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Label Class Base field Conductor norm Rank Torsion CM Regulator Period Leading coeff j-invariant Weierstrass coefficients Weierstrass equation
1.1-a1 1.1-a 6.6.300125.1 \( 1 \) $0$ $\mathsf{trivial}$ $1$ \( -162677523113838677 \) \( \bigl[-2 a^{5} + a^{4} + 14 a^{3} + 4 a^{2} - 9 a - 2\) , \( -3 a^{5} + 2 a^{4} + 20 a^{3} + 3 a^{2} - 12 a\) , \( -5 a^{5} + a^{4} + 37 a^{3} + 18 a^{2} - 26 a - 7\) , \( 321037 a^{5} - 77286 a^{4} - 2300766 a^{3} - 1111743 a^{2} + 1379267 a + 398326\) , \( 54665451 a^{5} - 12782935 a^{4} - 392075036 a^{3} - 191607310 a^{2} + 234159226 a + 69935775\bigr] \) ${y}^2+\left(-2a^{5}+a^{4}+14a^{3}+4a^{2}-9a-2\right){x}{y}+\left(-5a^{5}+a^{4}+37a^{3}+18a^{2}-26a-7\right){y}={x}^{3}+\left(-3a^{5}+2a^{4}+20a^{3}+3a^{2}-12a\right){x}^{2}+\left(321037a^{5}-77286a^{4}-2300766a^{3}-1111743a^{2}+1379267a+398326\right){x}+54665451a^{5}-12782935a^{4}-392075036a^{3}-191607310a^{2}+234159226a+69935775$
1.1-a2 1.1-a 6.6.300125.1 \( 1 \) $0$ $\Z/37\Z$ $1$ \( -9317 \) \( \bigl[-2 a^{5} + a^{4} + 14 a^{3} + 4 a^{2} - 9 a - 2\) , \( -3 a^{5} + 2 a^{4} + 20 a^{3} + 3 a^{2} - 12 a\) , \( -5 a^{5} + a^{4} + 37 a^{3} + 18 a^{2} - 26 a - 7\) , \( 7 a^{5} - a^{4} - 51 a^{3} - 28 a^{2} + 27 a + 11\) , \( -13 a^{5} + 4 a^{4} + 92 a^{3} + 40 a^{2} - 56 a - 16\bigr] \) ${y}^2+\left(-2a^{5}+a^{4}+14a^{3}+4a^{2}-9a-2\right){x}{y}+\left(-5a^{5}+a^{4}+37a^{3}+18a^{2}-26a-7\right){y}={x}^{3}+\left(-3a^{5}+2a^{4}+20a^{3}+3a^{2}-12a\right){x}^{2}+\left(7a^{5}-a^{4}-51a^{3}-28a^{2}+27a+11\right){x}-13a^{5}+4a^{4}+92a^{3}+40a^{2}-56a-16$
49.1-a1 49.1-a 6.6.300125.1 \( 7^{2} \) $0$ $\mathsf{trivial}$ $1$ \( -\frac{2887553024}{16807} \) \( \bigl[0\) , \( 4 a^{5} - a^{4} - 29 a^{3} - 13 a^{2} + 19 a + 5\) , \( 1\) , \( 120 a^{5} - 30 a^{4} - 870 a^{3} - 390 a^{2} + 570 a + 91\) , \( 408 a^{5} - 102 a^{4} - 2958 a^{3} - 1326 a^{2} + 1938 a + 324\bigr] \) ${y}^2+{y}={x}^{3}+\left(4a^{5}-a^{4}-29a^{3}-13a^{2}+19a+5\right){x}^{2}+\left(120a^{5}-30a^{4}-870a^{3}-390a^{2}+570a+91\right){x}+408a^{5}-102a^{4}-2958a^{3}-1326a^{2}+1938a+324$
49.1-a2 49.1-a 6.6.300125.1 \( 7^{2} \) $0$ $\Z/5\Z$ $1$ \( \frac{4096}{7} \) \( \bigl[0\) , \( 4 a^{5} - a^{4} - 29 a^{3} - 13 a^{2} + 19 a + 5\) , \( 1\) , \( 1\) , \( 0\bigr] \) ${y}^2+{y}={x}^{3}+\left(4a^{5}-a^{4}-29a^{3}-13a^{2}+19a+5\right){x}^{2}+{x}$
64.1-a1 64.1-a 6.6.300125.1 \( 2^{6} \) $0$ $\mathsf{trivial}$ $1$ \( -\frac{5745702166029}{8192} \) \( \bigl[-2 a^{5} + a^{4} + 14 a^{3} + 4 a^{2} - 9 a - 2\) , \( -3 a^{5} + a^{4} + 21 a^{3} + 8 a^{2} - 10 a - 1\) , \( -6 a^{5} + 2 a^{4} + 43 a^{3} + 17 a^{2} - 29 a - 6\) , \( 10524 a^{5} - 2534 a^{4} - 75422 a^{3} - 36441 a^{2} + 45216 a + 13058\) , \( 342107 a^{5} - 79925 a^{4} - 2453847 a^{3} - 1199258 a^{2} + 1465409 a + 437699\bigr] \) ${y}^2+\left(-2a^{5}+a^{4}+14a^{3}+4a^{2}-9a-2\right){x}{y}+\left(-6a^{5}+2a^{4}+43a^{3}+17a^{2}-29a-6\right){y}={x}^{3}+\left(-3a^{5}+a^{4}+21a^{3}+8a^{2}-10a-1\right){x}^{2}+\left(10524a^{5}-2534a^{4}-75422a^{3}-36441a^{2}+45216a+13058\right){x}+342107a^{5}-79925a^{4}-2453847a^{3}-1199258a^{2}+1465409a+437699$
64.1-a2 64.1-a 6.6.300125.1 \( 2^{6} \) $0$ $\Z/13\Z$ $1$ \( -\frac{189}{2} \) \( \bigl[-2 a^{5} + a^{4} + 14 a^{3} + 4 a^{2} - 9 a - 2\) , \( -3 a^{5} + a^{4} + 21 a^{3} + 8 a^{2} - 10 a - 1\) , \( -6 a^{5} + 2 a^{4} + 43 a^{3} + 17 a^{2} - 29 a - 6\) , \( -6 a^{5} + a^{4} + 43 a^{3} + 24 a^{2} - 24 a - 7\) , \( -10 a^{5} + 2 a^{4} + 72 a^{3} + 37 a^{2} - 42 a - 14\bigr] \) ${y}^2+\left(-2a^{5}+a^{4}+14a^{3}+4a^{2}-9a-2\right){x}{y}+\left(-6a^{5}+2a^{4}+43a^{3}+17a^{2}-29a-6\right){y}={x}^{3}+\left(-3a^{5}+a^{4}+21a^{3}+8a^{2}-10a-1\right){x}^{2}+\left(-6a^{5}+a^{4}+43a^{3}+24a^{2}-24a-7\right){x}-10a^{5}+2a^{4}+72a^{3}+37a^{2}-42a-14$
64.1-b1 64.1-b 6.6.300125.1 \( 2^{6} \) $0$ $\mathsf{trivial}$ $1$ \( \frac{1323}{256} \) \( \bigl[-2 a^{5} + a^{4} + 14 a^{3} + 4 a^{2} - 10 a - 2\) , \( 7 a^{5} - 2 a^{4} - 50 a^{3} - 22 a^{2} + 32 a + 10\) , \( -4 a^{5} + a^{4} + 29 a^{3} + 13 a^{2} - 18 a - 5\) , \( 11 a^{5} - 3 a^{4} - 79 a^{3} - 34 a^{2} + 51 a + 16\) , \( 7 a^{5} + a^{4} - 55 a^{3} - 37 a^{2} + 47 a + 8\bigr] \) ${y}^2+\left(-2a^{5}+a^{4}+14a^{3}+4a^{2}-10a-2\right){x}{y}+\left(-4a^{5}+a^{4}+29a^{3}+13a^{2}-18a-5\right){y}={x}^{3}+\left(7a^{5}-2a^{4}-50a^{3}-22a^{2}+32a+10\right){x}^{2}+\left(11a^{5}-3a^{4}-79a^{3}-34a^{2}+51a+16\right){x}+7a^{5}+a^{4}-55a^{3}-37a^{2}+47a+8$
71.1-a1 71.1-a 6.6.300125.1 \( 71 \) $0$ $\Z/2\Z$ $1$ \( -\frac{2098710915405748}{1804229351} a^{5} + \frac{2683537051449484}{1804229351} a^{4} + \frac{13974658584141464}{1804229351} a^{3} - \frac{8128924082191888}{1804229351} a^{2} - \frac{12613327929279580}{1804229351} a + \frac{7776135079307907}{1804229351} \) \( \bigl[-8 a^{5} + 2 a^{4} + 58 a^{3} + 27 a^{2} - 38 a - 12\) , \( a + 1\) , \( -3 a^{5} + 23 a^{3} + 14 a^{2} - 17 a - 5\) , \( 17 a^{5} + a^{4} - 130 a^{3} - 87 a^{2} + 99 a + 31\) , \( 13 a^{5} + 10 a^{4} - 112 a^{3} - 119 a^{2} + 104 a + 35\bigr] \) ${y}^2+\left(-8a^{5}+2a^{4}+58a^{3}+27a^{2}-38a-12\right){x}{y}+\left(-3a^{5}+23a^{3}+14a^{2}-17a-5\right){y}={x}^{3}+\left(a+1\right){x}^{2}+\left(17a^{5}+a^{4}-130a^{3}-87a^{2}+99a+31\right){x}+13a^{5}+10a^{4}-112a^{3}-119a^{2}+104a+35$
71.1-a2 71.1-a 6.6.300125.1 \( 71 \) $0$ $\Z/2\Z$ $1$ \( \frac{182367117100063826098201858}{3255243551009881201} a^{5} - \frac{50495473559193738950995130}{3255243551009881201} a^{4} - \frac{1314604738469846691446620746}{3255243551009881201} a^{3} - \frac{582379993113800706094818270}{3255243551009881201} a^{2} + \frac{859358590365859284077183254}{3255243551009881201} a + \frac{253657973068162907887516563}{3255243551009881201} \) \( \bigl[-6 a^{5} + 2 a^{4} + 43 a^{3} + 17 a^{2} - 28 a - 7\) , \( -7 a^{5} + 2 a^{4} + 50 a^{3} + 22 a^{2} - 30 a - 10\) , \( -a^{5} + 8 a^{3} + 5 a^{2} - 7 a - 2\) , \( 2 a^{5} + 7 a^{4} - 24 a^{3} - 51 a^{2} + 29 a + 8\) , \( -327 a^{5} + 677 a^{4} + 1538 a^{3} - 2267 a^{2} + 286 a + 277\bigr] \) ${y}^2+\left(-6a^{5}+2a^{4}+43a^{3}+17a^{2}-28a-7\right){x}{y}+\left(-a^{5}+8a^{3}+5a^{2}-7a-2\right){y}={x}^{3}+\left(-7a^{5}+2a^{4}+50a^{3}+22a^{2}-30a-10\right){x}^{2}+\left(2a^{5}+7a^{4}-24a^{3}-51a^{2}+29a+8\right){x}-327a^{5}+677a^{4}+1538a^{3}-2267a^{2}+286a+277$
71.1-b1 71.1-b 6.6.300125.1 \( 71 \) $1$ $\Z/2\Z$ $0.006077565$ \( -\frac{76660720898}{5041} a^{5} - \frac{40221525214}{5041} a^{4} + \frac{566215800511}{5041} a^{3} + \frac{1013166984912}{5041} a^{2} - \frac{649398492666}{5041} a - \frac{243375195538}{5041} \) \( \bigl[a^{5} - 7 a^{3} - 5 a^{2} + 3 a + 2\) , \( -3 a^{5} + a^{4} + 21 a^{3} + 9 a^{2} - 11 a - 5\) , \( -2 a^{5} + 15 a^{3} + 10 a^{2} - 9 a - 5\) , \( 78 a^{5} - 17 a^{4} - 560 a^{3} - 282 a^{2} + 331 a + 105\) , \( -183 a^{5} + 43 a^{4} + 1314 a^{3} + 637 a^{2} - 791 a - 228\bigr] \) ${y}^2+\left(a^{5}-7a^{3}-5a^{2}+3a+2\right){x}{y}+\left(-2a^{5}+15a^{3}+10a^{2}-9a-5\right){y}={x}^{3}+\left(-3a^{5}+a^{4}+21a^{3}+9a^{2}-11a-5\right){x}^{2}+\left(78a^{5}-17a^{4}-560a^{3}-282a^{2}+331a+105\right){x}-183a^{5}+43a^{4}+1314a^{3}+637a^{2}-791a-228$
71.1-b2 71.1-b 6.6.300125.1 \( 71 \) $1$ $\Z/2\Z$ $0.003038782$ \( \frac{620271}{71} a^{5} - \frac{86075}{71} a^{4} - \frac{4244894}{71} a^{3} - \frac{3223697}{71} a^{2} + \frac{1638134}{71} a + \frac{2219991}{71} \) \( \bigl[-4 a^{5} + a^{4} + 29 a^{3} + 14 a^{2} - 20 a - 6\) , \( -a^{5} - a^{4} + 9 a^{3} + 10 a^{2} - 8 a - 4\) , \( -3 a^{5} + 23 a^{3} + 14 a^{2} - 17 a - 6\) , \( -8 a^{5} + a^{4} + 59 a^{3} + 33 a^{2} - 42 a - 13\) , \( -3 a^{5} + 23 a^{3} + 14 a^{2} - 17 a - 5\bigr] \) ${y}^2+\left(-4a^{5}+a^{4}+29a^{3}+14a^{2}-20a-6\right){x}{y}+\left(-3a^{5}+23a^{3}+14a^{2}-17a-6\right){y}={x}^{3}+\left(-a^{5}-a^{4}+9a^{3}+10a^{2}-8a-4\right){x}^{2}+\left(-8a^{5}+a^{4}+59a^{3}+33a^{2}-42a-13\right){x}-3a^{5}+23a^{3}+14a^{2}-17a-5$
71.1-c1 71.1-c 6.6.300125.1 \( 71 \) $0$ $\Z/2\Z$ $1$ \( \frac{587708941038435059}{357911} a^{5} - \frac{1265603492393330221}{357911} a^{4} - \frac{2777805214368944418}{357911} a^{3} + \frac{4226938618080494427}{357911} a^{2} - \frac{557463680741173951}{357911} a - \frac{522744849211037800}{357911} \) \( \bigl[a^{5} - 7 a^{3} - 5 a^{2} + 3 a + 3\) , \( 5 a^{5} - a^{4} - 36 a^{3} - 18 a^{2} + 22 a + 7\) , \( a^{5} - 7 a^{3} - 5 a^{2} + 3 a + 2\) , \( -528 a^{5} + 146 a^{4} + 3805 a^{3} + 1699 a^{2} - 2485 a - 750\) , \( -3732 a^{5} + 1043 a^{4} + 26879 a^{3} + 11901 a^{2} - 17570 a - 5200\bigr] \) ${y}^2+\left(a^{5}-7a^{3}-5a^{2}+3a+3\right){x}{y}+\left(a^{5}-7a^{3}-5a^{2}+3a+2\right){y}={x}^{3}+\left(5a^{5}-a^{4}-36a^{3}-18a^{2}+22a+7\right){x}^{2}+\left(-528a^{5}+146a^{4}+3805a^{3}+1699a^{2}-2485a-750\right){x}-3732a^{5}+1043a^{4}+26879a^{3}+11901a^{2}-17570a-5200$
71.1-c2 71.1-c 6.6.300125.1 \( 71 \) $0$ $\Z/6\Z$ $1$ \( -\frac{394331071}{71} a^{5} + \frac{502982191}{71} a^{4} + \frac{2622161216}{71} a^{3} - \frac{1511726364}{71} a^{2} - \frac{2346682133}{71} a + \frac{1435940762}{71} \) \( \bigl[-a^{5} + 8 a^{3} + 5 a^{2} - 8 a - 3\) , \( a^{5} - 7 a^{3} - 5 a^{2} + 3 a + 2\) , \( -a^{5} + 8 a^{3} + 5 a^{2} - 8 a - 3\) , \( -5 a^{5} + 2 a^{4} + 36 a^{3} + 13 a^{2} - 24 a - 7\) , \( -6 a^{5} + 2 a^{4} + 43 a^{3} + 18 a^{2} - 27 a - 8\bigr] \) ${y}^2+\left(-a^{5}+8a^{3}+5a^{2}-8a-3\right){x}{y}+\left(-a^{5}+8a^{3}+5a^{2}-8a-3\right){y}={x}^{3}+\left(a^{5}-7a^{3}-5a^{2}+3a+2\right){x}^{2}+\left(-5a^{5}+2a^{4}+36a^{3}+13a^{2}-24a-7\right){x}-6a^{5}+2a^{4}+43a^{3}+18a^{2}-27a-8$
71.1-c3 71.1-c 6.6.300125.1 \( 71 \) $0$ $\Z/6\Z$ $1$ \( -\frac{756505033288550895}{5041} a^{5} + \frac{964582520701492616}{5041} a^{4} + \frac{5030225884885221547}{5041} a^{3} - \frac{2896578761117562289}{5041} a^{2} - \frac{4498828390434099007}{5041} a + \frac{2750417335307539161}{5041} \) \( \bigl[-4 a^{5} + a^{4} + 29 a^{3} + 14 a^{2} - 20 a - 7\) , \( a^{5} - a^{4} - 6 a^{3} + 2 a\) , \( -4 a^{5} + a^{4} + 29 a^{3} + 13 a^{2} - 19 a - 5\) , \( 6 a^{5} - 19 a^{4} - 16 a^{3} + 68 a^{2} - 19 a - 13\) , \( -302 a^{5} + 643 a^{4} + 1380 a^{3} - 2136 a^{2} + 291 a + 268\bigr] \) ${y}^2+\left(-4a^{5}+a^{4}+29a^{3}+14a^{2}-20a-7\right){x}{y}+\left(-4a^{5}+a^{4}+29a^{3}+13a^{2}-19a-5\right){y}={x}^{3}+\left(a^{5}-a^{4}-6a^{3}+2a\right){x}^{2}+\left(6a^{5}-19a^{4}-16a^{3}+68a^{2}-19a-13\right){x}-302a^{5}+643a^{4}+1380a^{3}-2136a^{2}+291a+268$
71.1-c4 71.1-c 6.6.300125.1 \( 71 \) $0$ $\Z/2\Z$ $1$ \( \frac{24327541810858910206327477464951723}{128100283921} a^{5} + \frac{46601753998625156702376967642738182}{128100283921} a^{4} - \frac{34420881723880340993543691529150699}{128100283921} a^{3} - \frac{51702318733114454996968879886689215}{128100283921} a^{2} + \frac{19549693025048094255769506332868936}{128100283921} a + \frac{8343932980086826206566398495478311}{128100283921} \) \( \bigl[a^{5} - 7 a^{3} - 5 a^{2} + 3 a + 3\) , \( 5 a^{5} - a^{4} - 36 a^{3} - 18 a^{2} + 22 a + 7\) , \( a^{5} - 7 a^{3} - 5 a^{2} + 3 a + 2\) , \( -243 a^{5} + 51 a^{4} + 1770 a^{3} + 874 a^{2} - 1225 a - 500\) , \( -2706 a^{5} + 885 a^{4} + 19377 a^{3} + 7454 a^{2} - 13313 a - 3305\bigr] \) ${y}^2+\left(a^{5}-7a^{3}-5a^{2}+3a+3\right){x}{y}+\left(a^{5}-7a^{3}-5a^{2}+3a+2\right){y}={x}^{3}+\left(5a^{5}-a^{4}-36a^{3}-18a^{2}+22a+7\right){x}^{2}+\left(-243a^{5}+51a^{4}+1770a^{3}+874a^{2}-1225a-500\right){x}-2706a^{5}+885a^{4}+19377a^{3}+7454a^{2}-13313a-3305$
71.2-a1 71.2-a 6.6.300125.1 \( 71 \) $0$ $\Z/2\Z$ $1$ \( -\frac{17404523687941240}{1804229351} a^{5} + \frac{4026524689721292}{1804229351} a^{4} + \frac{1758994589897560}{25411681} a^{3} + \frac{61208366868367188}{1804229351} a^{2} - \frac{74522937160518480}{1804229351} a - \frac{22417514740858745}{1804229351} \) \( \bigl[-8 a^{5} + 2 a^{4} + 58 a^{3} + 27 a^{2} - 38 a - 12\) , \( 4 a^{5} - a^{4} - 29 a^{3} - 13 a^{2} + 18 a + 6\) , \( -4 a^{5} + a^{4} + 29 a^{3} + 14 a^{2} - 19 a - 7\) , \( 41 a^{5} - 12 a^{4} - 293 a^{3} - 130 a^{2} + 184 a + 51\) , \( 48 a^{5} - 13 a^{4} - 345 a^{3} - 156 a^{2} + 217 a + 61\bigr] \) ${y}^2+\left(-8a^{5}+2a^{4}+58a^{3}+27a^{2}-38a-12\right){x}{y}+\left(-4a^{5}+a^{4}+29a^{3}+14a^{2}-19a-7\right){y}={x}^{3}+\left(4a^{5}-a^{4}-29a^{3}-13a^{2}+18a+6\right){x}^{2}+\left(41a^{5}-12a^{4}-293a^{3}-130a^{2}+184a+51\right){x}+48a^{5}-13a^{4}-345a^{3}-156a^{2}+217a+61$
71.2-a2 71.2-a 6.6.300125.1 \( 71 \) $0$ $\Z/2\Z$ $1$ \( -\frac{1668650325888148369768956}{3255243551009881201} a^{5} + \frac{5219910255636454759202144}{3255243551009881201} a^{4} + \frac{21392722809897168726356}{45848500718449031} a^{3} - \frac{6568705647496259706365286}{3255243551009881201} a^{2} + \frac{1274604017322331465353592}{3255243551009881201} a + \frac{846617325226222670995543}{3255243551009881201} \) \( \bigl[-a^{5} + 8 a^{3} + 5 a^{2} - 8 a - 2\) , \( -3 a^{5} + a^{4} + 21 a^{3} + 8 a^{2} - 10 a - 2\) , \( -3 a^{5} + 23 a^{3} + 14 a^{2} - 17 a - 6\) , \( -20 a^{5} + 4 a^{4} + 141 a^{3} + 70 a^{2} - 82 a - 32\) , \( 14 a^{5} - 46 a^{4} - 93 a^{3} + 229 a^{2} + 129 a - 177\bigr] \) ${y}^2+\left(-a^{5}+8a^{3}+5a^{2}-8a-2\right){x}{y}+\left(-3a^{5}+23a^{3}+14a^{2}-17a-6\right){y}={x}^{3}+\left(-3a^{5}+a^{4}+21a^{3}+8a^{2}-10a-2\right){x}^{2}+\left(-20a^{5}+4a^{4}+141a^{3}+70a^{2}-82a-32\right){x}+14a^{5}-46a^{4}-93a^{3}+229a^{2}+129a-177$
71.2-b1 71.2-b 6.6.300125.1 \( 71 \) $1$ $\Z/2\Z$ $0.003038782$ \( -\frac{5033651}{71} a^{5} + \frac{1531845}{71} a^{4} + 506333 a^{3} + \frac{15162761}{71} a^{2} - \frac{22635572}{71} a - \frac{5576043}{71} \) \( \bigl[-8 a^{5} + 2 a^{4} + 58 a^{3} + 27 a^{2} - 39 a - 12\) , \( 4 a^{5} - 2 a^{4} - 28 a^{3} - 7 a^{2} + 18 a + 1\) , \( -5 a^{5} + a^{4} + 37 a^{3} + 18 a^{2} - 26 a - 7\) , \( 22 a^{5} - 4 a^{4} - 160 a^{3} - 84 a^{2} + 102 a + 36\) , \( 12 a^{5} - 4 a^{4} - 87 a^{3} - 34 a^{2} + 62 a + 16\bigr] \) ${y}^2+\left(-8a^{5}+2a^{4}+58a^{3}+27a^{2}-39a-12\right){x}{y}+\left(-5a^{5}+a^{4}+37a^{3}+18a^{2}-26a-7\right){y}={x}^{3}+\left(4a^{5}-2a^{4}-28a^{3}-7a^{2}+18a+1\right){x}^{2}+\left(22a^{5}-4a^{4}-160a^{3}-84a^{2}+102a+36\right){x}+12a^{5}-4a^{4}-87a^{3}-34a^{2}+62a+16$
71.2-b2 71.2-b 6.6.300125.1 \( 71 \) $1$ $\Z/2\Z$ $0.006077565$ \( \frac{2420952621619}{5041} a^{5} - \frac{464004317169}{5041} a^{4} - \frac{246254617652}{71} a^{3} - \frac{9103530423609}{5041} a^{2} + \frac{11054899265248}{5041} a + \frac{4395816073739}{5041} \) \( \bigl[-8 a^{5} + 2 a^{4} + 58 a^{3} + 27 a^{2} - 39 a - 12\) , \( 4 a^{5} - 2 a^{4} - 28 a^{3} - 7 a^{2} + 18 a + 1\) , \( -5 a^{5} + a^{4} + 37 a^{3} + 18 a^{2} - 26 a - 7\) , \( -8 a^{5} + 11 a^{4} + 45 a^{3} - 24 a^{2} - 8 a + 1\) , \( -10 a^{5} - 15 a^{4} + 96 a^{3} + 131 a^{2} - 97 a - 27\bigr] \) ${y}^2+\left(-8a^{5}+2a^{4}+58a^{3}+27a^{2}-39a-12\right){x}{y}+\left(-5a^{5}+a^{4}+37a^{3}+18a^{2}-26a-7\right){y}={x}^{3}+\left(4a^{5}-2a^{4}-28a^{3}-7a^{2}+18a+1\right){x}^{2}+\left(-8a^{5}+11a^{4}+45a^{3}-24a^{2}-8a+1\right){x}-10a^{5}-15a^{4}+96a^{3}+131a^{2}-97a-27$
71.2-c1 71.2-c 6.6.300125.1 \( 71 \) $0$ $\Z/6\Z$ $1$ \( -\frac{6157671897988358782}{5041} a^{5} + \frac{1412103138451778648}{5041} a^{4} + \frac{622422211559407244}{71} a^{3} + \frac{21742343764072550057}{5041} a^{2} - \frac{26347405019322727241}{5041} a - \frac{7989963906425124537}{5041} \) \( \bigl[3 a^{5} - a^{4} - 21 a^{3} - 9 a^{2} + 13 a + 4\) , \( -4 a^{5} + 2 a^{4} + 28 a^{3} + 7 a^{2} - 18 a - 1\) , \( 3 a^{5} - a^{4} - 21 a^{3} - 9 a^{2} + 12 a + 5\) , \( -11 a^{5} + 17 a^{4} + 67 a^{3} - 64 a^{2} - 10 a + 12\) , \( 34 a^{5} - 62 a^{4} - 194 a^{3} + 257 a^{2} + a - 52\bigr] \) ${y}^2+\left(3a^{5}-a^{4}-21a^{3}-9a^{2}+13a+4\right){x}{y}+\left(3a^{5}-a^{4}-21a^{3}-9a^{2}+12a+5\right){y}={x}^{3}+\left(-4a^{5}+2a^{4}+28a^{3}+7a^{2}-18a-1\right){x}^{2}+\left(-11a^{5}+17a^{4}+67a^{3}-64a^{2}-10a+12\right){x}+34a^{5}-62a^{4}-194a^{3}+257a^{2}+a-52$
71.2-c2 71.2-c 6.6.300125.1 \( 71 \) $0$ $\Z/2\Z$ $1$ \( -\frac{6140993876369732421}{357911} a^{5} + \frac{2995509711003984271}{357911} a^{4} + \frac{612900763840498642}{5041} a^{3} + \frac{10566077573872713846}{357911} a^{2} - \frac{30490423575898921834}{357911} a - \frac{2083391722503246749}{357911} \) \( \bigl[a^{5} - 7 a^{3} - 5 a^{2} + 3 a + 3\) , \( 3 a^{5} - a^{4} - 21 a^{3} - 8 a^{2} + 10 a + 1\) , \( a^{5} - 7 a^{3} - 5 a^{2} + 2 a + 2\) , \( 160 a^{5} - 32 a^{4} - 1154 a^{3} - 592 a^{2} + 710 a + 205\) , \( -79 a^{5} + 80 a^{4} + 491 a^{3} - 91 a^{2} - 150 a - 35\bigr] \) ${y}^2+\left(a^{5}-7a^{3}-5a^{2}+3a+3\right){x}{y}+\left(a^{5}-7a^{3}-5a^{2}+2a+2\right){y}={x}^{3}+\left(3a^{5}-a^{4}-21a^{3}-8a^{2}+10a+1\right){x}^{2}+\left(160a^{5}-32a^{4}-1154a^{3}-592a^{2}+710a+205\right){x}-79a^{5}+80a^{4}+491a^{3}-91a^{2}-150a-35$
71.2-c3 71.2-c 6.6.300125.1 \( 71 \) $0$ $\Z/6\Z$ $1$ \( -\frac{3216855688}{71} a^{5} + \frac{738239635}{71} a^{4} + 325159938 a^{3} + \frac{11354798953}{71} a^{2} - \frac{13765934730}{71} a - \frac{4172364585}{71} \) \( \bigl[3 a^{5} - a^{4} - 21 a^{3} - 9 a^{2} + 13 a + 5\) , \( a^{2} - 2\) , \( -2 a^{5} + 15 a^{3} + 10 a^{2} - 9 a - 4\) , \( -5 a^{5} + 2 a^{4} + 37 a^{3} + 15 a^{2} - 25 a - 6\) , \( -2 a^{5} + a^{4} + 17 a^{3} + 9 a^{2} - 12 a - 4\bigr] \) ${y}^2+\left(3a^{5}-a^{4}-21a^{3}-9a^{2}+13a+5\right){x}{y}+\left(-2a^{5}+15a^{3}+10a^{2}-9a-4\right){y}={x}^{3}+\left(a^{2}-2\right){x}^{2}+\left(-5a^{5}+2a^{4}+37a^{3}+15a^{2}-25a-6\right){x}-2a^{5}+a^{4}+17a^{3}+9a^{2}-12a-4$
71.2-c4 71.2-c 6.6.300125.1 \( 71 \) $0$ $\Z/2\Z$ $1$ \( \frac{13095517607526612645584064951122712336}{128100283921} a^{5} - \frac{3665528766419602968970206427128430838}{128100283921} a^{4} - \frac{1328283723625316342810710439778618405}{1804229351} a^{3} - \frac{41719587011381709944839357304641516914}{128100283921} a^{2} + \frac{61626646160707263603014646395583798619}{128100283921} a + \frac{18185873207131769963818333659583160916}{128100283921} \) \( \bigl[-4 a^{5} + a^{4} + 29 a^{3} + 13 a^{2} - 18 a - 4\) , \( -3 a^{5} + 23 a^{3} + 14 a^{2} - 17 a - 5\) , \( -3 a^{5} + 23 a^{3} + 14 a^{2} - 16 a - 5\) , \( -1192 a^{5} + 784 a^{4} + 7943 a^{3} + 1280 a^{2} - 4145 a - 1190\) , \( -14256 a^{5} + 14083 a^{4} + 88506 a^{3} - 11460 a^{2} - 35243 a - 7572\bigr] \) ${y}^2+\left(-4a^{5}+a^{4}+29a^{3}+13a^{2}-18a-4\right){x}{y}+\left(-3a^{5}+23a^{3}+14a^{2}-16a-5\right){y}={x}^{3}+\left(-3a^{5}+23a^{3}+14a^{2}-17a-5\right){x}^{2}+\left(-1192a^{5}+784a^{4}+7943a^{3}+1280a^{2}-4145a-1190\right){x}-14256a^{5}+14083a^{4}+88506a^{3}-11460a^{2}-35243a-7572$
71.3-a1 71.3-a 6.6.300125.1 \( 71 \) $0$ $\Z/2\Z$ $1$ \( \frac{28618507660868}{1804229351} a^{5} + \frac{72913497392328}{1804229351} a^{4} - \frac{19705446541660}{1804229351} a^{3} - \frac{57325413156020}{1804229351} a^{2} + \frac{151711549020}{25411681} a + \frac{4220073576031}{1804229351} \) \( \bigl[a\) , \( -7 a^{5} + 3 a^{4} + 49 a^{3} + 16 a^{2} - 32 a - 5\) , \( -a^{5} + 8 a^{3} + 5 a^{2} - 7 a - 3\) , \( -a^{5} - a^{4} + 9 a^{3} + 8 a^{2} - 4 a - 2\) , \( 2 a^{5} - 10 a^{4} + 2 a^{3} + 30 a^{2} - 16\bigr] \) ${y}^2+a{x}{y}+\left(-a^{5}+8a^{3}+5a^{2}-7a-3\right){y}={x}^{3}+\left(-7a^{5}+3a^{4}+49a^{3}+16a^{2}-32a-5\right){x}^{2}+\left(-a^{5}-a^{4}+9a^{3}+8a^{2}-4a-2\right){x}+2a^{5}-10a^{4}+2a^{3}+30a^{2}-16$
71.3-a2 71.3-a 6.6.300125.1 \( 71 \) $0$ $\Z/2\Z$ $1$ \( \frac{7245137537592799459668364}{3255243551009881201} a^{5} - \frac{17175864433733831866928686}{3255243551009881201} a^{4} - \frac{29002126063391338539879632}{3255243551009881201} a^{3} + \frac{59053137968044220795988828}{3255243551009881201} a^{2} - \frac{333346305063766203121436}{45848500718449031} a + \frac{536537380242287614298139}{3255243551009881201} \) \( \bigl[3 a^{5} - a^{4} - 21 a^{3} - 9 a^{2} + 13 a + 4\) , \( -2 a^{5} + a^{4} + 14 a^{3} + 4 a^{2} - 11 a - 1\) , \( -3 a^{5} + 23 a^{3} + 14 a^{2} - 17 a - 6\) , \( -7 a^{5} - 2 a^{4} + 55 a^{3} + 44 a^{2} - 32 a - 25\) , \( 88 a^{5} - 195 a^{4} - 254 a^{3} + 186 a^{2} + 98 a - 25\bigr] \) ${y}^2+\left(3a^{5}-a^{4}-21a^{3}-9a^{2}+13a+4\right){x}{y}+\left(-3a^{5}+23a^{3}+14a^{2}-17a-6\right){y}={x}^{3}+\left(-2a^{5}+a^{4}+14a^{3}+4a^{2}-11a-1\right){x}^{2}+\left(-7a^{5}-2a^{4}+55a^{3}+44a^{2}-32a-25\right){x}+88a^{5}-195a^{4}-254a^{3}+186a^{2}+98a-25$
71.3-b1 71.3-b 6.6.300125.1 \( 71 \) $1$ $\Z/2\Z$ $0.006077565$ \( -\frac{2806479973455}{5041} a^{5} + \frac{1209517831721}{5041} a^{4} + \frac{19764644332781}{5041} a^{3} + \frac{6136368206763}{5041} a^{2} - \frac{178823365318}{71} a - \frac{1119026433909}{5041} \) \( \bigl[-6 a^{5} + a^{4} + 44 a^{3} + 23 a^{2} - 28 a - 10\) , \( 3 a^{5} - a^{4} - 21 a^{3} - 8 a^{2} + 12 a + 3\) , \( -5 a^{5} + a^{4} + 37 a^{3} + 18 a^{2} - 26 a - 7\) , \( -82 a^{5} + 24 a^{4} + 591 a^{3} + 257 a^{2} - 391 a - 116\) , \( 161 a^{5} - 45 a^{4} - 1160 a^{3} - 509 a^{2} + 769 a + 227\bigr] \) ${y}^2+\left(-6a^{5}+a^{4}+44a^{3}+23a^{2}-28a-10\right){x}{y}+\left(-5a^{5}+a^{4}+37a^{3}+18a^{2}-26a-7\right){y}={x}^{3}+\left(3a^{5}-a^{4}-21a^{3}-8a^{2}+12a+3\right){x}^{2}+\left(-82a^{5}+24a^{4}+591a^{3}+257a^{2}-391a-116\right){x}+161a^{5}-45a^{4}-1160a^{3}-509a^{2}+769a+227$
71.3-b2 71.3-b 6.6.300125.1 \( 71 \) $1$ $\Z/2\Z$ $0.003038782$ \( \frac{1827756}{71} a^{5} - \frac{703934}{71} a^{4} - \frac{12966589}{71} a^{3} - \frac{4193644}{71} a^{2} + 114206 a + \frac{775598}{71} \) \( \bigl[-5 a^{5} + a^{4} + 37 a^{3} + 18 a^{2} - 26 a - 7\) , \( 3 a^{5} - a^{4} - 21 a^{3} - 9 a^{2} + 13 a + 3\) , \( 3 a^{5} - a^{4} - 21 a^{3} - 9 a^{2} + 13 a + 4\) , \( 13 a^{5} - 3 a^{4} - 93 a^{3} - 43 a^{2} + 59 a + 17\) , \( -7 a^{5} + 2 a^{4} + 52 a^{3} + 25 a^{2} - 31 a - 9\bigr] \) ${y}^2+\left(-5a^{5}+a^{4}+37a^{3}+18a^{2}-26a-7\right){x}{y}+\left(3a^{5}-a^{4}-21a^{3}-9a^{2}+13a+4\right){y}={x}^{3}+\left(3a^{5}-a^{4}-21a^{3}-9a^{2}+13a+3\right){x}^{2}+\left(13a^{5}-3a^{4}-93a^{3}-43a^{2}+59a+17\right){x}-7a^{5}+2a^{4}+52a^{3}+25a^{2}-31a-9$
71.3-c1 71.3-c 6.6.300125.1 \( 71 \) $0$ $\Z/2\Z$ $1$ \( -\frac{12188349191966910976545591421520911263}{128100283921} a^{5} + \frac{2795083691338226342388959981793334127}{128100283921} a^{4} + \frac{87472547643214485589591447553049289390}{128100283921} a^{3} + \frac{43036275357468336314681380908411365576}{128100283921} a^{2} - \frac{734527173722240035758902620347146720}{1804229351} a - \frac{15815145011644535445549863476994175471}{128100283921} \) \( \bigl[-6 a^{5} + a^{4} + 44 a^{3} + 23 a^{2} - 28 a - 9\) , \( 3 a^{5} - a^{4} - 21 a^{3} - 10 a^{2} + 12 a + 6\) , \( a^{5} - 7 a^{3} - 5 a^{2} + 3 a + 2\) , \( 301 a^{5} - 10 a^{4} - 2223 a^{3} - 1411 a^{2} + 1326 a + 389\) , \( 2885 a^{5} - 180 a^{4} - 21196 a^{3} - 12957 a^{2} + 12811 a + 3947\bigr] \) ${y}^2+\left(-6a^{5}+a^{4}+44a^{3}+23a^{2}-28a-9\right){x}{y}+\left(a^{5}-7a^{3}-5a^{2}+3a+2\right){y}={x}^{3}+\left(3a^{5}-a^{4}-21a^{3}-10a^{2}+12a+6\right){x}^{2}+\left(301a^{5}-10a^{4}-2223a^{3}-1411a^{2}+1326a+389\right){x}+2885a^{5}-180a^{4}-21196a^{3}-12957a^{2}+12811a+3947$
71.3-c2 71.3-c 6.6.300125.1 \( 71 \) $0$ $\Z/6\Z$ $1$ \( \frac{8686953}{71} a^{5} + \frac{11816056}{71} a^{4} - \frac{25529599}{71} a^{3} - \frac{21656895}{71} a^{2} + 210469 a + \frac{5162701}{71} \) \( \bigl[-6 a^{5} + 2 a^{4} + 43 a^{3} + 17 a^{2} - 28 a - 6\) , \( -a^{2} + a + 3\) , \( a^{5} - a^{4} - 6 a^{3} + a^{2} + 3 a - 1\) , \( 8 a^{5} - a^{4} - 59 a^{3} - 34 a^{2} + 38 a + 18\) , \( 20 a^{5} - 5 a^{4} - 144 a^{3} - 69 a^{2} + 91 a + 29\bigr] \) ${y}^2+\left(-6a^{5}+2a^{4}+43a^{3}+17a^{2}-28a-6\right){x}{y}+\left(a^{5}-a^{4}-6a^{3}+a^{2}+3a-1\right){y}={x}^{3}+\left(-a^{2}+a+3\right){x}^{2}+\left(8a^{5}-a^{4}-59a^{3}-34a^{2}+38a+18\right){x}+20a^{5}-5a^{4}-144a^{3}-69a^{2}+91a+29$
71.3-c3 71.3-c 6.6.300125.1 \( 71 \) $0$ $\Z/6\Z$ $1$ \( \frac{12287267278054020}{5041} a^{5} + \frac{23544415398400945}{5041} a^{4} - \frac{17366454259785204}{5041} a^{3} - \frac{26109054624611151}{5041} a^{2} + \frac{138912635005304}{71} a + \frac{4211222685079557}{5041} \) \( \bigl[-6 a^{5} + 2 a^{4} + 43 a^{3} + 17 a^{2} - 28 a - 6\) , \( -a^{2} + a + 3\) , \( a^{5} - a^{4} - 6 a^{3} + a^{2} + 3 a - 1\) , \( 48 a^{5} - 11 a^{4} - 344 a^{3} - 169 a^{2} + 198 a + 53\) , \( 315 a^{5} - 72 a^{4} - 2261 a^{3} - 1115 a^{2} + 1350 a + 413\bigr] \) ${y}^2+\left(-6a^{5}+2a^{4}+43a^{3}+17a^{2}-28a-6\right){x}{y}+\left(a^{5}-a^{4}-6a^{3}+a^{2}+3a-1\right){y}={x}^{3}+\left(-a^{2}+a+3\right){x}^{2}+\left(48a^{5}-11a^{4}-344a^{3}-169a^{2}+198a+53\right){x}+315a^{5}-72a^{4}-2261a^{3}-1115a^{2}+1350a+413$
71.3-c4 71.3-c 6.6.300125.1 \( 71 \) $0$ $\Z/2\Z$ $1$ \( \frac{4417193206959849167}{357911} a^{5} - \frac{721150030079876042}{357911} a^{4} - \frac{32357369288619010195}{357911} a^{3} - \frac{16366003801804012761}{357911} a^{2} + \frac{273597199434573362}{5041} a + \frac{5918888612952222917}{357911} \) \( \bigl[-6 a^{5} + a^{4} + 44 a^{3} + 23 a^{2} - 28 a - 9\) , \( 3 a^{5} - a^{4} - 21 a^{3} - 10 a^{2} + 12 a + 6\) , \( a^{5} - 7 a^{3} - 5 a^{2} + 3 a + 2\) , \( -4 a^{5} + 55 a^{4} - 43 a^{3} - 296 a^{2} + 126 a + 59\) , \( -181 a^{5} + 461 a^{4} + 739 a^{3} - 1746 a^{2} + 376 a + 244\bigr] \) ${y}^2+\left(-6a^{5}+a^{4}+44a^{3}+23a^{2}-28a-9\right){x}{y}+\left(a^{5}-7a^{3}-5a^{2}+3a+2\right){y}={x}^{3}+\left(3a^{5}-a^{4}-21a^{3}-10a^{2}+12a+6\right){x}^{2}+\left(-4a^{5}+55a^{4}-43a^{3}-296a^{2}+126a+59\right){x}-181a^{5}+461a^{4}+739a^{3}-1746a^{2}+376a+244$
71.4-a1 71.4-a 6.6.300125.1 \( 71 \) $0$ $\Z/2\Z$ $1$ \( \frac{704803031197900}{1804229351} a^{5} - \frac{2010453848133504}{1804229351} a^{4} - \frac{2574645568787336}{1804229351} a^{3} + \frac{8015459823309236}{1804229351} a^{2} - \frac{2156284877910108}{1804229351} a - \frac{1240401241894705}{1804229351} \) \( \bigl[-4 a^{5} + a^{4} + 29 a^{3} + 14 a^{2} - 19 a - 6\) , \( 11 a^{5} - 3 a^{4} - 79 a^{3} - 36 a^{2} + 52 a + 17\) , \( -5 a^{5} + a^{4} + 37 a^{3} + 18 a^{2} - 27 a - 8\) , \( -74 a^{5} + 22 a^{4} + 533 a^{3} + 231 a^{2} - 348 a - 101\) , \( -794 a^{5} + 224 a^{4} + 5719 a^{3} + 2523 a^{2} - 3738 a - 1101\bigr] \) ${y}^2+\left(-4a^{5}+a^{4}+29a^{3}+14a^{2}-19a-6\right){x}{y}+\left(-5a^{5}+a^{4}+37a^{3}+18a^{2}-27a-8\right){y}={x}^{3}+\left(11a^{5}-3a^{4}-79a^{3}-36a^{2}+52a+17\right){x}^{2}+\left(-74a^{5}+22a^{4}+533a^{3}+231a^{2}-348a-101\right){x}-794a^{5}+224a^{4}+5719a^{3}+2523a^{2}-3738a-1101$
71.4-a2 71.4-a 6.6.300125.1 \( 71 \) $0$ $\Z/2\Z$ $1$ \( \frac{21967998164354285461425122}{3255243551009881201} a^{5} - \frac{5391052931075206605671520}{3255243551009881201} a^{4} - \frac{156246015653998240659421204}{3255243551009881201} a^{3} - \frac{69717312288925414565855022}{3255243551009881201} a^{2} + \frac{102032514074835709609288768}{3255243551009881201} a + \frac{30222798799898190818601583}{3255243551009881201} \) \( \bigl[a\) , \( -a^{5} + a^{4} + 7 a^{3} - 2 a^{2} - 7 a + 3\) , \( -6 a^{5} + a^{4} + 44 a^{3} + 23 a^{2} - 29 a - 10\) , \( 61 a^{5} - 13 a^{4} - 437 a^{3} - 222 a^{2} + 251 a + 75\) , \( 5699 a^{5} - 1304 a^{4} - 40900 a^{3} - 20142 a^{2} + 24368 a + 7391\bigr] \) ${y}^2+a{x}{y}+\left(-6a^{5}+a^{4}+44a^{3}+23a^{2}-29a-10\right){y}={x}^{3}+\left(-a^{5}+a^{4}+7a^{3}-2a^{2}-7a+3\right){x}^{2}+\left(61a^{5}-13a^{4}-437a^{3}-222a^{2}+251a+75\right){x}+5699a^{5}-1304a^{4}-40900a^{3}-20142a^{2}+24368a+7391$
71.4-b1 71.4-b 6.6.300125.1 \( 71 \) $1$ $\Z/2\Z$ $0.003038782$ \( -\frac{4285612}{71} a^{5} + \frac{728978}{71} a^{4} + \frac{31362943}{71} a^{3} + \frac{16332660}{71} a^{2} - \frac{20322774}{71} a - \frac{6420718}{71} \) \( \bigl[-3 a^{5} + a^{4} + 22 a^{3} + 8 a^{2} - 16 a - 2\) , \( -4 a^{5} + 30 a^{3} + 19 a^{2} - 19 a - 7\) , \( -3 a^{5} + a^{4} + 22 a^{3} + 8 a^{2} - 16 a - 2\) , \( -5 a^{5} + 37 a^{3} + 25 a^{2} - 23 a - 11\) , \( -a^{5} + 7 a^{3} + 6 a^{2} - 4 a - 3\bigr] \) ${y}^2+\left(-3a^{5}+a^{4}+22a^{3}+8a^{2}-16a-2\right){x}{y}+\left(-3a^{5}+a^{4}+22a^{3}+8a^{2}-16a-2\right){y}={x}^{3}+\left(-4a^{5}+30a^{3}+19a^{2}-19a-7\right){x}^{2}+\left(-5a^{5}+37a^{3}+25a^{2}-23a-11\right){x}-a^{5}+7a^{3}+6a^{2}-4a-3$
71.4-b2 71.4-b 6.6.300125.1 \( 71 \) $1$ $\Z/2\Z$ $0.006077565$ \( \frac{2634370822463}{5041} a^{5} - \frac{740439838413}{5041} a^{4} - \frac{19177442690303}{5041} a^{3} - \frac{8090290411651}{5041} a^{2} + \frac{13243147162542}{5041} a + \frac{3945985807101}{5041} \) \( \bigl[-3 a^{5} + 23 a^{3} + 14 a^{2} - 16 a - 5\) , \( -4 a^{5} + a^{4} + 29 a^{3} + 14 a^{2} - 21 a - 7\) , \( a^{5} - 7 a^{3} - 5 a^{2} + 3 a + 3\) , \( 23 a^{5} - 17 a^{4} - 160 a^{3} + 3 a^{2} + 116 a - 21\) , \( -39 a^{5} + 37 a^{4} + 268 a^{3} - 63 a^{2} - 227 a + 94\bigr] \) ${y}^2+\left(-3a^{5}+23a^{3}+14a^{2}-16a-5\right){x}{y}+\left(a^{5}-7a^{3}-5a^{2}+3a+3\right){y}={x}^{3}+\left(-4a^{5}+a^{4}+29a^{3}+14a^{2}-21a-7\right){x}^{2}+\left(23a^{5}-17a^{4}-160a^{3}+3a^{2}+116a-21\right){x}-39a^{5}+37a^{4}+268a^{3}-63a^{2}-227a+94$
71.4-c1 71.4-c 6.6.300125.1 \( 71 \) $0$ $\Z/6\Z$ $1$ \( \frac{347779040612919069}{5041} a^{5} - \frac{735086186487273612}{5041} a^{4} - \frac{1615818198289203963}{5041} a^{3} + \frac{2495028141702981708}{5041} a^{2} - \frac{344156570897129140}{5041} a - \frac{312285111948345602}{5041} \) \( \bigl[-a^{5} + 8 a^{3} + 4 a^{2} - 7 a - 1\) , \( -6 a^{5} + a^{4} + 44 a^{3} + 23 a^{2} - 29 a - 11\) , \( -a^{5} + 8 a^{3} + 4 a^{2} - 7 a\) , \( 24 a^{5} - 63 a^{4} - 44 a^{3} + 68 a^{2} + 5 a - 6\) , \( 297 a^{5} - 821 a^{4} - 439 a^{3} + 939 a^{2} - 86 a - 98\bigr] \) ${y}^2+\left(-a^{5}+8a^{3}+4a^{2}-7a-1\right){x}{y}+\left(-a^{5}+8a^{3}+4a^{2}-7a\right){y}={x}^{3}+\left(-6a^{5}+a^{4}+44a^{3}+23a^{2}-29a-11\right){x}^{2}+\left(24a^{5}-63a^{4}-44a^{3}+68a^{2}+5a-6\right){x}+297a^{5}-821a^{4}-439a^{3}+939a^{2}-86a-98$
71.4-c2 71.4-c 6.6.300125.1 \( 71 \) $0$ $\Z/2\Z$ $1$ \( -\frac{10394847966890026874}{357911} a^{5} + \frac{2257127006944677009}{357911} a^{4} + \frac{74885814522798141547}{357911} a^{3} + \frac{37038415740266095494}{357911} a^{2} - \frac{44705744028911194336}{357911} a - \frac{13569453503150492597}{357911} \) \( \bigl[-8 a^{5} + 2 a^{4} + 58 a^{3} + 27 a^{2} - 38 a - 11\) , \( -a^{5} + 8 a^{3} + 5 a^{2} - 9 a - 4\) , \( -a^{5} + 8 a^{3} + 5 a^{2} - 7 a - 2\) , \( 24 a^{5} - 21 a^{4} - 145 a^{3} - 27 a^{2} + 88 a + 6\) , \( 11 a^{5} - 92 a^{4} + 101 a^{3} + 251 a^{2} - 84 a - 106\bigr] \) ${y}^2+\left(-8a^{5}+2a^{4}+58a^{3}+27a^{2}-38a-11\right){x}{y}+\left(-a^{5}+8a^{3}+5a^{2}-7a-2\right){y}={x}^{3}+\left(-a^{5}+8a^{3}+5a^{2}-9a-4\right){x}^{2}+\left(24a^{5}-21a^{4}-145a^{3}-27a^{2}+88a+6\right){x}+11a^{5}-92a^{4}+101a^{3}+251a^{2}-84a-106$
71.4-c3 71.4-c 6.6.300125.1 \( 71 \) $0$ $\Z/6\Z$ $1$ \( \frac{178368935}{71} a^{5} - \frac{383017370}{71} a^{4} - \frac{820587590}{71} a^{3} + \frac{1313585339}{71} a^{2} - \frac{193267801}{71} a - \frac{167117569}{71} \) \( \bigl[-8 a^{5} + 2 a^{4} + 58 a^{3} + 27 a^{2} - 38 a - 11\) , \( -a^{5} + 8 a^{3} + 5 a^{2} - 9 a - 4\) , \( -a^{5} + 8 a^{3} + 5 a^{2} - 7 a - 2\) , \( -16 a^{5} + 4 a^{4} + 115 a^{3} + 53 a^{2} - 72 a - 19\) , \( 5 a^{5} - a^{4} - 36 a^{3} - 20 a^{2} + 21 a + 8\bigr] \) ${y}^2+\left(-8a^{5}+2a^{4}+58a^{3}+27a^{2}-38a-11\right){x}{y}+\left(-a^{5}+8a^{3}+5a^{2}-7a-2\right){y}={x}^{3}+\left(-a^{5}+8a^{3}+5a^{2}-9a-4\right){x}^{2}+\left(-16a^{5}+4a^{4}+115a^{3}+53a^{2}-72a-19\right){x}+5a^{5}-a^{4}-36a^{3}-20a^{2}+21a+8$
71.4-c4 71.4-c 6.6.300125.1 \( 71 \) $0$ $\Z/2\Z$ $1$ \( -\frac{122473963803363478904490388871087231}{128100283921} a^{5} + \frac{369584216037450793046353949556548449}{128100283921} a^{4} + \frac{111624163999057123131195127865875451}{128100283921} a^{3} - \frac{470167022871026850042855444550668562}{128100283921} a^{2} + \frac{91317277554701667937618786737072378}{128100283921} a + \frac{60701131070426909908677598532343306}{128100283921} \) \( \bigl[-3 a^{5} + 23 a^{3} + 14 a^{2} - 16 a - 6\) , \( -3 a^{5} + 23 a^{3} + 14 a^{2} - 16 a - 5\) , \( a^{5} - 7 a^{3} - 5 a^{2} + 2 a + 3\) , \( -42 a^{5} - 18 a^{4} + 323 a^{3} + 285 a^{2} - 118 a - 210\) , \( 84 a^{5} - 417 a^{4} - 158 a^{3} + 1621 a^{2} + 169 a - 898\bigr] \) ${y}^2+\left(-3a^{5}+23a^{3}+14a^{2}-16a-6\right){x}{y}+\left(a^{5}-7a^{3}-5a^{2}+2a+3\right){y}={x}^{3}+\left(-3a^{5}+23a^{3}+14a^{2}-16a-5\right){x}^{2}+\left(-42a^{5}-18a^{4}+323a^{3}+285a^{2}-118a-210\right){x}+84a^{5}-417a^{4}-158a^{3}+1621a^{2}+169a-898$
71.5-a1 71.5-a 6.6.300125.1 \( 71 \) $0$ $\Z/2\Z$ $1$ \( \frac{18671790400300000}{1804229351} a^{5} - \frac{5223136808131864}{1804229351} a^{4} - \frac{134463355085824784}{1804229351} a^{3} - \frac{59498874802185092}{1804229351} a^{2} + \frac{87859926083703700}{1804229351} a + \frac{25940020939985535}{1804229351} \) \( \bigl[-6 a^{5} + 2 a^{4} + 43 a^{3} + 17 a^{2} - 29 a - 7\) , \( a^{5} - 8 a^{3} - 4 a^{2} + 7 a + 2\) , \( -6 a^{5} + a^{4} + 44 a^{3} + 23 a^{2} - 28 a - 10\) , \( 108 a^{5} - 25 a^{4} - 776 a^{3} - 378 a^{2} + 466 a + 140\) , \( 536 a^{5} - 123 a^{4} - 3847 a^{3} - 1892 a^{2} + 2295 a + 696\bigr] \) ${y}^2+\left(-6a^{5}+2a^{4}+43a^{3}+17a^{2}-29a-7\right){x}{y}+\left(-6a^{5}+a^{4}+44a^{3}+23a^{2}-28a-10\right){y}={x}^{3}+\left(a^{5}-8a^{3}-4a^{2}+7a+2\right){x}^{2}+\left(108a^{5}-25a^{4}-776a^{3}-378a^{2}+466a+140\right){x}+536a^{5}-123a^{4}-3847a^{3}-1892a^{2}+2295a+696$
71.5-a2 71.5-a 6.6.300125.1 \( 71 \) $0$ $\Z/2\Z$ $1$ \( -\frac{41014241389245672911233616}{3255243551009881201} a^{5} + \frac{31251665362953723702641564}{3255243551009881201} a^{4} + \frac{283323882933070565416889280}{3255243551009881201} a^{3} - \frac{8921536262849968349901544}{3255243551009881201} a^{2} - \frac{210325636400488563887402742}{3255243551009881201} a + \frac{49837787027906807246579723}{3255243551009881201} \) \( \bigl[-8 a^{5} + 2 a^{4} + 58 a^{3} + 27 a^{2} - 38 a - 12\) , \( -6 a^{5} + 2 a^{4} + 43 a^{3} + 17 a^{2} - 30 a - 6\) , \( -3 a^{5} + 23 a^{3} + 14 a^{2} - 17 a - 6\) , \( 10 a^{5} - 2 a^{4} - 72 a^{3} - 41 a^{2} + 36 a + 12\) , \( 15 a^{5} - 27 a^{4} - 174 a^{3} - 76 a^{2} + 101 a + 30\bigr] \) ${y}^2+\left(-8a^{5}+2a^{4}+58a^{3}+27a^{2}-38a-12\right){x}{y}+\left(-3a^{5}+23a^{3}+14a^{2}-17a-6\right){y}={x}^{3}+\left(-6a^{5}+2a^{4}+43a^{3}+17a^{2}-30a-6\right){x}^{2}+\left(10a^{5}-2a^{4}-72a^{3}-41a^{2}+36a+12\right){x}+15a^{5}-27a^{4}-174a^{3}-76a^{2}+101a+30$
71.5-b1 71.5-b 6.6.300125.1 \( 71 \) $1$ $\Z/2\Z$ $0.006077565$ \( -\frac{3949307338048}{5041} a^{5} + \frac{657783939680}{5041} a^{4} + \frac{28702201019885}{5041} a^{3} + \frac{15411298823022}{5041} a^{2} - \frac{17627754558666}{5041} a - \frac{5427054812636}{5041} \) \( \bigl[-a^{5} + 8 a^{3} + 5 a^{2} - 7 a - 2\) , \( -6 a^{5} + 2 a^{4} + 43 a^{3} + 17 a^{2} - 28 a - 8\) , \( -3 a^{5} + 23 a^{3} + 14 a^{2} - 17 a - 5\) , \( 10 a^{5} - 2 a^{4} - 69 a^{3} - 40 a^{2} + 49 a + 14\) , \( 12 a^{5} + 4 a^{4} - 100 a^{3} - 51 a^{2} + 68 a + 20\bigr] \) ${y}^2+\left(-a^{5}+8a^{3}+5a^{2}-7a-2\right){x}{y}+\left(-3a^{5}+23a^{3}+14a^{2}-17a-5\right){y}={x}^{3}+\left(-6a^{5}+2a^{4}+43a^{3}+17a^{2}-28a-8\right){x}^{2}+\left(10a^{5}-2a^{4}-69a^{3}-40a^{2}+49a+14\right){x}+12a^{5}+4a^{4}-100a^{3}-51a^{2}+68a+20$
71.5-b2 71.5-b 6.6.300125.1 \( 71 \) $1$ $\Z/2\Z$ $0.003038782$ \( \frac{5286451}{71} a^{5} - \frac{1105287}{71} a^{4} - \frac{38268478}{71} a^{3} - \frac{19161741}{71} a^{2} + \frac{24321390}{71} a + \frac{7597551}{71} \) \( \bigl[a^{5} - 7 a^{3} - 5 a^{2} + 2 a + 2\) , \( a^{5} - 7 a^{3} - 5 a^{2} + 3 a + 1\) , \( -3 a^{5} + 23 a^{3} + 14 a^{2} - 17 a - 5\) , \( -3 a^{5} + 2 a^{4} + 20 a^{3} + 4 a^{2} - 10 a - 4\) , \( -2 a^{5} + a^{4} + 14 a^{3} + 4 a^{2} - 8 a - 2\bigr] \) ${y}^2+\left(a^{5}-7a^{3}-5a^{2}+2a+2\right){x}{y}+\left(-3a^{5}+23a^{3}+14a^{2}-17a-5\right){y}={x}^{3}+\left(a^{5}-7a^{3}-5a^{2}+3a+1\right){x}^{2}+\left(-3a^{5}+2a^{4}+20a^{3}+4a^{2}-10a-4\right){x}-2a^{5}+a^{4}+14a^{3}+4a^{2}-8a-2$
71.5-c1 71.5-c 6.6.300125.1 \( 71 \) $0$ $\Z/2\Z$ $1$ \( \frac{688385227545894441783394700691160040}{128100283921} a^{5} - \frac{1455011470820246681274446975813913565}{128100283921} a^{4} - \frac{3198310313219337512071267632384924449}{128100283921} a^{3} + \frac{4938596772879076842480778038133182698}{128100283921} a^{2} - \frac{681214996706145908023368640065836270}{128100283921} a - \frac{618129402248792677846156102081913073}{128100283921} \) \( \bigl[-8 a^{5} + 2 a^{4} + 58 a^{3} + 27 a^{2} - 39 a - 12\) , \( -4 a^{5} + a^{4} + 29 a^{3} + 14 a^{2} - 21 a - 6\) , \( 1\) , \( -944 a^{5} + 1869 a^{4} + 4540 a^{3} - 6026 a^{2} + 652 a + 593\) , \( -34009 a^{5} + 72266 a^{4} + 157382 a^{3} - 246003 a^{2} + 35333 a + 30593\bigr] \) ${y}^2+\left(-8a^{5}+2a^{4}+58a^{3}+27a^{2}-39a-12\right){x}{y}+{y}={x}^{3}+\left(-4a^{5}+a^{4}+29a^{3}+14a^{2}-21a-6\right){x}^{2}+\left(-944a^{5}+1869a^{4}+4540a^{3}-6026a^{2}+652a+593\right){x}-34009a^{5}+72266a^{4}+157382a^{3}-246003a^{2}+35333a+30593$
71.5-c2 71.5-c 6.6.300125.1 \( 71 \) $0$ $\Z/6\Z$ $1$ \( \frac{3453103834}{71} a^{5} - \frac{966256218}{71} a^{4} - \frac{24868045898}{71} a^{3} - \frac{11002493289}{71} a^{2} + \frac{16250723867}{71} a + \frac{4795868035}{71} \) \( \bigl[-2 a^{5} + a^{4} + 14 a^{3} + 4 a^{2} - 10 a - 1\) , \( -7 a^{5} + a^{4} + 51 a^{3} + 28 a^{2} - 32 a - 13\) , \( -a^{5} + 8 a^{3} + 4 a^{2} - 6 a - 1\) , \( 5 a^{5} - 38 a^{3} - 22 a^{2} + 26 a + 9\) , \( -3 a^{5} + a^{4} + 21 a^{3} + 8 a^{2} - 12 a - 4\bigr] \) ${y}^2+\left(-2a^{5}+a^{4}+14a^{3}+4a^{2}-10a-1\right){x}{y}+\left(-a^{5}+8a^{3}+4a^{2}-6a-1\right){y}={x}^{3}+\left(-7a^{5}+a^{4}+51a^{3}+28a^{2}-32a-13\right){x}^{2}+\left(5a^{5}-38a^{3}-22a^{2}+26a+9\right){x}-3a^{5}+a^{4}+21a^{3}+8a^{2}-12a-4$
71.5-c3 71.5-c 6.6.300125.1 \( 71 \) $0$ $\Z/2\Z$ $1$ \( -\frac{235353321428599978}{357911} a^{5} + \frac{580741577725442818}{357911} a^{4} + \frac{1162430939297012415}{357911} a^{3} - \frac{1879545228122345414}{357911} a^{2} + \frac{264656034786687147}{357911} a + \frac{239407872830503392}{357911} \) \( \bigl[a^{5} - a^{4} - 6 a^{3} + a^{2} + 3 a\) , \( -4 a^{5} + 30 a^{3} + 19 a^{2} - 18 a - 9\) , \( -6 a^{5} + 2 a^{4} + 43 a^{3} + 17 a^{2} - 29 a - 6\) , \( -36 a^{5} - 3 a^{4} + 278 a^{3} + 176 a^{2} - 156 a - 75\) , \( 1119 a^{5} - 361 a^{4} - 7802 a^{3} - 3654 a^{2} + 4623 a + 1358\bigr] \) ${y}^2+\left(a^{5}-a^{4}-6a^{3}+a^{2}+3a\right){x}{y}+\left(-6a^{5}+2a^{4}+43a^{3}+17a^{2}-29a-6\right){y}={x}^{3}+\left(-4a^{5}+30a^{3}+19a^{2}-18a-9\right){x}^{2}+\left(-36a^{5}-3a^{4}+278a^{3}+176a^{2}-156a-75\right){x}+1119a^{5}-361a^{4}-7802a^{3}-3654a^{2}+4623a+1358$
71.5-c4 71.5-c 6.6.300125.1 \( 71 \) $0$ $\Z/6\Z$ $1$ \( \frac{6615986088905408509}{5041} a^{5} - \frac{1851862023389315072}{5041} a^{4} - \frac{47645414547979919968}{5041} a^{3} - \frac{21077149500839791045}{5041} a^{2} + \frac{31134395160454919709}{5041} a + \frac{9187684081459759389}{5041} \) \( \bigl[-2 a^{5} + 15 a^{3} + 10 a^{2} - 9 a - 5\) , \( a^{5} - 7 a^{3} - 5 a^{2} + a + 3\) , \( a + 1\) , \( 1534 a^{5} - 351 a^{4} - 11009 a^{3} - 5421 a^{2} + 6557 a + 1992\) , \( -18999 a^{5} + 4356 a^{4} + 136350 a^{3} + 67090 a^{2} - 81287 a - 24651\bigr] \) ${y}^2+\left(-2a^{5}+15a^{3}+10a^{2}-9a-5\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a^{5}-7a^{3}-5a^{2}+a+3\right){x}^{2}+\left(1534a^{5}-351a^{4}-11009a^{3}-5421a^{2}+6557a+1992\right){x}-18999a^{5}+4356a^{4}+136350a^{3}+67090a^{2}-81287a-24651$
71.6-a1 71.6-a 6.6.300125.1 \( 71 \) $0$ $\Z/2\Z$ $1$ \( -\frac{168897361086877089738292772}{3255243551009881201} a^{5} + \frac{36590815305412598961751628}{3255243551009881201} a^{4} + \frac{1215010113934663006249461026}{3255243551009881201} a^{3} + \frac{608534409345028127920951294}{3255243551009881201} a^{2} - \frac{728672484398001360842800916}{3255243551009881201} a - \frac{221646481326554190660944727}{3255243551009881201} \) \( \bigl[-2 a^{5} + a^{4} + 14 a^{3} + 4 a^{2} - 10 a - 2\) , \( -3 a^{5} + 2 a^{4} + 20 a^{3} + 3 a^{2} - 13 a - 1\) , \( a^{5} - a^{4} - 6 a^{3} + a^{2} + 3 a\) , \( -a^{5} + 20 a^{4} - 20 a^{3} - 104 a^{2} + 46 a + 16\) , \( -403 a^{5} + 171 a^{4} + 2816 a^{3} + 961 a^{2} - 1694 a - 488\bigr] \) ${y}^2+\left(-2a^{5}+a^{4}+14a^{3}+4a^{2}-10a-2\right){x}{y}+\left(a^{5}-a^{4}-6a^{3}+a^{2}+3a\right){y}={x}^{3}+\left(-3a^{5}+2a^{4}+20a^{3}+3a^{2}-13a-1\right){x}^{2}+\left(-a^{5}+20a^{4}-20a^{3}-104a^{2}+46a+16\right){x}-403a^{5}+171a^{4}+2816a^{3}+961a^{2}-1694a-488$
71.6-a2 71.6-a 6.6.300125.1 \( 71 \) $0$ $\Z/2\Z$ $1$ \( \frac{98022664188220}{1804229351} a^{5} + \frac{450615417702264}{1804229351} a^{4} - \frac{1805568365714444}{1804229351} a^{3} - \frac{1538702394143424}{1804229351} a^{2} + \frac{1421852364024048}{1804229351} a + \frac{470449120328339}{1804229351} \) \( \bigl[-4 a^{5} + a^{4} + 29 a^{3} + 13 a^{2} - 19 a - 5\) , \( -a^{2} + a + 3\) , \( -6 a^{5} + a^{4} + 44 a^{3} + 23 a^{2} - 29 a - 10\) , \( -42 a^{5} + 38 a^{4} + 266 a^{3} - 15 a^{2} - 116 a - 22\) , \( -177 a^{5} + 241 a^{4} + 1008 a^{3} - 518 a^{2} - 238 a - 6\bigr] \) ${y}^2+\left(-4a^{5}+a^{4}+29a^{3}+13a^{2}-19a-5\right){x}{y}+\left(-6a^{5}+a^{4}+44a^{3}+23a^{2}-29a-10\right){y}={x}^{3}+\left(-a^{2}+a+3\right){x}^{2}+\left(-42a^{5}+38a^{4}+266a^{3}-15a^{2}-116a-22\right){x}-177a^{5}+241a^{4}+1008a^{3}-518a^{2}-238a-6$
71.6-b1 71.6-b 6.6.300125.1 \( 71 \) $1$ $\Z/2\Z$ $0.003038782$ \( \frac{1584785}{71} a^{5} - \frac{365527}{71} a^{4} - \frac{11832625}{71} a^{3} - \frac{4916339}{71} a^{2} + \frac{8890196}{71} a + \frac{1422813}{71} \) \( \bigl[-3 a^{5} + a^{4} + 22 a^{3} + 8 a^{2} - 17 a - 3\) , \( a^{5} - a^{4} - 6 a^{3} + a^{2} + a - 2\) , \( -6 a^{5} + a^{4} + 44 a^{3} + 23 a^{2} - 29 a - 10\) , \( -14 a^{5} + 3 a^{4} + 102 a^{3} + 49 a^{2} - 67 a - 19\) , \( -4 a^{5} + a^{4} + 29 a^{3} + 14 a^{2} - 20 a - 6\bigr] \) ${y}^2+\left(-3a^{5}+a^{4}+22a^{3}+8a^{2}-17a-3\right){x}{y}+\left(-6a^{5}+a^{4}+44a^{3}+23a^{2}-29a-10\right){y}={x}^{3}+\left(a^{5}-a^{4}-6a^{3}+a^{2}+a-2\right){x}^{2}+\left(-14a^{5}+3a^{4}+102a^{3}+49a^{2}-67a-19\right){x}-4a^{5}+a^{4}+29a^{3}+14a^{2}-20a-6$
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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.