+12a-9$
25.1-a2 25.1-a 3.3.148.1 \( 5^{2} \) $0$ $\Z/2\Z$ $1$ $54.64870337$ 1.123023936 \( -\frac{227751}{5} a^{2} + \frac{569694}{5} a - \frac{154858}{5} \) \( \bigl[1\) , \( -a - 1\) , \( 1\) , \( a\) , \( -1\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}+\left(-a-1\right){x}^{2}+a{x}-1$
25.2-a1 25.2-a 3.3.148.1 \( 5^{2} \) $0$ $\Z/2\Z$ $1$ $37.43514264$ 1.538574885 \( 7028736 a^{2} - 17440800 a + 4747984 \) \( \bigl[a^{2} - a - 2\) , \( a^{2} - a - 2\) , \( 1\) , \( 58786385 a^{2} + 68785155 a - 27089419\) , \( 1275216929162 a^{2} + 1492114096329 a - 587634150538\bigr] \) ${y}^2+\left(a^{2}-a-2\right){x}{y}+{y}={x}^{3}+\left(a^{2}-a-2\right){x}^{2}+\left(58786385a^{2}+68785155a-27089419\right){x}+1275216929162a^{2}+1492114096329a-587634150538$
25.2-a2 25.2-a 3.3.148.1 \( 5^{2} \) $0$ $\Z/2\Z$ $1$ $37.43514264$ 1.538574885 \( 4096 a \) \( \bigl[0\) , \( a + 1\) , \( a\) , \( -3046 a^{2} - 3557 a + 1402\) , \( 147974 a^{2} + 173152 a - 68191\bigr] \) ${y}^2+a{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-3046a^{2}-3557a+1402\right){x}+147974a^{2}+173152a-68191$
25.2-a3 25.2-a 3.3.148.1 \( 5^{2} \) $0$ $\Z/2\Z$ $1$ $37.43514264$ 1.538574885 \( 491380736 a^{2} + 574509056 a - 227098624 \) \( \bigl[0\) , \( a + 1\) , \( 1\) , \( -4 a^{2} + a\) , \( 95 a^{2} - 265 a + 73\bigr] \) ${y}^2+{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-4a^{2}+a\right){x}+95a^{2}-265a+73$
25.2-a4 25.2-a 3.3.148.1 \( 5^{2} \) $0$ $\Z/2\Z$ $1$ $37.43514264$ 1.538574885 \( -194645795136 a^{2} + 134089931040 a + 625653842512 \) \( \bigl[a + 1\) , \( -a^{2} + 2\) , \( a^{2} - a - 1\) , \( -41518 a^{2} - 48578 a + 19134\) , \( -8607796 a^{2} - 10071865 a + 3966568\bigr] \) ${y}^2+\left(a+1\right){x}{y}+\left(a^{2}-a-1\right){y}={x}^{3}+\left(-a^{2}+2\right){x}^{2}+\left(-41518a^{2}-48578a+19134\right){x}-8607796a^{2}-10071865a+3966568$
25.2-b1 25.2-b 3.3.148.1 \( 5^{2} \) $0$ $\Z/10\Z$ $1$ $271.5184057$ 0.446373509 \( 7028736 a^{2} - 17440800 a + 4747984 \) \( \bigl[a^{2} - a - 2\) , \( a^{2} - a - 3\) , \( a^{2} - a - 1\) , \( 10713 a^{2} + 12536 a - 4937\) , \( 3135860 a^{2} + 3669228 a - 1445040\bigr] \) ${y}^2+\left(a^{2}-a-2\right){x}{y}+\left(a^{2}-a-1\right){y}={x}^{3}+\left(a^{2}-a-3\right){x}^{2}+\left(10713a^{2}+12536a-4937\right){x}+3135860a^{2}+3669228a-1445040$
25.2-b2 25.2-b 3.3.148.1 \( 5^{2} \) $0$ $\Z/2\Z$ $1$ $10.86073623$ 0.446373509 \( 491380736 a^{2} + 574509056 a - 227098624 \) \( \bigl[0\) , \( a^{2} - 2 a - 3\) , \( 1\) , \( -377381 a^{2} - 441567 a + 173905\) , \( -232144315 a^{2} - 271628927 a + 106974682\bigr] \) ${y}^2+{y}={x}^{3}+\left(a^{2}-2a-3\right){x}^{2}+\left(-377381a^{2}-441567a+173905\right){x}-232144315a^{2}-271628927a+106974682$
25.2-b3 25.2-b 3.3.148.1 \( 5^{2} \) $0$ $\Z/10\Z$ $1$ $271.5184057$ 0.446373509 \( 4096 a \) \( \bigl[0\) , \( -a^{2} + 2 a + 2\) , \( a\) , \( -a^{2} - a + 4\) , \( -a^{2} + a + 2\bigr] \) ${y}^2+a{y}={x}^{3}+\left(-a^{2}+2a+2\right){x}^{2}+\left(-a^{2}-a+4\right){x}-a^{2}+a+2$
25.2-b4 25.2-b 3.3.148.1 \( 5^{2} \) $0$ $\Z/2\Z$ $1$ $10.86073623$ 0.446373509 \( -194645795136 a^{2} + 134089931040 a + 625653842512 \) \( \bigl[a + 1\) , \( a^{2} - 2 a - 1\) , \( a^{2} - 2\) , \( -5312850765 a^{2} - 6216494888 a + 2448220752\) , \( -394174470602711 a^{2} - 461218221425205 a + 181639982107606\bigr] \) ${y}^2+\left(a+1\right){x}{y}+\left(a^{2}-2\right){y}={x}^{3}+\left(a^{2}-2a-1\right){x}^{2}+\left(-5312850765a^{2}-6216494888a+2448220752\right){x}-394174470602711a^{2}-461218221425205a+181639982107606$
26.1-a1 26.1-a 3.3.148.1 \( 2 \cdot 13 \) $0$ $\Z/3\Z$ $1$ $83.69718755$ 0.764429604 \( \frac{47519}{26} a^{2} - \frac{15283}{13} a - \frac{161671}{26} \) \( \bigl[1\) , \( a^{2} - 2 a - 3\) , \( a^{2} - 2\) , \( -a^{2} + 4\) , \( -a - 1\bigr] \) ${y}^2+{x}{y}+\left(a^{2}-2\right){y}={x}^{3}+\left(a^{2}-2a-3\right){x}^{2}+\left(-a^{2}+4\right){x}-a-1$
26.1-a2 26.1-a 3.3.148.1 \( 2 \cdot 13 \) $0$ $\mathsf{trivial}$ $1$ $3.099895835$ 0.764429604 \( -\frac{936828579535}{4394} a^{2} + \frac{1669497916531}{4394} a - \frac{428712816945}{4394} \) \( \bigl[1\) , \( a^{2} - 2 a - 3\) , \( a^{2} - 2\) , \( -26 a^{2} - 25 a + 19\) , \( -93 a^{2} - 111 a + 36\bigr] \) ${y}^2+{x}{y}+\left(a^{2}-2\right){y}={x}^{3}+\left(a^{2}-2a-3\right){x}^{2}+\left(-26a^{2}-25a+19\right){x}-93a^{2}-111a+36$
26.1-b1 26.1-b 3.3.148.1 \( 2 \cdot 13 \) $0$ $\mathsf{trivial}$ $1$ $0.292786373$ 1.179277689 \( \frac{2930762217049733062408935}{125497034} a^{2} - \frac{1009489594983775464711535}{62748517} a - \frac{9420406871887862637780499}{125497034} \) \( \bigl[1\) , \( a^{2} - a - 1\) , \( a\) , \( -412332 a^{2} - 482491 a + 189971\) , \( -265768689 a^{2} - 310972408 a + 122469086\bigr] \) ${y}^2+{x}{y}+a{y}={x}^{3}+\left(a^{2}-a-1\right){x}^{2}+\left(-412332a^{2}-482491a+189971\right){x}-265768689a^{2}-310972408a+122469086$
26.1-b2 26.1-b 3.3.148.1 \( 2 \cdot 13 \) $0$ $\Z/7\Z$ $1$ $100.4257259$ 1.179277689 \( -\frac{192290305}{104} a^{2} + \frac{119296865}{26} a - \frac{129845369}{104} \) \( \bigl[1\) , \( -a^{2} + 1\) , \( a + 1\) , \( a^{2} - 2\) , \( 20 a^{2} - 15 a - 66\bigr] \) ${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a^{2}+1\right){x}^{2}+\left(a^{2}-2\right){x}+20a^{2}-15a-66$
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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.