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Label Class Base field Conductor norm Rank Torsion CM Regulator Period Leading coeff j-invariant Weierstrass coefficients Weierstrass equation
7.1-a1 7.1-a 5.5.70601.1 \( 7 \) $1$ $\mathsf{trivial}$ $0.032410606$ $1352.120669$ 1.649290596 \( -\frac{3986622664}{117649} a^{4} + \frac{2668349896}{117649} a^{3} + \frac{20834045607}{117649} a^{2} - \frac{162996513}{16807} a - \frac{12309440397}{117649} \) \( \bigl[2 a^{4} - a^{3} - 11 a^{2} + a + 5\) , \( -a^{4} + a^{3} + 4 a^{2} - 2 a - 1\) , \( a^{4} - a^{3} - 5 a^{2} + 2 a + 2\) , \( -a^{4} - a^{3} + 9 a^{2} + 3 a - 3\) , \( -2 a^{3} + 4 a^{2} + 2 a - 1\bigr] \) ${y}^2+\left(2a^{4}-a^{3}-11a^{2}+a+5\right){x}{y}+\left(a^{4}-a^{3}-5a^{2}+2a+2\right){y}={x}^{3}+\left(-a^{4}+a^{3}+4a^{2}-2a-1\right){x}^{2}+\left(-a^{4}-a^{3}+9a^{2}+3a-3\right){x}-2a^{3}+4a^{2}+2a-1$
7.1-a2 7.1-a 5.5.70601.1 \( 7 \) $1$ $\mathsf{trivial}$ $0.010803535$ $4056.362009$ 1.649290596 \( \frac{392767}{49} a^{4} + \frac{404875}{49} a^{3} - \frac{2995121}{49} a^{2} - \frac{227585}{7} a + \frac{856140}{49} \) \( \bigl[2 a^{4} - 2 a^{3} - 9 a^{2} + 4 a + 3\) , \( a^{4} - 7 a^{2} + 5\) , \( a^{4} - a^{3} - 5 a^{2} + 2 a + 2\) , \( 6 a^{4} - 4 a^{3} - 29 a^{2} - 2 a + 20\) , \( 5 a^{4} - a^{3} - 31 a^{2} - 4 a + 22\bigr] \) ${y}^2+\left(2a^{4}-2a^{3}-9a^{2}+4a+3\right){x}{y}+\left(a^{4}-a^{3}-5a^{2}+2a+2\right){y}={x}^{3}+\left(a^{4}-7a^{2}+5\right){x}^{2}+\left(6a^{4}-4a^{3}-29a^{2}-2a+20\right){x}+5a^{4}-a^{3}-31a^{2}-4a+22$
9.1-a1 9.1-a 5.5.70601.1 \( 3^{2} \) $0$ $\Z/2\Z$ $1$ $1710.965141$ 1.609814162 \( -\frac{11789717}{3} a^{4} - \frac{17781848}{3} a^{3} + \frac{14349812}{3} a^{2} + 4099056 a - \frac{4680884}{3} \) \( \bigl[a^{4} - 6 a^{2} - 2 a + 3\) , \( -a^{3} + a^{2} + 3 a - 1\) , \( 2 a^{4} - 2 a^{3} - 9 a^{2} + 3 a + 3\) , \( 5 a^{4} - 26 a^{2} - 18 a + 6\) , \( 19 a^{4} - 4 a^{3} - 97 a^{2} - 41 a + 21\bigr] \) ${y}^2+\left(a^{4}-6a^{2}-2a+3\right){x}{y}+\left(2a^{4}-2a^{3}-9a^{2}+3a+3\right){y}={x}^{3}+\left(-a^{3}+a^{2}+3a-1\right){x}^{2}+\left(5a^{4}-26a^{2}-18a+6\right){x}+19a^{4}-4a^{3}-97a^{2}-41a+21$
9.1-a2 9.1-a 5.5.70601.1 \( 3^{2} \) $0$ $\Z/2\Z$ $1$ $213.8706426$ 1.609814162 \( \frac{7445209725993104}{9} a^{4} + \frac{11242578476007568}{9} a^{3} - \frac{9006704860332653}{9} a^{2} - \frac{7716787206817004}{9} a + \frac{2966169438852970}{9} \) \( \bigl[2 a^{4} - a^{3} - 11 a^{2} + a + 6\) , \( 2 a^{4} - a^{3} - 11 a^{2} + a + 5\) , \( a^{4} - a^{3} - 5 a^{2} + 2 a + 2\) , \( 8 a^{4} - 10 a^{3} - 41 a^{2} + 30 a + 29\) , \( 3787 a^{4} - 715 a^{3} - 19529 a^{2} - 8243 a + 4717\bigr] \) ${y}^2+\left(2a^{4}-a^{3}-11a^{2}+a+6\right){x}{y}+\left(a^{4}-a^{3}-5a^{2}+2a+2\right){y}={x}^{3}+\left(2a^{4}-a^{3}-11a^{2}+a+5\right){x}^{2}+\left(8a^{4}-10a^{3}-41a^{2}+30a+29\right){x}+3787a^{4}-715a^{3}-19529a^{2}-8243a+4717$
9.1-b1 9.1-b 5.5.70601.1 \( 3^{2} \) $0$ $\Z/2\Z$ $1$ $0.271983840$ 1.279521797 \( \frac{1241019728491478667854287148915537}{9} a^{4} - \frac{3466470975193904516888121233549840}{9} a^{3} + \frac{11129815715759114365727588897188}{9} a^{2} + \frac{2462080981149287745534356743321450}{9} a - \frac{692052889851961102412512823946311}{9} \) \( \bigl[2 a^{4} - a^{3} - 10 a^{2} + 4\) , \( -a^{3} + a^{2} + 3 a - 1\) , \( 2 a^{4} - a^{3} - 10 a^{2} + 4\) , \( -10860 a^{4} + 7306 a^{3} + 56621 a^{2} - 3366 a - 33769\) , \( -719344 a^{4} + 486907 a^{3} + 3752939 a^{2} - 228180 a - 2231590\bigr] \) ${y}^2+\left(2a^{4}-a^{3}-10a^{2}+4\right){x}{y}+\left(2a^{4}-a^{3}-10a^{2}+4\right){y}={x}^{3}+\left(-a^{3}+a^{2}+3a-1\right){x}^{2}+\left(-10860a^{4}+7306a^{3}+56621a^{2}-3366a-33769\right){x}-719344a^{4}+486907a^{3}+3752939a^{2}-228180a-2231590$
9.1-b2 9.1-b 5.5.70601.1 \( 3^{2} \) $0$ $\Z/2\Z$ $1$ $2.175870724$ 1.279521797 \( \frac{5509279887890632}{3} a^{4} - \frac{20491442675990639}{3} a^{3} + \frac{10059517521112475}{3} a^{2} + 6420413926184387 a - \frac{6356914243347758}{3} \) \( \bigl[a^{4} - 6 a^{2} - 2 a + 4\) , \( -a^{3} + a^{2} + 3 a\) , \( a^{4} - 6 a^{2} - 2 a + 4\) , \( -160 a^{4} + 15 a^{3} + 634 a^{2} - 12 a - 373\) , \( -1777 a^{4} - 692 a^{3} + 5689 a^{2} + 563 a - 3148\bigr] \) ${y}^2+\left(a^{4}-6a^{2}-2a+4\right){x}{y}+\left(a^{4}-6a^{2}-2a+4\right){y}={x}^{3}+\left(-a^{3}+a^{2}+3a\right){x}^{2}+\left(-160a^{4}+15a^{3}+634a^{2}-12a-373\right){x}-1777a^{4}-692a^{3}+5689a^{2}+563a-3148$
9.1-b3 9.1-b 5.5.70601.1 \( 3^{2} \) $0$ $\Z/10\Z$ $1$ $6799.596013$ 1.279521797 \( \frac{1226891}{243} a^{4} - \frac{2337049}{243} a^{3} - \frac{4118459}{243} a^{2} + \frac{2062492}{81} a - \frac{1078507}{243} \) \( \bigl[2 a^{4} - 2 a^{3} - 9 a^{2} + 4 a + 3\) , \( a^{4} - a^{3} - 5 a^{2} + a + 1\) , \( a^{4} - 6 a^{2} - a + 3\) , \( -2 a^{4} + 5 a^{3} + a^{2} - 5 a + 2\) , \( -2 a^{4} + 6 a^{3} - a^{2} - 5 a + 2\bigr] \) ${y}^2+\left(2a^{4}-2a^{3}-9a^{2}+4a+3\right){x}{y}+\left(a^{4}-6a^{2}-a+3\right){y}={x}^{3}+\left(a^{4}-a^{3}-5a^{2}+a+1\right){x}^{2}+\left(-2a^{4}+5a^{3}+a^{2}-5a+2\right){x}-2a^{4}+6a^{3}-a^{2}-5a+2$
9.1-b4 9.1-b 5.5.70601.1 \( 3^{2} \) $0$ $\Z/10\Z$ $1$ $849.9495016$ 1.279521797 \( -\frac{8901429979126}{59049} a^{4} + \frac{16455365224771}{59049} a^{3} + \frac{30554549264677}{59049} a^{2} - \frac{43774816239536}{59049} a + \frac{10480360169644}{59049} \) \( \bigl[2 a^{4} - a^{3} - 10 a^{2} + 4\) , \( -a^{3} + a^{2} + 3 a - 1\) , \( 2 a^{4} - a^{3} - 10 a^{2} + 4\) , \( 100 a^{4} - 74 a^{3} - 514 a^{2} + 54 a + 291\) , \( 8 a^{4} + 8 a^{3} - 63 a^{2} - 51 a + 75\bigr] \) ${y}^2+\left(2a^{4}-a^{3}-10a^{2}+4\right){x}{y}+\left(2a^{4}-a^{3}-10a^{2}+4\right){y}={x}^{3}+\left(-a^{3}+a^{2}+3a-1\right){x}^{2}+\left(100a^{4}-74a^{3}-514a^{2}+54a+291\right){x}+8a^{4}+8a^{3}-63a^{2}-51a+75$
9.1-c1 9.1-c 5.5.70601.1 \( 3^{2} \) $1$ $\Z/2\Z$ $0.153197021$ $1322.482006$ 1.906227260 \( \frac{8746388488795}{9} a^{4} - \frac{24430797586567}{9} a^{3} + \frac{78450258911}{9} a^{2} + \frac{17352098839361}{9} a - \frac{4877404922344}{9} \) \( \bigl[a^{4} - a^{3} - 5 a^{2} + 2 a + 2\) , \( -3 a^{4} + 2 a^{3} + 15 a^{2} - 5\) , \( 2 a^{4} - a^{3} - 11 a^{2} + a + 6\) , \( -28 a^{4} + 18 a^{3} + 143 a^{2} - 4 a - 77\) , \( -110 a^{4} + 46 a^{3} + 566 a^{2} + 107 a - 231\bigr] \) ${y}^2+\left(a^{4}-a^{3}-5a^{2}+2a+2\right){x}{y}+\left(2a^{4}-a^{3}-11a^{2}+a+6\right){y}={x}^{3}+\left(-3a^{4}+2a^{3}+15a^{2}-5\right){x}^{2}+\left(-28a^{4}+18a^{3}+143a^{2}-4a-77\right){x}-110a^{4}+46a^{3}+566a^{2}+107a-231$
9.1-c2 9.1-c 5.5.70601.1 \( 3^{2} \) $1$ $\Z/2\Z$ $0.076598510$ $5289.928027$ 1.906227260 \( 197745 a^{4} - \frac{1743040}{3} a^{3} + 57475 a^{2} + \frac{1319857}{3} a - \frac{386164}{3} \) \( \bigl[a^{4} - a^{3} - 5 a^{2} + 3 a + 3\) , \( a^{3} - a^{2} - 5 a + 1\) , \( 2 a^{4} - 2 a^{3} - 9 a^{2} + 4 a + 3\) , \( -3 a^{4} + 2 a^{3} + 14 a^{2} - 2 a - 6\) , \( -a^{4} + 5 a^{2} + a - 4\bigr] \) ${y}^2+\left(a^{4}-a^{3}-5a^{2}+3a+3\right){x}{y}+\left(2a^{4}-2a^{3}-9a^{2}+4a+3\right){y}={x}^{3}+\left(a^{3}-a^{2}-5a+1\right){x}^{2}+\left(-3a^{4}+2a^{3}+14a^{2}-2a-6\right){x}-a^{4}+5a^{2}+a-4$
9.1-c3 9.1-c 5.5.70601.1 \( 3^{2} \) $1$ $\Z/2\Z$ $0.229795532$ $1763.309342$ 1.906227260 \( \frac{1164861712}{27} a^{4} - \frac{789665072}{27} a^{3} - \frac{6078769117}{27} a^{2} + \frac{123910703}{9} a + \frac{3614971135}{27} \) \( \bigl[a^{4} - a^{3} - 4 a^{2} + a\) , \( a^{4} - 7 a^{2} - 2 a + 4\) , \( 3 a^{4} - 2 a^{3} - 15 a^{2} + 2 a + 5\) , \( a^{4} + 2 a^{3} - 9 a^{2} - 5 a + 5\) , \( -2 a^{4} + 3 a^{3} + 7 a^{2} - 7 a - 2\bigr] \) ${y}^2+\left(a^{4}-a^{3}-4a^{2}+a\right){x}{y}+\left(3a^{4}-2a^{3}-15a^{2}+2a+5\right){y}={x}^{3}+\left(a^{4}-7a^{2}-2a+4\right){x}^{2}+\left(a^{4}+2a^{3}-9a^{2}-5a+5\right){x}-2a^{4}+3a^{3}+7a^{2}-7a-2$
9.1-c4 9.1-c 5.5.70601.1 \( 3^{2} \) $1$ $\Z/2\Z$ $0.459591064$ $440.8273356$ 1.906227260 \( \frac{3600304971482332529}{729} a^{4} - \frac{2439850098107900843}{729} a^{3} - \frac{18787940441387297450}{729} a^{2} + \frac{1144857105745347907}{729} a + \frac{11169926711558310001}{729} \) \( \bigl[2 a^{4} - 2 a^{3} - 9 a^{2} + 4 a + 3\) , \( a^{4} - 2 a^{3} - 3 a^{2} + 6 a - 1\) , \( 3 a^{4} - 2 a^{3} - 15 a^{2} + 2 a + 6\) , \( 8 a^{4} - 45 a^{2} - 16 a + 5\) , \( 1359 a^{4} - 262 a^{3} - 6993 a^{2} - 2955 a + 1668\bigr] \) ${y}^2+\left(2a^{4}-2a^{3}-9a^{2}+4a+3\right){x}{y}+\left(3a^{4}-2a^{3}-15a^{2}+2a+6\right){y}={x}^{3}+\left(a^{4}-2a^{3}-3a^{2}+6a-1\right){x}^{2}+\left(8a^{4}-45a^{2}-16a+5\right){x}+1359a^{4}-262a^{3}-6993a^{2}-2955a+1668$
11.2-a1 11.2-a 5.5.70601.1 \( 11 \) $0$ $\mathsf{trivial}$ $1$ $3.026255417$ 1.423672731 \( \frac{2419492877372724132926}{161051} a^{4} - \frac{4448947514199103019972}{161051} a^{3} - \frac{8274801601497550822783}{161051} a^{2} + \frac{11839841097468876790712}{161051} a - \frac{2833690910755968015329}{161051} \) \( \bigl[2 a^{4} - 2 a^{3} - 9 a^{2} + 4 a + 2\) , \( -a^{4} + 6 a^{2} + 2 a - 2\) , \( 3 a^{4} - 2 a^{3} - 15 a^{2} + 2 a + 6\) , \( -73 a^{4} + 29 a^{3} + 403 a^{2} + 60 a - 263\) , \( -329 a^{4} + 126 a^{3} + 1875 a^{2} + 263 a - 1434\bigr] \) ${y}^2+\left(2a^{4}-2a^{3}-9a^{2}+4a+2\right){x}{y}+\left(3a^{4}-2a^{3}-15a^{2}+2a+6\right){y}={x}^{3}+\left(-a^{4}+6a^{2}+2a-2\right){x}^{2}+\left(-73a^{4}+29a^{3}+403a^{2}+60a-263\right){x}-329a^{4}+126a^{3}+1875a^{2}+263a-1434$
11.2-a2 11.2-a 5.5.70601.1 \( 11 \) $0$ $\mathsf{trivial}$ $1$ $1.008751805$ 1.423672731 \( -\frac{8205693349407499126130881172}{4177248169415651} a^{4} + \frac{5560827331783947650405359349}{4177248169415651} a^{3} + \frac{42820830025831262432181359037}{4177248169415651} a^{2} - \frac{2609321773754481822746200000}{4177248169415651} a - \frac{25458114683827965125866617974}{4177248169415651} \) \( \bigl[a^{4} - 6 a^{2} - a + 4\) , \( -1\) , \( 2 a^{4} - a^{3} - 11 a^{2} + 5\) , \( 111 a^{4} - 121 a^{3} - 452 a^{2} + 176 a - 91\) , \( 867 a^{4} - 1021 a^{3} - 3514 a^{2} + 1727 a - 475\bigr] \) ${y}^2+\left(a^{4}-6a^{2}-a+4\right){x}{y}+\left(2a^{4}-a^{3}-11a^{2}+5\right){y}={x}^{3}-{x}^{2}+\left(111a^{4}-121a^{3}-452a^{2}+176a-91\right){x}+867a^{4}-1021a^{3}-3514a^{2}+1727a-475$
11.2-a3 11.2-a 5.5.70601.1 \( 11 \) $0$ $\Z/5\Z$ $1$ $9457.048180$ 1.423672731 \( \frac{503992}{11} a^{4} - \frac{87885}{11} a^{3} - \frac{2613846}{11} a^{2} - \frac{1093926}{11} a + \frac{621783}{11} \) \( \bigl[2 a^{4} - a^{3} - 10 a^{2} + 4\) , \( -a^{4} + a^{3} + 5 a^{2} - 3 a - 2\) , \( a^{4} - a^{3} - 4 a^{2} + a\) , \( a^{4} - 5 a^{2} - 4 a + 2\) , \( 0\bigr] \) ${y}^2+\left(2a^{4}-a^{3}-10a^{2}+4\right){x}{y}+\left(a^{4}-a^{3}-4a^{2}+a\right){y}={x}^{3}+\left(-a^{4}+a^{3}+5a^{2}-3a-2\right){x}^{2}+\left(a^{4}-5a^{2}-4a+2\right){x}$
11.2-a4 11.2-a 5.5.70601.1 \( 11 \) $0$ $\Z/5\Z$ $1$ $3152.349393$ 1.423672731 \( \frac{428200040}{1331} a^{4} + \frac{647357011}{1331} a^{3} - \frac{516344269}{1331} a^{2} - \frac{444536251}{1331} a + \frac{170612026}{1331} \) \( \bigl[3 a^{4} - 2 a^{3} - 15 a^{2} + a + 6\) , \( a^{3} - 2 a^{2} - 2 a + 3\) , \( a^{4} - a^{3} - 5 a^{2} + 3 a + 2\) , \( 3 a^{4} - 3 a^{3} - 16 a^{2} + 2 a + 13\) , \( -4 a^{4} + 4 a^{3} + 19 a^{2} - 3 a - 10\bigr] \) ${y}^2+\left(3a^{4}-2a^{3}-15a^{2}+a+6\right){x}{y}+\left(a^{4}-a^{3}-5a^{2}+3a+2\right){y}={x}^{3}+\left(a^{3}-2a^{2}-2a+3\right){x}^{2}+\left(3a^{4}-3a^{3}-16a^{2}+2a+13\right){x}-4a^{4}+4a^{3}+19a^{2}-3a-10$
11.2-b1 11.2-b 5.5.70601.1 \( 11 \) $0$ $\Z/5\Z$ $1$ $3139.012854$ 0.945099764 \( \frac{403291}{121} a^{4} - \frac{737596}{121} a^{3} - \frac{1377634}{121} a^{2} + \frac{1964751}{121} a - \frac{468458}{121} \) \( \bigl[a^{4} - a^{3} - 5 a^{2} + 3 a + 3\) , \( a^{3} - 2 a^{2} - 3 a + 3\) , \( 2 a^{4} - a^{3} - 10 a^{2} - a + 3\) , \( -a^{2} + 5\) , \( 2 a^{4} - 12 a^{2} - 4 a + 6\bigr] \) ${y}^2+\left(a^{4}-a^{3}-5a^{2}+3a+3\right){x}{y}+\left(2a^{4}-a^{3}-10a^{2}-a+3\right){y}={x}^{3}+\left(a^{3}-2a^{2}-3a+3\right){x}^{2}+\left(-a^{2}+5\right){x}+2a^{4}-12a^{2}-4a+6$
11.2-b2 11.2-b 5.5.70601.1 \( 11 \) $0$ $\mathsf{trivial}$ $1$ $1.004484113$ 0.945099764 \( \frac{8307402570253990872274}{25937424601} a^{4} - \frac{1338226591259999802327}{25937424601} a^{3} - \frac{43272833962783971491091}{25937424601} a^{2} - \frac{18472674003862592516490}{25937424601} a + \frac{10404941001339037312187}{25937424601} \) \( \bigl[2 a^{4} - a^{3} - 10 a^{2} + 4\) , \( a^{4} - a^{3} - 5 a^{2} + a + 2\) , \( a^{4} - 6 a^{2} - 2 a + 3\) , \( -28 a^{4} + 4 a^{3} + 105 a^{2} - 20 a - 66\) , \( -172 a^{4} - 86 a^{3} + 571 a^{2} + 100 a - 379\bigr] \) ${y}^2+\left(2a^{4}-a^{3}-10a^{2}+4\right){x}{y}+\left(a^{4}-6a^{2}-2a+3\right){y}={x}^{3}+\left(a^{4}-a^{3}-5a^{2}+a+2\right){x}^{2}+\left(-28a^{4}+4a^{3}+105a^{2}-20a-66\right){x}-172a^{4}-86a^{3}+571a^{2}+100a-379$
17.1-a1 17.1-a 5.5.70601.1 \( 17 \) $1$ $\mathsf{trivial}$ $0.125400656$ $962.3659708$ 2.270934700 \( \frac{293778407}{289} a^{4} - \frac{543407845}{289} a^{3} - \frac{1007035812}{289} a^{2} + \frac{1443156771}{289} a - \frac{345466559}{289} \) \( \bigl[a^{4} - a^{3} - 5 a^{2} + 2 a + 3\) , \( -a^{4} + 6 a^{2} + 3 a - 3\) , \( 3 a^{4} - 2 a^{3} - 15 a^{2} + a + 6\) , \( -3 a^{4} + 2 a^{3} + 14 a^{2} + 3 a - 6\) , \( -5 a^{4} + 5 a^{3} + 22 a^{2} - 2 a - 14\bigr] \) ${y}^2+\left(a^{4}-a^{3}-5a^{2}+2a+3\right){x}{y}+\left(3a^{4}-2a^{3}-15a^{2}+a+6\right){y}={x}^{3}+\left(-a^{4}+6a^{2}+3a-3\right){x}^{2}+\left(-3a^{4}+2a^{3}+14a^{2}+3a-6\right){x}-5a^{4}+5a^{3}+22a^{2}-2a-14$
17.1-a2 17.1-a 5.5.70601.1 \( 17 \) $1$ $\mathsf{trivial}$ $0.041800218$ $2887.097912$ 2.270934700 \( -\frac{541923}{17} a^{4} - \frac{814933}{17} a^{3} + \frac{667123}{17} a^{2} + \frac{563417}{17} a - \frac{220652}{17} \) \( \bigl[2 a^{4} - a^{3} - 10 a^{2} + 3\) , \( -a^{4} + 6 a^{2} + a - 2\) , \( 2 a^{4} - 2 a^{3} - 9 a^{2} + 3 a + 2\) , \( -6 a^{4} + a^{3} + 36 a^{2} + 6 a - 21\) , \( 24 a^{4} - 19 a^{3} - 121 a^{2} + 15 a + 71\bigr] \) ${y}^2+\left(2a^{4}-a^{3}-10a^{2}+3\right){x}{y}+\left(2a^{4}-2a^{3}-9a^{2}+3a+2\right){y}={x}^{3}+\left(-a^{4}+6a^{2}+a-2\right){x}^{2}+\left(-6a^{4}+a^{3}+36a^{2}+6a-21\right){x}+24a^{4}-19a^{3}-121a^{2}+15a+71$
23.1-a1 23.1-a 5.5.70601.1 \( 23 \) $1$ $\Z/2\Z$ $0.289345509$ $862.9900285$ 2.349400770 \( \frac{390105677339719991}{529} a^{4} - \frac{1089663767831678793}{529} a^{3} + \frac{3510982897333356}{529} a^{2} + \frac{773926975640782522}{529} a - \frac{217539643409513153}{529} \) \( \bigl[1\) , \( -a^{4} + 7 a^{2} - 6\) , \( a\) , \( -90 a^{4} + 56 a^{3} + 477 a^{2} - 15 a - 294\) , \( 410 a^{4} - 270 a^{3} - 2148 a^{2} + 101 a + 1297\bigr] \) ${y}^2+{x}{y}+a{y}={x}^{3}+\left(-a^{4}+7a^{2}-6\right){x}^{2}+\left(-90a^{4}+56a^{3}+477a^{2}-15a-294\right){x}+410a^{4}-270a^{3}-2148a^{2}+101a+1297$
23.1-a2 23.1-a 5.5.70601.1 \( 23 \) $1$ $\Z/2\Z$ $0.144672754$ $3451.960114$ 2.349400770 \( \frac{244420132}{23} a^{4} - \frac{201883474}{23} a^{3} - \frac{136447512}{23} a^{2} + \frac{150154481}{23} a - \frac{30067803}{23} \) \( \bigl[1\) , \( -a^{4} + 7 a^{2} - 6\) , \( a\) , \( 25 a^{4} - 19 a^{3} - 128 a^{2} + 10 a + 76\) , \( -7 a^{4} + 5 a^{3} + 40 a^{2} - 3 a - 24\bigr] \) ${y}^2+{x}{y}+a{y}={x}^{3}+\left(-a^{4}+7a^{2}-6\right){x}^{2}+\left(25a^{4}-19a^{3}-128a^{2}+10a+76\right){x}-7a^{4}+5a^{3}+40a^{2}-3a-24$
23.1-a3 23.1-a 5.5.70601.1 \( 23 \) $1$ $\Z/2\Z$ $0.048224251$ $10355.88034$ 2.349400770 \( -\frac{183399301}{12167} a^{4} + \frac{125042119}{12167} a^{3} + \frac{961492697}{12167} a^{2} - \frac{65243956}{12167} a - \frac{570265911}{12167} \) \( \bigl[a^{4} - a^{3} - 4 a^{2} + 2 a\) , \( a^{4} - a^{3} - 4 a^{2} + 1\) , \( a^{4} - a^{3} - 4 a^{2} + 2 a\) , \( a^{4} - 2 a^{3} - 3 a^{2} + 3 a - 1\) , \( -a^{3} + a^{2} + 3 a - 1\bigr] \) ${y}^2+\left(a^{4}-a^{3}-4a^{2}+2a\right){x}{y}+\left(a^{4}-a^{3}-4a^{2}+2a\right){y}={x}^{3}+\left(a^{4}-a^{3}-4a^{2}+1\right){x}^{2}+\left(a^{4}-2a^{3}-3a^{2}+3a-1\right){x}-a^{3}+a^{2}+3a-1$
23.1-a4 23.1-a 5.5.70601.1 \( 23 \) $1$ $\Z/2\Z$ $0.096448503$ $2588.970085$ 2.349400770 \( \frac{93598253132532104}{148035889} a^{4} - \frac{63446863598677057}{148035889} a^{3} - \frac{488429136542190831}{148035889} a^{2} + \frac{29836445874686692}{148035889} a + \frac{290435397221009784}{148035889} \) \( \bigl[a^{4} - a^{3} - 4 a^{2} + 2 a\) , \( a^{4} - a^{3} - 4 a^{2} + 1\) , \( a^{4} - a^{3} - 4 a^{2} + 2 a\) , \( 6 a^{4} - 2 a^{3} - 28 a^{2} - 12 a - 1\) , \( -16 a^{4} + a^{3} + 83 a^{2} + 45 a - 16\bigr] \) ${y}^2+\left(a^{4}-a^{3}-4a^{2}+2a\right){x}{y}+\left(a^{4}-a^{3}-4a^{2}+2a\right){y}={x}^{3}+\left(a^{4}-a^{3}-4a^{2}+1\right){x}^{2}+\left(6a^{4}-2a^{3}-28a^{2}-12a-1\right){x}-16a^{4}+a^{3}+83a^{2}+45a-16$
29.1-a1 29.1-a 5.5.70601.1 \( 29 \) $0$ $\mathsf{trivial}$ $1$ $0.610692715$ 0.788336133 \( \frac{1499741787190786782165925}{17249876309} a^{4} - \frac{4214003745944059872006099}{17249876309} a^{3} + \frac{74873005092991374350620}{17249876309} a^{2} + \frac{2994939658199456178076242}{17249876309} a - \frac{879336253518581869182340}{17249876309} \) \( \bigl[a^{4} - 6 a^{2} - a + 3\) , \( -a^{4} + 7 a^{2} + a - 6\) , \( a^{4} - a^{3} - 4 a^{2} + a\) , \( 27 a^{4} + 49 a^{3} - 206 a^{2} - 213 a - 28\) , \( 2022 a^{4} + 73 a^{3} - 11190 a^{2} - 5360 a + 2507\bigr] \) ${y}^2+\left(a^{4}-6a^{2}-a+3\right){x}{y}+\left(a^{4}-a^{3}-4a^{2}+a\right){y}={x}^{3}+\left(-a^{4}+7a^{2}+a-6\right){x}^{2}+\left(27a^{4}+49a^{3}-206a^{2}-213a-28\right){x}+2022a^{4}+73a^{3}-11190a^{2}-5360a+2507$
29.1-a2 29.1-a 5.5.70601.1 \( 29 \) $0$ $\Z/7\Z$ $1$ $10263.91246$ 0.788336133 \( \frac{455575}{29} a^{4} - \frac{100246}{29} a^{3} - \frac{2321756}{29} a^{2} - \frac{953052}{29} a + \frac{566128}{29} \) \( \bigl[2 a^{4} - 2 a^{3} - 9 a^{2} + 3 a + 3\) , \( 2 a^{4} - 2 a^{3} - 9 a^{2} + 2 a + 1\) , \( 2 a^{4} - a^{3} - 10 a^{2} + 3\) , \( a^{4} - 2 a^{3} - 4 a^{2} + 6 a + 1\) , \( a^{4} - 6 a^{2} - 3 a + 2\bigr] \) ${y}^2+\left(2a^{4}-2a^{3}-9a^{2}+3a+3\right){x}{y}+\left(2a^{4}-a^{3}-10a^{2}+3\right){y}={x}^{3}+\left(2a^{4}-2a^{3}-9a^{2}+2a+1\right){x}^{2}+\left(a^{4}-2a^{3}-4a^{2}+6a+1\right){x}+a^{4}-6a^{2}-3a+2$
32.1-a1 32.1-a 5.5.70601.1 \( 2^{5} \) $1$ $\mathsf{trivial}$ $0.801650473$ $176.9150737$ 2.668790415 \( -\frac{2485641}{2} a^{4} + 1159797 a^{3} + 4981591 a^{2} - 2602560 a - 1253263 \) \( \bigl[a^{4} - a^{3} - 4 a^{2} + 2 a + 1\) , \( a^{4} - 2 a^{3} - 3 a^{2} + 4 a\) , \( 2 a^{4} - a^{3} - 11 a^{2} + a + 6\) , \( -3 a^{3} + 5 a^{2} + 9 a - 9\) , \( -3 a^{4} + a^{3} + 16 a^{2} + 4 a - 13\bigr] \) ${y}^2+\left(a^{4}-a^{3}-4a^{2}+2a+1\right){x}{y}+\left(2a^{4}-a^{3}-11a^{2}+a+6\right){y}={x}^{3}+\left(a^{4}-2a^{3}-3a^{2}+4a\right){x}^{2}+\left(-3a^{3}+5a^{2}+9a-9\right){x}-3a^{4}+a^{3}+16a^{2}+4a-13$
32.1-b1 32.1-b 5.5.70601.1 \( 2^{5} \) $1$ $\mathsf{trivial}$ $0.011385182$ $12116.38451$ 2.595838189 \( \frac{141897}{2} a^{4} - 47459 a^{3} - 370176 a^{2} + \frac{38961}{2} a + \frac{435239}{2} \) \( \bigl[2 a^{4} - a^{3} - 11 a^{2} + a + 5\) , \( -a^{4} + a^{3} + 5 a^{2} - 3 a - 3\) , \( 3 a^{4} - 2 a^{3} - 15 a^{2} + a + 5\) , \( 9 a^{4} - 4 a^{3} - 39 a^{2} - 20 a + 3\) , \( -31 a^{4} + a^{3} + 170 a^{2} + 75 a - 45\bigr] \) ${y}^2+\left(2a^{4}-a^{3}-11a^{2}+a+5\right){x}{y}+\left(3a^{4}-2a^{3}-15a^{2}+a+5\right){y}={x}^{3}+\left(-a^{4}+a^{3}+5a^{2}-3a-3\right){x}^{2}+\left(9a^{4}-4a^{3}-39a^{2}-20a+3\right){x}-31a^{4}+a^{3}+170a^{2}+75a-45$
32.1-c1 32.1-c 5.5.70601.1 \( 2^{5} \) $1$ $\mathsf{trivial}$ $0.023197209$ $5637.474343$ 2.460848625 \( -\frac{32857413}{2} a^{4} - \frac{99317097}{4} a^{3} + \frac{79437623}{4} a^{2} + 17064543 a - \frac{52421865}{8} \) \( \bigl[a^{4} - a^{3} - 5 a^{2} + 2 a + 2\) , \( -a^{4} + 5 a^{2} + 3 a - 2\) , \( a\) , \( -7 a^{4} + a^{3} + 37 a^{2} + 17 a - 11\) , \( 2 a^{4} - 11 a^{2} - 6 a + 3\bigr] \) ${y}^2+\left(a^{4}-a^{3}-5a^{2}+2a+2\right){x}{y}+a{y}={x}^{3}+\left(-a^{4}+5a^{2}+3a-2\right){x}^{2}+\left(-7a^{4}+a^{3}+37a^{2}+17a-11\right){x}+2a^{4}-11a^{2}-6a+3$
32.1-c2 32.1-c 5.5.70601.1 \( 2^{5} \) $1$ $\mathsf{trivial}$ $0.007732403$ $16912.42303$ 2.460848625 \( 410269356 a^{4} - 278026353 a^{3} - 2140972273 a^{2} + 130455752 a + \frac{2545730995}{2} \) \( \bigl[2 a^{4} - a^{3} - 11 a^{2} + 5\) , \( 2 a^{4} - a^{3} - 10 a^{2} - 2 a + 4\) , \( a^{4} - a^{3} - 4 a^{2} + a\) , \( 9 a^{4} - 5 a^{3} - 44 a^{2} - 8 a + 19\) , \( -11 a^{4} + 58 a^{2} + 32 a - 9\bigr] \) ${y}^2+\left(2a^{4}-a^{3}-11a^{2}+5\right){x}{y}+\left(a^{4}-a^{3}-4a^{2}+a\right){y}={x}^{3}+\left(2a^{4}-a^{3}-10a^{2}-2a+4\right){x}^{2}+\left(9a^{4}-5a^{3}-44a^{2}-8a+19\right){x}-11a^{4}+58a^{2}+32a-9$
32.1-d1 32.1-d 5.5.70601.1 \( 2^{5} \) $1$ $\mathsf{trivial}$ $0.015698445$ $8567.434520$ 2.530882735 \( \frac{454837}{2} a^{4} - 635149 a^{3} + \frac{3677}{2} a^{2} + \frac{902141}{2} a - 126645 \) \( \bigl[a\) , \( -a^{4} + 5 a^{2} + 3 a - 2\) , \( a^{4} - 6 a^{2} - a + 4\) , \( -2 a^{4} + a^{3} + 9 a^{2} + 2 a - 2\) , \( -336 a^{4} + 64 a^{3} + 1731 a^{2} + 730 a - 416\bigr] \) ${y}^2+a{x}{y}+\left(a^{4}-6a^{2}-a+4\right){y}={x}^{3}+\left(-a^{4}+5a^{2}+3a-2\right){x}^{2}+\left(-2a^{4}+a^{3}+9a^{2}+2a-2\right){x}-336a^{4}+64a^{3}+1731a^{2}+730a-416$
47.1-a1 47.1-a 5.5.70601.1 \( 47 \) $0$ $\Z/2\Z$ $1$ $275.9239989$ 2.336504207 \( \frac{179345009019}{47} a^{4} - \frac{500938110541}{47} a^{3} + \frac{1614256427}{47} a^{2} + \frac{355794086849}{47} a - \frac{100015596996}{47} \) \( \bigl[2 a^{4} - a^{3} - 10 a^{2} + 3\) , \( a^{3} - a^{2} - 3 a + 1\) , \( 2 a^{4} - 2 a^{3} - 9 a^{2} + 4 a + 2\) , \( -3 a^{4} + 8 a^{3} + 3 a^{2} - 7 a - 2\) , \( -6 a^{4} + 17 a^{3} - 10 a\bigr] \) ${y}^2+\left(2a^{4}-a^{3}-10a^{2}+3\right){x}{y}+\left(2a^{4}-2a^{3}-9a^{2}+4a+2\right){y}={x}^{3}+\left(a^{3}-a^{2}-3a+1\right){x}^{2}+\left(-3a^{4}+8a^{3}+3a^{2}-7a-2\right){x}-6a^{4}+17a^{3}-10a$
47.1-a2 47.1-a 5.5.70601.1 \( 47 \) $0$ $\Z/2\Z$ $1$ $827.7719969$ 2.336504207 \( \frac{5215486471}{103823} a^{4} - \frac{9695772757}{103823} a^{3} - \frac{17753063912}{103823} a^{2} + \frac{25718276651}{103823} a - \frac{6096977969}{103823} \) \( \bigl[2 a^{4} - 2 a^{3} - 9 a^{2} + 3 a + 3\) , \( a^{4} - 6 a^{2} - a + 3\) , \( a^{4} - 6 a^{2} - 2 a + 4\) , \( 47 a^{4} - 31 a^{3} - 246 a^{2} + 10 a + 150\) , \( -159 a^{4} + 108 a^{3} + 829 a^{2} - 51 a - 493\bigr] \) ${y}^2+\left(2a^{4}-2a^{3}-9a^{2}+3a+3\right){x}{y}+\left(a^{4}-6a^{2}-2a+4\right){y}={x}^{3}+\left(a^{4}-6a^{2}-a+3\right){x}^{2}+\left(47a^{4}-31a^{3}-246a^{2}+10a+150\right){x}-159a^{4}+108a^{3}+829a^{2}-51a-493$
47.1-a3 47.1-a 5.5.70601.1 \( 47 \) $0$ $\Z/2\Z$ $1$ $413.8859984$ 2.336504207 \( -\frac{167855641818319871333}{10779215329} a^{4} + \frac{310535321180235825494}{10779215329} a^{3} + \frac{575318853593468791079}{10779215329} a^{2} - \frac{824740447065649903509}{10779215329} a + \frac{197474025812370152222}{10779215329} \) \( \bigl[a\) , \( a^{4} - 7 a^{2} - a + 5\) , \( 0\) , \( -24 a^{4} + 12 a^{3} + 136 a^{2} - 4 a - 84\) , \( -115 a^{4} + 96 a^{3} + 555 a^{2} - 49 a - 327\bigr] \) ${y}^2+a{x}{y}={x}^{3}+\left(a^{4}-7a^{2}-a+5\right){x}^{2}+\left(-24a^{4}+12a^{3}+136a^{2}-4a-84\right){x}-115a^{4}+96a^{3}+555a^{2}-49a-327$
47.1-a4 47.1-a 5.5.70601.1 \( 47 \) $0$ $\Z/2\Z$ $1$ $137.9619994$ 2.336504207 \( \frac{1281280005366879}{2209} a^{4} + \frac{1897785737907518}{2209} a^{3} - \frac{1617538215559341}{2209} a^{2} - \frac{1304406721787548}{2209} a + \frac{556600979958669}{2209} \) \( \bigl[2 a^{4} - a^{3} - 10 a^{2} + 3\) , \( a^{3} - a^{2} - 3 a + 1\) , \( 2 a^{4} - 2 a^{3} - 9 a^{2} + 4 a + 2\) , \( -3 a^{4} + 8 a^{3} + 8 a^{2} - 12 a - 27\) , \( -6 a^{4} + 18 a^{3} + 12 a^{2} - 25 a - 60\bigr] \) ${y}^2+\left(2a^{4}-a^{3}-10a^{2}+3\right){x}{y}+\left(2a^{4}-2a^{3}-9a^{2}+4a+2\right){y}={x}^{3}+\left(a^{3}-a^{2}-3a+1\right){x}^{2}+\left(-3a^{4}+8a^{3}+8a^{2}-12a-27\right){x}-6a^{4}+18a^{3}+12a^{2}-25a-60$
47.1-b1 47.1-b 5.5.70601.1 \( 47 \) $0$ $\mathsf{trivial}$ $1$ $160.3669764$ 1.207089606 \( -\frac{748348097436098336}{2209} a^{4} + \frac{507139383100034180}{2209} a^{3} + \frac{3905202134108048419}{2209} a^{2} - \frac{237966136978112722}{2209} a - \frac{2321745885596950237}{2209} \) \( \bigl[a + 1\) , \( -a^{2} + a + 3\) , \( a^{4} - a^{3} - 4 a^{2} + 2 a + 1\) , \( -22 a^{4} - 3 a^{3} + 135 a^{2} + 65 a - 107\) , \( -173 a^{4} + 154 a^{3} + 840 a^{2} - 195 a - 374\bigr] \) ${y}^2+\left(a+1\right){x}{y}+\left(a^{4}-a^{3}-4a^{2}+2a+1\right){y}={x}^{3}+\left(-a^{2}+a+3\right){x}^{2}+\left(-22a^{4}-3a^{3}+135a^{2}+65a-107\right){x}-173a^{4}+154a^{3}+840a^{2}-195a-374$
47.2-a1 47.2-a 5.5.70601.1 \( 47 \) $0$ $\Z/2\Z$ $1$ $2238.811346$ 2.106454494 \( \frac{1877152}{47} a^{4} + \frac{2877117}{47} a^{3} - \frac{2158825}{47} a^{2} - \frac{1887071}{47} a + \frac{717218}{47} \) \( \bigl[a^{4} - a^{3} - 5 a^{2} + 3 a + 3\) , \( -a^{4} + a^{3} + 4 a^{2} + 1\) , \( a^{4} - a^{3} - 4 a^{2} + a\) , \( -a^{3} + 5 a + 5\) , \( a^{4} - a^{3} - 5 a^{2} + 2 a + 3\bigr] \) ${y}^2+\left(a^{4}-a^{3}-5a^{2}+3a+3\right){x}{y}+\left(a^{4}-a^{3}-4a^{2}+a\right){y}={x}^{3}+\left(-a^{4}+a^{3}+4a^{2}+1\right){x}^{2}+\left(-a^{3}+5a+5\right){x}+a^{4}-a^{3}-5a^{2}+2a+3$
47.2-a2 47.2-a 5.5.70601.1 \( 47 \) $0$ $\Z/2\Z$ $1$ $1119.405673$ 2.106454494 \( \frac{194915039076075}{2209} a^{4} + \frac{294330947080514}{2209} a^{3} - \frac{235793793475384}{2209} a^{2} - \frac{202027318016940}{2209} a + \frac{77654766827483}{2209} \) \( \bigl[a^{4} - 6 a^{2} - a + 4\) , \( a^{3} - 2 a^{2} - 4 a + 3\) , \( 0\) , \( -8 a^{4} + 48 a^{2} + 20 a - 36\) , \( -17 a^{4} - 7 a^{3} + 119 a^{2} + 66 a - 129\bigr] \) ${y}^2+\left(a^{4}-6a^{2}-a+4\right){x}{y}={x}^{3}+\left(a^{3}-2a^{2}-4a+3\right){x}^{2}+\left(-8a^{4}+48a^{2}+20a-36\right){x}-17a^{4}-7a^{3}+119a^{2}+66a-129$
47.2-b1 47.2-b 5.5.70601.1 \( 47 \) $1$ $\mathsf{trivial}$ $0.030642720$ $4853.403072$ 2.798583456 \( \frac{9074112}{103823} a^{4} + \frac{132922005}{103823} a^{3} - \frac{356032536}{103823} a^{2} - \frac{222800132}{103823} a + \frac{342458773}{103823} \) \( \bigl[a^{4} - a^{3} - 5 a^{2} + 3 a + 3\) , \( -2 a^{4} + a^{3} + 11 a^{2} + a - 6\) , \( a + 1\) , \( -2 a^{4} + a^{3} + 11 a^{2} + a - 7\) , \( 0\bigr] \) ${y}^2+\left(a^{4}-a^{3}-5a^{2}+3a+3\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-2a^{4}+a^{3}+11a^{2}+a-6\right){x}^{2}+\left(-2a^{4}+a^{3}+11a^{2}+a-7\right){x}$
47.2-b2 47.2-b 5.5.70601.1 \( 47 \) $1$ $\mathsf{trivial}$ $0.091928162$ $1617.801024$ 2.798583456 \( \frac{42542580556}{47} a^{4} - \frac{21887546864}{47} a^{3} - \frac{232611726616}{47} a^{2} - \frac{13686260207}{47} a + \frac{157328368641}{47} \) \( \bigl[3 a^{4} - 2 a^{3} - 15 a^{2} + 2 a + 5\) , \( -a^{3} + 2 a^{2} + 4 a - 4\) , \( 2 a^{4} - a^{3} - 10 a^{2} + 3\) , \( 4 a^{4} - 6 a^{3} - 10 a^{2} + 2 a - 3\) , \( 19 a^{4} - 11 a^{3} - 83 a^{2} - 29 a + 17\bigr] \) ${y}^2+\left(3a^{4}-2a^{3}-15a^{2}+2a+5\right){x}{y}+\left(2a^{4}-a^{3}-10a^{2}+3\right){y}={x}^{3}+\left(-a^{3}+2a^{2}+4a-4\right){x}^{2}+\left(4a^{4}-6a^{3}-10a^{2}+2a-3\right){x}+19a^{4}-11a^{3}-83a^{2}-29a+17$
47.2-c1 47.2-c 5.5.70601.1 \( 47 \) $1$ $\mathsf{trivial}$ $0.010452360$ $11112.37363$ 2.185676081 \( -\frac{87216945}{47} a^{4} - \frac{132154029}{47} a^{3} + \frac{104407562}{47} a^{2} + \frac{90132064}{47} a - \frac{34286979}{47} \) \( \bigl[3 a^{4} - 2 a^{3} - 15 a^{2} + 2 a + 5\) , \( 3 a^{4} - 2 a^{3} - 15 a^{2} + a + 5\) , \( 1\) , \( 8 a^{4} - 5 a^{3} - 41 a^{2} - a + 23\) , \( 4 a^{4} - 4 a^{3} - 21 a^{2} + 8 a + 17\bigr] \) ${y}^2+\left(3a^{4}-2a^{3}-15a^{2}+2a+5\right){x}{y}+{y}={x}^{3}+\left(3a^{4}-2a^{3}-15a^{2}+a+5\right){x}^{2}+\left(8a^{4}-5a^{3}-41a^{2}-a+23\right){x}+4a^{4}-4a^{3}-21a^{2}+8a+17$
49.1-a1 49.1-a 5.5.70601.1 \( 7^{2} \) $0$ $\mathsf{trivial}$ $1$ $273.4817282$ 2.058509545 \( -\frac{3986622664}{117649} a^{4} + \frac{2668349896}{117649} a^{3} + \frac{20834045607}{117649} a^{2} - \frac{162996513}{16807} a - \frac{12309440397}{117649} \) \( \bigl[3 a^{4} - 2 a^{3} - 15 a^{2} + 2 a + 5\) , \( -a^{3} + a^{2} + 4 a - 2\) , \( a^{4} - a^{3} - 4 a^{2} + a + 1\) , \( -17 a^{4} + 92 a^{2} + 46 a - 22\) , \( 6 a^{4} - 2 a^{3} - 30 a^{2} - 11 a + 8\bigr] \) ${y}^2+\left(3a^{4}-2a^{3}-15a^{2}+2a+5\right){x}{y}+\left(a^{4}-a^{3}-4a^{2}+a+1\right){y}={x}^{3}+\left(-a^{3}+a^{2}+4a-2\right){x}^{2}+\left(-17a^{4}+92a^{2}+46a-22\right){x}+6a^{4}-2a^{3}-30a^{2}-11a+8$
49.1-a2 49.1-a 5.5.70601.1 \( 7^{2} \) $0$ $\mathsf{trivial}$ $1$ $273.4817282$ 2.058509545 \( \frac{392767}{49} a^{4} + \frac{404875}{49} a^{3} - \frac{2995121}{49} a^{2} - \frac{227585}{7} a + \frac{856140}{49} \) \( \bigl[3 a^{4} - 2 a^{3} - 15 a^{2} + a + 5\) , \( -3 a^{4} + 2 a^{3} + 15 a^{2} - 6\) , \( 3 a^{4} - 2 a^{3} - 15 a^{2} + a + 5\) , \( -2 a^{4} + a^{3} + 8 a^{2} + 3 a + 3\) , \( -11 a^{4} + 7 a^{3} + 56 a^{2} + a - 26\bigr] \) ${y}^2+\left(3a^{4}-2a^{3}-15a^{2}+a+5\right){x}{y}+\left(3a^{4}-2a^{3}-15a^{2}+a+5\right){y}={x}^{3}+\left(-3a^{4}+2a^{3}+15a^{2}-6\right){x}^{2}+\left(-2a^{4}+a^{3}+8a^{2}+3a+3\right){x}-11a^{4}+7a^{3}+56a^{2}+a-26$
49.1-b1 49.1-b 5.5.70601.1 \( 7^{2} \) $0$ $\mathsf{trivial}$ $1$ $336.2215358$ 1.265377481 \( -32590851870 a^{4} + 22201278229 a^{3} + 170088446312 a^{2} - 10951938243 a - 101553473094 \) \( \bigl[a^{4} - 6 a^{2} - 2 a + 3\) , \( -a^{4} + a^{3} + 4 a^{2} + 1\) , \( 2 a^{4} - a^{3} - 11 a^{2} + 6\) , \( -11 a^{4} + 16 a^{3} + 42 a^{2} - 35 a + 3\) , \( -89 a^{4} + 160 a^{3} + 310 a^{2} - 419 a + 92\bigr] \) ${y}^2+\left(a^{4}-6a^{2}-2a+3\right){x}{y}+\left(2a^{4}-a^{3}-11a^{2}+6\right){y}={x}^{3}+\left(-a^{4}+a^{3}+4a^{2}+1\right){x}^{2}+\left(-11a^{4}+16a^{3}+42a^{2}-35a+3\right){x}-89a^{4}+160a^{3}+310a^{2}-419a+92$
49.1-b2 49.1-b 5.5.70601.1 \( 7^{2} \) $0$ $\mathsf{trivial}$ $1$ $336.2215358$ 1.265377481 \( -78417003901 a^{4} + 219037828056 a^{3} - 703259394 a^{2} - 155572879252 a + 43729126161 \) \( \bigl[3 a^{4} - 2 a^{3} - 15 a^{2} + a + 6\) , \( a^{4} - a^{3} - 4 a^{2} + 2 a - 1\) , \( 2 a^{4} - a^{3} - 11 a^{2} + a + 6\) , \( a^{4} + 2 a^{3} - 8 a^{2} - 9 a - 1\) , \( -12 a^{4} + 4 a^{3} + 59 a^{2} + 22 a - 16\bigr] \) ${y}^2+\left(3a^{4}-2a^{3}-15a^{2}+a+6\right){x}{y}+\left(2a^{4}-a^{3}-11a^{2}+a+6\right){y}={x}^{3}+\left(a^{4}-a^{3}-4a^{2}+2a-1\right){x}^{2}+\left(a^{4}+2a^{3}-8a^{2}-9a-1\right){x}-12a^{4}+4a^{3}+59a^{2}+22a-16$
49.1-c1 49.1-c 5.5.70601.1 \( 7^{2} \) $1$ $\mathsf{trivial}$ $1.276891735$ $116.8049831$ 2.806596797 \( -32590851870 a^{4} + 22201278229 a^{3} + 170088446312 a^{2} - 10951938243 a - 101553473094 \) \( \bigl[a\) , \( -a^{4} + 5 a^{2} + 2 a\) , \( 3 a^{4} - 2 a^{3} - 15 a^{2} + 2 a + 5\) , \( -6 a^{4} + 16 a^{3} + 18 a^{2} - 53 a\) , \( -63 a^{4} + 161 a^{3} + 176 a^{2} - 503 a + 108\bigr] \) ${y}^2+a{x}{y}+\left(3a^{4}-2a^{3}-15a^{2}+2a+5\right){y}={x}^{3}+\left(-a^{4}+5a^{2}+2a\right){x}^{2}+\left(-6a^{4}+16a^{3}+18a^{2}-53a\right){x}-63a^{4}+161a^{3}+176a^{2}-503a+108$
49.1-c2 49.1-c 5.5.70601.1 \( 7^{2} \) $1$ $\mathsf{trivial}$ $0.425630578$ $350.4149495$ 2.806596797 \( -78417003901 a^{4} + 219037828056 a^{3} - 703259394 a^{2} - 155572879252 a + 43729126161 \) \( \bigl[2 a^{4} - 2 a^{3} - 9 a^{2} + 3 a + 3\) , \( -2 a^{4} + a^{3} + 10 a^{2} + a - 4\) , \( 0\) , \( -15 a^{4} + 12 a^{3} + 74 a^{2} - 8 a - 40\) , \( -33 a^{4} + 21 a^{3} + 176 a^{2} - 10 a - 106\bigr] \) ${y}^2+\left(2a^{4}-2a^{3}-9a^{2}+3a+3\right){x}{y}={x}^{3}+\left(-2a^{4}+a^{3}+10a^{2}+a-4\right){x}^{2}+\left(-15a^{4}+12a^{3}+74a^{2}-8a-40\right){x}-33a^{4}+21a^{3}+176a^{2}-10a-106$
53.1-a1 53.1-a 5.5.70601.1 \( 53 \) $1$ $\mathsf{trivial}$ $0.104754266$ $1594.251086$ 3.142628308 \( -\frac{561873647340}{53} a^{4} + \frac{106058296968}{53} a^{3} + \frac{2895622251362}{53} a^{2} + \frac{1224893580269}{53} a - \frac{693126760539}{53} \) \( \bigl[2 a^{4} - 2 a^{3} - 9 a^{2} + 4 a + 2\) , \( a^{4} - 2 a^{3} - 3 a^{2} + 5 a - 1\) , \( 2 a^{4} - a^{3} - 10 a^{2} - a + 3\) , \( 30 a^{4} - 5 a^{3} - 157 a^{2} - 65 a + 36\) , \( 142 a^{4} - 64 a^{3} - 658 a^{2} - 250 a + 149\bigr] \) ${y}^2+\left(2a^{4}-2a^{3}-9a^{2}+4a+2\right){x}{y}+\left(2a^{4}-a^{3}-10a^{2}-a+3\right){y}={x}^{3}+\left(a^{4}-2a^{3}-3a^{2}+5a-1\right){x}^{2}+\left(30a^{4}-5a^{3}-157a^{2}-65a+36\right){x}+142a^{4}-64a^{3}-658a^{2}-250a+149$
53.1-a2 53.1-a 5.5.70601.1 \( 53 \) $1$ $\mathsf{trivial}$ $0.034918088$ $4782.753259$ 3.142628308 \( -\frac{253459126857}{148877} a^{4} + \frac{707710137815}{148877} a^{3} - \frac{1843009819}{148877} a^{2} - \frac{502269847354}{148877} a + \frac{141355191473}{148877} \) \( \bigl[2 a^{4} - 2 a^{3} - 9 a^{2} + 4 a + 3\) , \( -a^{4} + a^{3} + 4 a^{2} - a - 1\) , \( a^{4} - 6 a^{2} - 2 a + 4\) , \( a^{4} + 6 a^{3} - 11 a^{2} - 29 a + 7\) , \( 7 a^{4} + 2 a^{3} - 39 a^{2} - 30 a + 12\bigr] \) ${y}^2+\left(2a^{4}-2a^{3}-9a^{2}+4a+3\right){x}{y}+\left(a^{4}-6a^{2}-2a+4\right){y}={x}^{3}+\left(-a^{4}+a^{3}+4a^{2}-a-1\right){x}^{2}+\left(a^{4}+6a^{3}-11a^{2}-29a+7\right){x}+7a^{4}+2a^{3}-39a^{2}-30a+12$
53.2-a1 53.2-a 5.5.70601.1 \( 53 \) $1$ $\mathsf{trivial}$ $0.065935189$ $2675.868786$ 3.320065502 \( -\frac{9071767}{53} a^{4} + \frac{11769744}{53} a^{3} + \frac{57578323}{53} a^{2} - \frac{6421884}{53} a - \frac{35004004}{53} \) \( \bigl[a + 1\) , \( -a^{4} + a^{3} + 4 a^{2}\) , \( a^{4} - a^{3} - 5 a^{2} + 3 a + 2\) , \( -7 a^{4} + 3 a^{3} + 39 a^{2} + 5 a - 25\) , \( 9 a^{4} - 7 a^{3} - 46 a^{2} + 8 a + 25\bigr] \) ${y}^2+\left(a+1\right){x}{y}+\left(a^{4}-a^{3}-5a^{2}+3a+2\right){y}={x}^{3}+\left(-a^{4}+a^{3}+4a^{2}\right){x}^{2}+\left(-7a^{4}+3a^{3}+39a^{2}+5a-25\right){x}+9a^{4}-7a^{3}-46a^{2}+8a+25$
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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.