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Label Class Base field Conductor norm Rank Torsion CM Regulator Period Leading coeff j-invariant Weierstrass coefficients Weierstrass equation
11.1-a1 11.1-a 5.5.38569.1 \( 11 \) $0$ $\Z/2\Z$ $1$ $205.2864036$ 1.045300112 \( -\frac{45325369488186869}{14641} a^{4} - \frac{35840628972993514}{14641} a^{3} + \frac{198286348576285195}{14641} a^{2} + \frac{156793317131501219}{14641} a - \frac{57319209614084853}{14641} \) \( \bigl[2 a^{4} + a^{3} - 9 a^{2} - 4 a + 4\) , \( 2 a^{4} + a^{3} - 10 a^{2} - 5 a + 7\) , \( 0\) , \( -12 a^{4} - 4 a^{3} + 60 a^{2} + 20 a - 48\) , \( -79 a^{4} - 24 a^{3} + 391 a^{2} + 116 a - 295\bigr] \) ${y}^2+\left(2a^{4}+a^{3}-9a^{2}-4a+4\right){x}{y}={x}^{3}+\left(2a^{4}+a^{3}-10a^{2}-5a+7\right){x}^{2}+\left(-12a^{4}-4a^{3}+60a^{2}+20a-48\right){x}-79a^{4}-24a^{3}+391a^{2}+116a-295$
11.1-a2 11.1-a 5.5.38569.1 \( 11 \) $0$ $\Z/2\Z$ $1$ $41.05728072$ 1.045300112 \( \frac{38267658849058227209117423964971}{672749994932560009201} a^{4} - \frac{78660601240615996179672423975313}{672749994932560009201} a^{3} - \frac{45362244803600084463716093252952}{672749994932560009201} a^{2} + \frac{92081451737609143763002263964608}{672749994932560009201} a - \frac{20518519684505025230375543625252}{672749994932560009201} \) \( \bigl[a^{2} - 2\) , \( 2 a^{4} + a^{3} - 9 a^{2} - 3 a + 4\) , \( 0\) , \( -96 a^{4} + 168 a^{3} + 661 a^{2} - 755 a - 1358\) , \( 5500 a^{4} + 560 a^{3} - 28426 a^{2} - 4444 a + 23872\bigr] \) ${y}^2+\left(a^{2}-2\right){x}{y}={x}^{3}+\left(2a^{4}+a^{3}-9a^{2}-3a+4\right){x}^{2}+\left(-96a^{4}+168a^{3}+661a^{2}-755a-1358\right){x}+5500a^{4}+560a^{3}-28426a^{2}-4444a+23872$
11.1-a3 11.1-a 5.5.38569.1 \( 11 \) $0$ $\Z/2\Z$ $1$ $410.5728072$ 1.045300112 \( \frac{114690314}{121} a^{4} + \frac{90982985}{121} a^{3} - \frac{501204949}{121} a^{2} - \frac{397451243}{121} a + \frac{143972139}{121} \) \( \bigl[2 a^{4} + a^{3} - 9 a^{2} - 4 a + 4\) , \( 2 a^{4} + a^{3} - 10 a^{2} - 5 a + 7\) , \( 0\) , \( 3 a^{4} + a^{3} - 15 a^{2} - 5 a + 12\) , \( 0\bigr] \) ${y}^2+\left(2a^{4}+a^{3}-9a^{2}-4a+4\right){x}{y}={x}^{3}+\left(2a^{4}+a^{3}-10a^{2}-5a+7\right){x}^{2}+\left(3a^{4}+a^{3}-15a^{2}-5a+12\right){x}$
11.1-a4 11.1-a 5.5.38569.1 \( 11 \) $0$ $\Z/2\Z$ $1$ $82.11456145$ 1.045300112 \( \frac{1473653245695872707204967042154}{25937424601} a^{4} + \frac{3004035201972045797772161182779}{25937424601} a^{3} - \frac{1244554615150765042221453203390}{25937424601} a^{2} - \frac{2537018722422878862920033049866}{25937424601} a + \frac{722912263852424824842374841442}{25937424601} \) \( \bigl[a^{4} - 4 a^{2} + 1\) , \( -a^{2} - a + 1\) , \( 2 a^{4} + a^{3} - 9 a^{2} - 4 a + 5\) , \( 10 a^{4} - 10 a^{3} - 54 a^{2} + 67 a + 4\) , \( 704 a^{4} + 215 a^{3} - 3442 a^{2} - 1166 a + 2698\bigr] \) ${y}^2+\left(a^{4}-4a^{2}+1\right){x}{y}+\left(2a^{4}+a^{3}-9a^{2}-4a+5\right){y}={x}^{3}+\left(-a^{2}-a+1\right){x}^{2}+\left(10a^{4}-10a^{3}-54a^{2}+67a+4\right){x}+704a^{4}+215a^{3}-3442a^{2}-1166a+2698$
11.1-b1 11.1-b 5.5.38569.1 \( 11 \) $0$ $\Z/10\Z$ $1$ $5039.265966$ 1.026379767 \( -\frac{45325369488186869}{14641} a^{4} - \frac{35840628972993514}{14641} a^{3} + \frac{198286348576285195}{14641} a^{2} + \frac{156793317131501219}{14641} a - \frac{57319209614084853}{14641} \) \( \bigl[a + 1\) , \( -a^{4} + a^{3} + 4 a^{2} - 3 a - 2\) , \( a^{4} + a^{3} - 4 a^{2} - 4 a + 2\) , \( -198 a^{4} - 54 a^{3} + 973 a^{2} + 267 a - 713\) , \( 1946 a^{4} + 536 a^{3} - 9581 a^{2} - 2643 a + 7053\bigr] \) ${y}^2+\left(a+1\right){x}{y}+\left(a^{4}+a^{3}-4a^{2}-4a+2\right){y}={x}^{3}+\left(-a^{4}+a^{3}+4a^{2}-3a-2\right){x}^{2}+\left(-198a^{4}-54a^{3}+973a^{2}+267a-713\right){x}+1946a^{4}+536a^{3}-9581a^{2}-2643a+7053$
11.1-b2 11.1-b 5.5.38569.1 \( 11 \) $0$ $\Z/2\Z$ $1$ $1.612565109$ 1.026379767 \( \frac{38267658849058227209117423964971}{672749994932560009201} a^{4} - \frac{78660601240615996179672423975313}{672749994932560009201} a^{3} - \frac{45362244803600084463716093252952}{672749994932560009201} a^{2} + \frac{92081451737609143763002263964608}{672749994932560009201} a - \frac{20518519684505025230375543625252}{672749994932560009201} \) \( \bigl[a^{4} - 4 a^{2} + 2\) , \( a^{2} + a - 3\) , \( a^{4} + a^{3} - 4 a^{2} - 3 a + 2\) , \( 1965 a^{4} + 1435 a^{3} - 8543 a^{2} - 6367 a + 2230\) , \( 9983 a^{4} + 6859 a^{3} - 43325 a^{2} - 30702 a + 11057\bigr] \) ${y}^2+\left(a^{4}-4a^{2}+2\right){x}{y}+\left(a^{4}+a^{3}-4a^{2}-3a+2\right){y}={x}^{3}+\left(a^{2}+a-3\right){x}^{2}+\left(1965a^{4}+1435a^{3}-8543a^{2}-6367a+2230\right){x}+9983a^{4}+6859a^{3}-43325a^{2}-30702a+11057$
11.1-b3 11.1-b 5.5.38569.1 \( 11 \) $0$ $\Z/10\Z$ $1$ $10078.53193$ 1.026379767 \( \frac{114690314}{121} a^{4} + \frac{90982985}{121} a^{3} - \frac{501204949}{121} a^{2} - \frac{397451243}{121} a + \frac{143972139}{121} \) \( \bigl[a^{4} + a^{3} - 4 a^{2} - 4 a + 1\) , \( -a^{4} + 4 a^{2} - a - 1\) , \( a^{2} + a - 1\) , \( -3 a^{4} + 12 a^{2} - 1\) , \( -5 a^{4} + 4 a^{3} + 18 a^{2} - 16 a + 3\bigr] \) ${y}^2+\left(a^{4}+a^{3}-4a^{2}-4a+1\right){x}{y}+\left(a^{2}+a-1\right){y}={x}^{3}+\left(-a^{4}+4a^{2}-a-1\right){x}^{2}+\left(-3a^{4}+12a^{2}-1\right){x}-5a^{4}+4a^{3}+18a^{2}-16a+3$
11.1-b4 11.1-b 5.5.38569.1 \( 11 \) $0$ $\Z/2\Z$ $1$ $3.225130218$ 1.026379767 \( \frac{1473653245695872707204967042154}{25937424601} a^{4} + \frac{3004035201972045797772161182779}{25937424601} a^{3} - \frac{1244554615150765042221453203390}{25937424601} a^{2} - \frac{2537018722422878862920033049866}{25937424601} a + \frac{722912263852424824842374841442}{25937424601} \) \( \bigl[2 a^{4} + a^{3} - 9 a^{2} - 3 a + 4\) , \( -a^{4} - a^{3} + 4 a^{2} + 5 a - 2\) , \( a^{4} - 4 a^{2} + 2\) , \( 59 a^{4} + 38 a^{3} - 336 a^{2} - 106 a + 267\) , \( -27636 a^{4} - 7484 a^{3} + 135836 a^{2} + 37315 a - 99920\bigr] \) ${y}^2+\left(2a^{4}+a^{3}-9a^{2}-3a+4\right){x}{y}+\left(a^{4}-4a^{2}+2\right){y}={x}^{3}+\left(-a^{4}-a^{3}+4a^{2}+5a-2\right){x}^{2}+\left(59a^{4}+38a^{3}-336a^{2}-106a+267\right){x}-27636a^{4}-7484a^{3}+135836a^{2}+37315a-99920$
11.2-a1 11.2-a 5.5.38569.1 \( 11 \) $0$ $\Z/5\Z$ $1$ $5802.035803$ 1.181738014 \( -\frac{47085}{11} a^{4} - \frac{72108}{11} a^{3} + \frac{99835}{11} a^{2} + \frac{108037}{11} a - \frac{35124}{11} \) \( \bigl[a^{2} - 2\) , \( 2 a^{4} + a^{3} - 9 a^{2} - 4 a + 3\) , \( a^{3} - 4 a + 1\) , \( -a^{4} + 3 a^{2} + a + 2\) , \( a^{4} - 4 a^{2} - 1\bigr] \) ${y}^2+\left(a^{2}-2\right){x}{y}+\left(a^{3}-4a+1\right){y}={x}^{3}+\left(2a^{4}+a^{3}-9a^{2}-4a+3\right){x}^{2}+\left(-a^{4}+3a^{2}+a+2\right){x}+a^{4}-4a^{2}-1$
11.2-a2 11.2-a 5.5.38569.1 \( 11 \) $0$ $\mathsf{trivial}$ $1$ $1.856651456$ 1.181738014 \( -\frac{189055389402903109375}{161051} a^{4} + \frac{369423059874161169972}{161051} a^{3} + \frac{223392156144464926449}{161051} a^{2} - \frac{436496489695753499092}{161051} a + \frac{96739883027171908222}{161051} \) \( \bigl[-a^{4} + 5 a^{2} + a - 2\) , \( a^{4} - a^{3} - 4 a^{2} + 3 a + 1\) , \( a^{4} + a^{3} - 4 a^{2} - 4 a + 2\) , \( -6 a^{4} - 90 a^{3} + 108 a^{2} + 359 a - 308\) , \( 40 a^{4} - 663 a^{3} + 389 a^{2} + 2588 a - 1988\bigr] \) ${y}^2+\left(-a^{4}+5a^{2}+a-2\right){x}{y}+\left(a^{4}+a^{3}-4a^{2}-4a+2\right){y}={x}^{3}+\left(a^{4}-a^{3}-4a^{2}+3a+1\right){x}^{2}+\left(-6a^{4}-90a^{3}+108a^{2}+359a-308\right){x}+40a^{4}-663a^{3}+389a^{2}+2588a-1988$
11.2-b1 11.2-b 5.5.38569.1 \( 11 \) $1$ $\mathsf{trivial}$ $0.005433471$ $9903.445669$ 1.369980892 \( -\frac{47085}{11} a^{4} - \frac{72108}{11} a^{3} + \frac{99835}{11} a^{2} + \frac{108037}{11} a - \frac{35124}{11} \) \( \bigl[a^{4} - 4 a^{2} + 2\) , \( -a^{4} - a^{3} + 5 a^{2} + 5 a - 4\) , \( -a^{4} + 5 a^{2} - 3\) , \( a^{3} - a^{2} - 3 a + 4\) , \( -a^{3} + a^{2} + 4 a - 3\bigr] \) ${y}^2+\left(a^{4}-4a^{2}+2\right){x}{y}+\left(-a^{4}+5a^{2}-3\right){y}={x}^{3}+\left(-a^{4}-a^{3}+5a^{2}+5a-4\right){x}^{2}+\left(a^{3}-a^{2}-3a+4\right){x}-a^{3}+a^{2}+4a-3$
11.2-b2 11.2-b 5.5.38569.1 \( 11 \) $1$ $\mathsf{trivial}$ $0.027167356$ $1980.689133$ 1.369980892 \( -\frac{189055389402903109375}{161051} a^{4} + \frac{369423059874161169972}{161051} a^{3} + \frac{223392156144464926449}{161051} a^{2} - \frac{436496489695753499092}{161051} a + \frac{96739883027171908222}{161051} \) \( \bigl[a^{4} - 4 a^{2} + 1\) , \( a^{4} - 5 a^{2} - a + 4\) , \( a^{4} + a^{3} - 4 a^{2} - 4 a + 2\) , \( -788 a^{4} - 219 a^{3} + 3884 a^{2} + 1089 a - 2876\) , \( 13707 a^{4} + 3782 a^{3} - 67511 a^{2} - 18659 a + 49736\bigr] \) ${y}^2+\left(a^{4}-4a^{2}+1\right){x}{y}+\left(a^{4}+a^{3}-4a^{2}-4a+2\right){y}={x}^{3}+\left(a^{4}-5a^{2}-a+4\right){x}^{2}+\left(-788a^{4}-219a^{3}+3884a^{2}+1089a-2876\right){x}+13707a^{4}+3782a^{3}-67511a^{2}-18659a+49736$
17.1-a1 17.1-a 5.5.38569.1 \( 17 \) $0$ $\mathsf{trivial}$ $1$ $281.9907424$ 1.435871784 \( \frac{315075396}{17} a^{4} - \frac{315033996}{17} a^{3} - \frac{1206535946}{17} a^{2} + \frac{1164182948}{17} a - \frac{133556319}{17} \) \( \bigl[a^{4} - 4 a^{2} + 1\) , \( -3 a^{4} - a^{3} + 14 a^{2} + 4 a - 8\) , \( a^{4} - 4 a^{2} + a + 2\) , \( 2 a^{4} - 2 a^{3} - 11 a^{2} + 6 a + 9\) , \( -a^{4} - 4 a^{3} + 7 a^{2} + 16 a - 12\bigr] \) ${y}^2+\left(a^{4}-4a^{2}+1\right){x}{y}+\left(a^{4}-4a^{2}+a+2\right){y}={x}^{3}+\left(-3a^{4}-a^{3}+14a^{2}+4a-8\right){x}^{2}+\left(2a^{4}-2a^{3}-11a^{2}+6a+9\right){x}-a^{4}-4a^{3}+7a^{2}+16a-12$
17.1-b1 17.1-b 5.5.38569.1 \( 17 \) $0$ $\Z/2\Z$ $1$ $3.731050729$ 1.215883425 \( -\frac{4610174704839696307681031019985}{48661191875666868481} a^{4} - \frac{3646564185715492789590081314801}{48661191875666868481} a^{3} + \frac{20165287106639313522557968182292}{48661191875666868481} a^{2} + \frac{15946358590737268511990785275315}{48661191875666868481} a - \frac{5829599632074986762576303718745}{48661191875666868481} \) \( \bigl[a^{4} + a^{3} - 4 a^{2} - 3 a + 1\) , \( 1\) , \( a^{4} + a^{3} - 4 a^{2} - 3 a + 1\) , \( 220 a^{4} + 180 a^{3} - 995 a^{2} - 755 a + 265\) , \( 2642 a^{4} + 2159 a^{3} - 11769 a^{2} - 9228 a + 3361\bigr] \) ${y}^2+\left(a^{4}+a^{3}-4a^{2}-3a+1\right){x}{y}+\left(a^{4}+a^{3}-4a^{2}-3a+1\right){y}={x}^{3}+{x}^{2}+\left(220a^{4}+180a^{3}-995a^{2}-755a+265\right){x}+2642a^{4}+2159a^{3}-11769a^{2}-9228a+3361$
17.1-b2 17.1-b 5.5.38569.1 \( 17 \) $0$ $\Z/8\Z$ $1$ $7641.191893$ 1.215883425 \( -\frac{2140052}{289} a^{4} - \frac{251468}{289} a^{3} + \frac{11446293}{289} a^{2} + \frac{3154266}{289} a - \frac{8210651}{289} \) \( \bigl[a^{4} + a^{3} - 4 a^{2} - 3 a + 1\) , \( 1\) , \( a^{4} + a^{3} - 4 a^{2} - 3 a + 1\) , \( 0\) , \( 0\bigr] \) ${y}^2+\left(a^{4}+a^{3}-4a^{2}-3a+1\right){x}{y}+\left(a^{4}+a^{3}-4a^{2}-3a+1\right){y}={x}^{3}+{x}^{2}$
17.1-b3 17.1-b 5.5.38569.1 \( 17 \) $0$ $\Z/2\Z\oplus\Z/4\Z$ $1$ $3820.595946$ 1.215883425 \( \frac{17040191647890}{83521} a^{4} + \frac{7351908656144}{83521} a^{3} - \frac{77790696866002}{83521} a^{2} - \frac{23717768350207}{83521} a + \frac{57097297334999}{83521} \) \( \bigl[a^{4} + a^{3} - 4 a^{2} - 3 a + 1\) , \( 1\) , \( a^{4} + a^{3} - 4 a^{2} - 3 a + 1\) , \( -5\) , \( 2 a^{4} + a^{3} - 11 a^{2} - 8 a + 6\bigr] \) ${y}^2+\left(a^{4}+a^{3}-4a^{2}-3a+1\right){x}{y}+\left(a^{4}+a^{3}-4a^{2}-3a+1\right){y}={x}^{3}+{x}^{2}-5{x}+2a^{4}+a^{3}-11a^{2}-8a+6$
17.1-b4 17.1-b 5.5.38569.1 \( 17 \) $0$ $\Z/2\Z\oplus\Z/2\Z$ $1$ $119.3936233$ 1.215883425 \( \frac{63035509038380061495748094}{6975757441} a^{4} + \frac{128497588344189495041715327}{6975757441} a^{3} - \frac{53235816441571130890411893}{6975757441} a^{2} - \frac{108520961136492735262181368}{6975757441} a + \frac{30922567893134525558722397}{6975757441} \) \( \bigl[a^{4} + a^{3} - 4 a^{2} - 3 a + 1\) , \( 1\) , \( a^{4} + a^{3} - 4 a^{2} - 3 a + 1\) , \( 10 a^{4} + 5 a^{3} - 55 a^{2} - 40 a + 10\) , \( 38 a^{4} + 12 a^{3} - 226 a^{2} - 161 a + 64\bigr] \) ${y}^2+\left(a^{4}+a^{3}-4a^{2}-3a+1\right){x}{y}+\left(a^{4}+a^{3}-4a^{2}-3a+1\right){y}={x}^{3}+{x}^{2}+\left(10a^{4}+5a^{3}-55a^{2}-40a+10\right){x}+38a^{4}+12a^{3}-226a^{2}-161a+64$
17.1-b5 17.1-b 5.5.38569.1 \( 17 \) $0$ $\Z/4\Z$ $1$ $1910.297973$ 1.215883425 \( \frac{28909732838037746498}{289} a^{4} + \frac{7974304313410177057}{289} a^{3} - \frac{142349091590829634411}{289} a^{2} - \frac{39264789065394150664}{289} a + \frac{104808408511901573715}{289} \) \( \bigl[a^{4} + a^{3} - 4 a^{2} - 3 a + 1\) , \( 1\) , \( a^{4} + a^{3} - 4 a^{2} - 3 a + 1\) , \( -10 a^{4} - 5 a^{3} + 55 a^{2} + 40 a - 100\) , \( 54 a^{4} + 34 a^{3} - 280 a^{2} - 207 a + 352\bigr] \) ${y}^2+\left(a^{4}+a^{3}-4a^{2}-3a+1\right){x}{y}+\left(a^{4}+a^{3}-4a^{2}-3a+1\right){y}={x}^{3}+{x}^{2}+\left(-10a^{4}-5a^{3}+55a^{2}+40a-100\right){x}+54a^{4}+34a^{3}-280a^{2}-207a+352$
17.1-b6 17.1-b 5.5.38569.1 \( 17 \) $0$ $\Z/2\Z$ $1$ $3.731050729$ 1.215883425 \( \frac{191010208049176061567432964418935750417}{83521} a^{4} + \frac{389373409648192880822797404169052473649}{83521} a^{3} - \frac{161315178223120659347331199752509351188}{83521} a^{2} - \frac{328840231180583481626805905878816700787}{83521} a + \frac{93701569431652774399214957840089814633}{83521} \) \( \bigl[a^{4} + a^{3} - 4 a^{2} - 3 a + 1\) , \( 1\) , \( a^{4} + a^{3} - 4 a^{2} - 3 a + 1\) , \( -40 a^{4} - 90 a^{3} + 5 a^{2} + 35 a - 5\) , \( -702 a^{4} - 1511 a^{3} + 317 a^{2} + 1054 a - 261\bigr] \) ${y}^2+\left(a^{4}+a^{3}-4a^{2}-3a+1\right){x}{y}+\left(a^{4}+a^{3}-4a^{2}-3a+1\right){y}={x}^{3}+{x}^{2}+\left(-40a^{4}-90a^{3}+5a^{2}+35a-5\right){x}-702a^{4}-1511a^{3}+317a^{2}+1054a-261$
17.1-c1 17.1-c 5.5.38569.1 \( 17 \) $1$ $\Z/2\Z$ $1.306405258$ $96.00912967$ 1.596655686 \( -\frac{4610174704839696307681031019985}{48661191875666868481} a^{4} - \frac{3646564185715492789590081314801}{48661191875666868481} a^{3} + \frac{20165287106639313522557968182292}{48661191875666868481} a^{2} + \frac{15946358590737268511990785275315}{48661191875666868481} a - \frac{5829599632074986762576303718745}{48661191875666868481} \) \( \bigl[2 a^{4} + a^{3} - 9 a^{2} - 3 a + 5\) , \( a^{3} - 3 a + 1\) , \( 0\) , \( 46 a^{4} - 88 a^{3} - 358 a^{2} - 19 a - 1\) , \( -1595 a^{4} - 2131 a^{3} + 3507 a^{2} + 2621 a - 912\bigr] \) ${y}^2+\left(2a^{4}+a^{3}-9a^{2}-3a+5\right){x}{y}={x}^{3}+\left(a^{3}-3a+1\right){x}^{2}+\left(46a^{4}-88a^{3}-358a^{2}-19a-1\right){x}-1595a^{4}-2131a^{3}+3507a^{2}+2621a-912$
17.1-c2 17.1-c 5.5.38569.1 \( 17 \) $1$ $\Z/4\Z$ $0.653202629$ $768.0730373$ 1.596655686 \( -\frac{2140052}{289} a^{4} - \frac{251468}{289} a^{3} + \frac{11446293}{289} a^{2} + \frac{3154266}{289} a - \frac{8210651}{289} \) \( \bigl[2 a^{4} + a^{3} - 9 a^{2} - 3 a + 5\) , \( a^{3} - 3 a + 1\) , \( 0\) , \( a^{4} + 2 a^{3} - 3 a^{2} - 4 a + 4\) , \( 0\bigr] \) ${y}^2+\left(2a^{4}+a^{3}-9a^{2}-3a+5\right){x}{y}={x}^{3}+\left(a^{3}-3a+1\right){x}^{2}+\left(a^{4}+2a^{3}-3a^{2}-4a+4\right){x}$
17.1-c3 17.1-c 5.5.38569.1 \( 17 \) $1$ $\Z/2\Z\oplus\Z/2\Z$ $1.306405258$ $384.0365186$ 1.596655686 \( \frac{17040191647890}{83521} a^{4} + \frac{7351908656144}{83521} a^{3} - \frac{77790696866002}{83521} a^{2} - \frac{23717768350207}{83521} a + \frac{57097297334999}{83521} \) \( \bigl[-a^{4} + 5 a^{2} + a - 2\) , \( -2 a^{4} - a^{3} + 9 a^{2} + 3 a - 5\) , \( a^{2} - 2\) , \( -11 a^{4} + 28 a^{3} + 5 a^{2} - 40 a + 10\) , \( -87 a^{4} + 174 a^{3} + 98 a^{2} - 209 a + 46\bigr] \) ${y}^2+\left(-a^{4}+5a^{2}+a-2\right){x}{y}+\left(a^{2}-2\right){y}={x}^{3}+\left(-2a^{4}-a^{3}+9a^{2}+3a-5\right){x}^{2}+\left(-11a^{4}+28a^{3}+5a^{2}-40a+10\right){x}-87a^{4}+174a^{3}+98a^{2}-209a+46$
17.1-c4 17.1-c 5.5.38569.1 \( 17 \) $1$ $\Z/2\Z\oplus\Z/2\Z$ $2.612810517$ $192.0182593$ 1.596655686 \( \frac{63035509038380061495748094}{6975757441} a^{4} + \frac{128497588344189495041715327}{6975757441} a^{3} - \frac{53235816441571130890411893}{6975757441} a^{2} - \frac{108520961136492735262181368}{6975757441} a + \frac{30922567893134525558722397}{6975757441} \) \( \bigl[-a^{4} + 5 a^{2} + a - 3\) , \( -a^{4} + a^{3} + 4 a^{2} - 4 a\) , \( 0\) , \( 72 a^{4} + 36 a^{3} - 313 a^{2} - 173 a + 70\) , \( -339 a^{4} - 336 a^{3} + 1494 a^{2} + 1418 a - 496\bigr] \) ${y}^2+\left(-a^{4}+5a^{2}+a-3\right){x}{y}={x}^{3}+\left(-a^{4}+a^{3}+4a^{2}-4a\right){x}^{2}+\left(72a^{4}+36a^{3}-313a^{2}-173a+70\right){x}-339a^{4}-336a^{3}+1494a^{2}+1418a-496$
17.1-c5 17.1-c 5.5.38569.1 \( 17 \) $1$ $\Z/2\Z$ $2.612810517$ $12.00114120$ 1.596655686 \( \frac{28909732838037746498}{289} a^{4} + \frac{7974304313410177057}{289} a^{3} - \frac{142349091590829634411}{289} a^{2} - \frac{39264789065394150664}{289} a + \frac{104808408511901573715}{289} \) \( \bigl[a^{4} + a^{3} - 4 a^{2} - 4 a + 2\) , \( 3 a^{4} + a^{3} - 14 a^{2} - 5 a + 6\) , \( a^{4} + a^{3} - 4 a^{2} - 4 a + 2\) , \( -335 a^{4} - 75 a^{3} + 1619 a^{2} + 424 a - 1189\) , \( -4388 a^{4} - 1128 a^{3} + 21464 a^{2} + 5822 a - 15755\bigr] \) ${y}^2+\left(a^{4}+a^{3}-4a^{2}-4a+2\right){x}{y}+\left(a^{4}+a^{3}-4a^{2}-4a+2\right){y}={x}^{3}+\left(3a^{4}+a^{3}-14a^{2}-5a+6\right){x}^{2}+\left(-335a^{4}-75a^{3}+1619a^{2}+424a-1189\right){x}-4388a^{4}-1128a^{3}+21464a^{2}+5822a-15755$
17.1-c6 17.1-c 5.5.38569.1 \( 17 \) $1$ $\Z/2\Z$ $5.225621035$ $6.000570604$ 1.596655686 \( \frac{191010208049176061567432964418935750417}{83521} a^{4} + \frac{389373409648192880822797404169052473649}{83521} a^{3} - \frac{161315178223120659347331199752509351188}{83521} a^{2} - \frac{328840231180583481626805905878816700787}{83521} a + \frac{93701569431652774399214957840089814633}{83521} \) \( \bigl[-a^{4} + 5 a^{2} + a - 3\) , \( -a^{4} + a^{3} + 4 a^{2} - 4 a\) , \( 0\) , \( -28 a^{4} + 51 a^{3} + 17 a^{2} - 333 a + 90\) , \( -855 a^{4} - 796 a^{3} + 3008 a^{2} + 2115 a - 791\bigr] \) ${y}^2+\left(-a^{4}+5a^{2}+a-3\right){x}{y}={x}^{3}+\left(-a^{4}+a^{3}+4a^{2}-4a\right){x}^{2}+\left(-28a^{4}+51a^{3}+17a^{2}-333a+90\right){x}-855a^{4}-796a^{3}+3008a^{2}+2115a-791$
17.1-d1 17.1-d 5.5.38569.1 \( 17 \) $1$ $\mathsf{trivial}$ $0.002724519$ $22204.28979$ 1.540201717 \( \frac{315075396}{17} a^{4} - \frac{315033996}{17} a^{3} - \frac{1206535946}{17} a^{2} + \frac{1164182948}{17} a - \frac{133556319}{17} \) \( \bigl[2 a^{4} + a^{3} - 9 a^{2} - 3 a + 4\) , \( -2 a^{4} - a^{3} + 10 a^{2} + 5 a - 7\) , \( a^{4} - 4 a^{2} + 1\) , \( -2 a^{4} - 2 a^{3} + 9 a^{2} + 8 a - 6\) , \( 3 a^{4} - 15 a^{2} - a + 12\bigr] \) ${y}^2+\left(2a^{4}+a^{3}-9a^{2}-3a+4\right){x}{y}+\left(a^{4}-4a^{2}+1\right){y}={x}^{3}+\left(-2a^{4}-a^{3}+10a^{2}+5a-7\right){x}^{2}+\left(-2a^{4}-2a^{3}+9a^{2}+8a-6\right){x}+3a^{4}-15a^{2}-a+12$
37.1-a1 37.1-a 5.5.38569.1 \( 37 \) $0$ $\mathsf{trivial}$ $1$ $292.7912956$ 1.490867241 \( \frac{682639360}{37} a^{4} - \frac{785629184}{37} a^{3} - \frac{2508931072}{37} a^{2} + \frac{2887372800}{37} a - \frac{592875520}{37} \) \( \bigl[0\) , \( -a^{4} + 5 a^{2} - a - 2\) , \( a^{4} + a^{3} - 5 a^{2} - 3 a + 3\) , \( a^{4} + a^{3} - 4 a^{2} - 6 a + 3\) , \( a^{4} + a^{3} - 5 a^{2} - 6 a + 1\bigr] \) ${y}^2+\left(a^{4}+a^{3}-5a^{2}-3a+3\right){y}={x}^{3}+\left(-a^{4}+5a^{2}-a-2\right){x}^{2}+\left(a^{4}+a^{3}-4a^{2}-6a+3\right){x}+a^{4}+a^{3}-5a^{2}-6a+1$
37.1-b1 37.1-b 5.5.38569.1 \( 37 \) $0$ $\Z/3\Z$ $1$ $2626.669541$ 1.486085303 \( \frac{3805184}{37} a^{4} + \frac{2985984}{37} a^{3} - \frac{16666624}{37} a^{2} - \frac{13082624}{37} a + \frac{4898816}{37} \) \( \bigl[0\) , \( a^{4} + a^{3} - 5 a^{2} - 5 a + 4\) , \( a^{3} - 3 a + 1\) , \( -5 a^{4} - a^{3} + 24 a^{2} + 5 a - 15\) , \( a^{4} - 5 a^{2} - a + 3\bigr] \) ${y}^2+\left(a^{3}-3a+1\right){y}={x}^{3}+\left(a^{4}+a^{3}-5a^{2}-5a+4\right){x}^{2}+\left(-5a^{4}-a^{3}+24a^{2}+5a-15\right){x}+a^{4}-5a^{2}-a+3$
37.1-b2 37.1-b 5.5.38569.1 \( 37 \) $0$ $\mathsf{trivial}$ $1$ $10.80933967$ 1.486085303 \( \frac{631396984641001648128}{50653} a^{4} + \frac{499267254836904431616}{50653} a^{3} - \frac{2762197178156919664640}{50653} a^{2} - \frac{2184164061589806465024}{50653} a + \frac{798494490468990795776}{50653} \) \( \bigl[0\) , \( a^{4} + a^{3} - 5 a^{2} - 5 a + 4\) , \( a^{3} - 3 a + 1\) , \( -155 a^{4} - 41 a^{3} + 764 a^{2} + 205 a - 565\) , \( -1406 a^{4} - 388 a^{3} + 6922 a^{2} + 1910 a - 5100\bigr] \) ${y}^2+\left(a^{3}-3a+1\right){y}={x}^{3}+\left(a^{4}+a^{3}-5a^{2}-5a+4\right){x}^{2}+\left(-155a^{4}-41a^{3}+764a^{2}+205a-565\right){x}-1406a^{4}-388a^{3}+6922a^{2}+1910a-5100$
37.1-c1 37.1-c 5.5.38569.1 \( 37 \) $1$ $\mathsf{trivial}$ $0.007513104$ $10381.22174$ 1.985723098 \( \frac{3805184}{37} a^{4} + \frac{2985984}{37} a^{3} - \frac{16666624}{37} a^{2} - \frac{13082624}{37} a + \frac{4898816}{37} \) \( \bigl[0\) , \( a^{2} - 1\) , \( a\) , \( a^{2} - 1\) , \( 0\bigr] \) ${y}^2+a{y}={x}^{3}+\left(a^{2}-1\right){x}^{2}+\left(a^{2}-1\right){x}$
37.1-c2 37.1-c 5.5.38569.1 \( 37 \) $1$ $\mathsf{trivial}$ $0.022539312$ $3460.407248$ 1.985723098 \( \frac{631396984641001648128}{50653} a^{4} + \frac{499267254836904431616}{50653} a^{3} - \frac{2762197178156919664640}{50653} a^{2} - \frac{2184164061589806465024}{50653} a + \frac{798494490468990795776}{50653} \) \( \bigl[0\) , \( a^{2} - 1\) , \( a\) , \( 11 a^{2} - 41\) , \( 8 a^{4} - 61 a^{2} + 116\bigr] \) ${y}^2+a{y}={x}^{3}+\left(a^{2}-1\right){x}^{2}+\left(11a^{2}-41\right){x}+8a^{4}-61a^{2}+116$
37.1-d1 37.1-d 5.5.38569.1 \( 37 \) $1$ $\mathsf{trivial}$ $0.005988410$ $12153.67333$ 1.852976501 \( \frac{682639360}{37} a^{4} - \frac{785629184}{37} a^{3} - \frac{2508931072}{37} a^{2} + \frac{2887372800}{37} a - \frac{592875520}{37} \) \( \bigl[0\) , \( -a^{4} + a^{3} + 4 a^{2} - 3 a - 1\) , \( a + 1\) , \( -a^{4} + a^{3} + 4 a^{2} - 4 a\) , \( -a^{4} - a^{3} + a^{2} - a + 1\bigr] \) ${y}^2+\left(a+1\right){y}={x}^{3}+\left(-a^{4}+a^{3}+4a^{2}-3a-1\right){x}^{2}+\left(-a^{4}+a^{3}+4a^{2}-4a\right){x}-a^{4}-a^{3}+a^{2}-a+1$
43.2-a1 43.2-a 5.5.38569.1 \( 43 \) $0$ $\mathsf{trivial}$ $1$ $0.856262961$ 1.495485096 \( \frac{503430677683141400412260203661}{271818611107} a^{4} - \frac{983743624658765679781695980679}{271818611107} a^{3} - \frac{594840025499343907143854406374}{271818611107} a^{2} + \frac{1162364767809040613354336495114}{271818611107} a - \frac{257630586761460389878355097065}{271818611107} \) \( \bigl[a^{4} - 4 a^{2} + 1\) , \( a^{4} - a^{3} - 4 a^{2} + 5 a\) , \( -a^{4} + 5 a^{2} - 3\) , \( -438 a^{4} - 108 a^{3} + 2123 a^{2} + 558 a - 1557\) , \( -6146 a^{4} - 1666 a^{3} + 30140 a^{2} + 8257 a - 22182\bigr] \) ${y}^2+\left(a^{4}-4a^{2}+1\right){x}{y}+\left(-a^{4}+5a^{2}-3\right){y}={x}^{3}+\left(a^{4}-a^{3}-4a^{2}+5a\right){x}^{2}+\left(-438a^{4}-108a^{3}+2123a^{2}+558a-1557\right){x}-6146a^{4}-1666a^{3}+30140a^{2}+8257a-22182$
43.2-a2 43.2-a 5.5.38569.1 \( 43 \) $0$ $\Z/7\Z$ $1$ $14391.21159$ 1.495485096 \( \frac{76659}{43} a^{4} + \frac{48039}{43} a^{3} - \frac{312145}{43} a^{2} - \frac{219027}{43} a + \frac{79541}{43} \) \( \bigl[a^{3} - 3 a + 1\) , \( a^{4} - 4 a^{2} - a + 2\) , \( a^{2} + a - 1\) , \( -a + 1\) , \( 0\bigr] \) ${y}^2+\left(a^{3}-3a+1\right){x}{y}+\left(a^{2}+a-1\right){y}={x}^{3}+\left(a^{4}-4a^{2}-a+2\right){x}^{2}+\left(-a+1\right){x}$
43.2-b1 43.2-b 5.5.38569.1 \( 43 \) $0$ $\mathsf{trivial}$ $1$ $338.5842133$ 1.724040705 \( \frac{434298794}{43} a^{4} + \frac{343516845}{43} a^{3} - \frac{1899978901}{43} a^{2} - \frac{1502757203}{43} a + \frac{549334398}{43} \) \( \bigl[-a^{4} + 5 a^{2} - 3\) , \( a^{2} + a - 1\) , \( a^{4} - 4 a^{2} + a + 2\) , \( a^{4} + a^{3} - 4 a^{2} - 3 a + 4\) , \( -3 a^{4} + 5 a^{3} + 4 a^{2} - 5 a\bigr] \) ${y}^2+\left(-a^{4}+5a^{2}-3\right){x}{y}+\left(a^{4}-4a^{2}+a+2\right){y}={x}^{3}+\left(a^{2}+a-1\right){x}^{2}+\left(a^{4}+a^{3}-4a^{2}-3a+4\right){x}-3a^{4}+5a^{3}+4a^{2}-5a$
43.2-c1 43.2-c 5.5.38569.1 \( 43 \) $0$ $\mathsf{trivial}$ $1$ $286.1746394$ 1.457175816 \( -\frac{51665932627}{43} a^{4} - \frac{10018445802}{43} a^{3} + \frac{250693585412}{43} a^{2} + \frac{53592431783}{43} a - \frac{173974818865}{43} \) \( \bigl[a^{3} - 4 a\) , \( -3 a^{4} - a^{3} + 14 a^{2} + 4 a - 7\) , \( -a^{4} + 5 a^{2} - 2\) , \( -2 a^{4} - 3 a^{3} + 4 a^{2} + 5 a + 3\) , \( 2 a^{4} + 5 a^{3} + a^{2} - 3 a - 2\bigr] \) ${y}^2+\left(a^{3}-4a\right){x}{y}+\left(-a^{4}+5a^{2}-2\right){y}={x}^{3}+\left(-3a^{4}-a^{3}+14a^{2}+4a-7\right){x}^{2}+\left(-2a^{4}-3a^{3}+4a^{2}+5a+3\right){x}+2a^{4}+5a^{3}+a^{2}-3a-2$
43.2-d1 43.2-d 5.5.38569.1 \( 43 \) $1$ $\mathsf{trivial}$ $0.006318915$ $12588.52134$ 2.025200877 \( -\frac{51665932627}{43} a^{4} - \frac{10018445802}{43} a^{3} + \frac{250693585412}{43} a^{2} + \frac{53592431783}{43} a - \frac{173974818865}{43} \) \( \bigl[2 a^{4} + a^{3} - 9 a^{2} - 3 a + 5\) , \( 2 a^{4} - 9 a^{2} + 3\) , \( a^{2} + a - 2\) , \( 6 a^{4} + 2 a^{3} - 27 a^{2} - 14 a + 18\) , \( -9 a^{4} + 14 a^{3} + 12 a^{2} - 10 a + 6\bigr] \) ${y}^2+\left(2a^{4}+a^{3}-9a^{2}-3a+5\right){x}{y}+\left(a^{2}+a-2\right){y}={x}^{3}+\left(2a^{4}-9a^{2}+3\right){x}^{2}+\left(6a^{4}+2a^{3}-27a^{2}-14a+18\right){x}-9a^{4}+14a^{3}+12a^{2}-10a+6$
43.2-e1 43.2-e 5.5.38569.1 \( 43 \) $1$ $\mathsf{trivial}$ $0.008342728$ $9825.480120$ 2.086953262 \( \frac{434298794}{43} a^{4} + \frac{343516845}{43} a^{3} - \frac{1899978901}{43} a^{2} - \frac{1502757203}{43} a + \frac{549334398}{43} \) \( \bigl[a^{2} + a - 2\) , \( -1\) , \( a^{4} + a^{3} - 5 a^{2} - 3 a + 4\) , \( a^{4} - 5 a^{2} - a + 3\) , \( -2 a^{3} + 3 a^{2} + 3 a - 3\bigr] \) ${y}^2+\left(a^{2}+a-2\right){x}{y}+\left(a^{4}+a^{3}-5a^{2}-3a+4\right){y}={x}^{3}-{x}^{2}+\left(a^{4}-5a^{2}-a+3\right){x}-2a^{3}+3a^{2}+3a-3$
43.2-f1 43.2-f 5.5.38569.1 \( 43 \) $1$ $\mathsf{trivial}$ $0.453019257$ $172.5067413$ 1.989635632 \( \frac{503430677683141400412260203661}{271818611107} a^{4} - \frac{983743624658765679781695980679}{271818611107} a^{3} - \frac{594840025499343907143854406374}{271818611107} a^{2} + \frac{1162364767809040613354336495114}{271818611107} a - \frac{257630586761460389878355097065}{271818611107} \) \( \bigl[-a^{4} + 5 a^{2} + a - 2\) , \( a^{4} + a^{3} - 5 a^{2} - 4 a + 3\) , \( 2 a^{4} + a^{3} - 9 a^{2} - 3 a + 4\) , \( -15 a^{4} - 5 a^{3} + 79 a^{2} + 29 a - 122\) , \( 27 a^{4} - 24 a^{3} - 192 a^{2} + 18 a + 392\bigr] \) ${y}^2+\left(-a^{4}+5a^{2}+a-2\right){x}{y}+\left(2a^{4}+a^{3}-9a^{2}-3a+4\right){y}={x}^{3}+\left(a^{4}+a^{3}-5a^{2}-4a+3\right){x}^{2}+\left(-15a^{4}-5a^{3}+79a^{2}+29a-122\right){x}+27a^{4}-24a^{3}-192a^{2}+18a+392$
43.2-f2 43.2-f 5.5.38569.1 \( 43 \) $1$ $\mathsf{trivial}$ $0.064717036$ $1207.547189$ 1.989635632 \( \frac{76659}{43} a^{4} + \frac{48039}{43} a^{3} - \frac{312145}{43} a^{2} - \frac{219027}{43} a + \frac{79541}{43} \) \( \bigl[a^{2} - 1\) , \( -a^{3} + 5 a + 1\) , \( 0\) , \( -a^{4} + 5 a^{2} + 3 a + 1\) , \( a^{2} + 2 a\bigr] \) ${y}^2+\left(a^{2}-1\right){x}{y}={x}^{3}+\left(-a^{3}+5a+1\right){x}^{2}+\left(-a^{4}+5a^{2}+3a+1\right){x}+a^{2}+2a$
49.1-a1 49.1-a 5.5.38569.1 \( 7^{2} \) $0$ $\Z/2\Z$ $1$ $308.4021177$ 1.570356158 \( -\frac{5175181428463393170}{5764801} a^{4} - \frac{4092193575688521122}{5764801} a^{3} + \frac{22640069243029692952}{5764801} a^{2} + \frac{17902279789885167463}{5764801} a - \frac{6544778460145840534}{5764801} \) \( \bigl[2 a^{4} + a^{3} - 9 a^{2} - 4 a + 5\) , \( a^{4} - 4 a^{2} + 2\) , \( a^{3} - 3 a + 1\) , \( 15 a^{4} - 4 a^{3} - 65 a^{2} + 4 a + 7\) , \( -24 a^{4} + 3 a^{3} + 20 a^{2} - 133 a + 36\bigr] \) ${y}^2+\left(2a^{4}+a^{3}-9a^{2}-4a+5\right){x}{y}+\left(a^{3}-3a+1\right){y}={x}^{3}+\left(a^{4}-4a^{2}+2\right){x}^{2}+\left(15a^{4}-4a^{3}-65a^{2}+4a+7\right){x}-24a^{4}+3a^{3}+20a^{2}-133a+36$
49.1-a2 49.1-a 5.5.38569.1 \( 7^{2} \) $0$ $\Z/2\Z$ $1$ $616.8042354$ 1.570356158 \( \frac{1243808100}{2401} a^{4} + \frac{1002203176}{2401} a^{3} - \frac{5388495975}{2401} a^{2} - \frac{4276678300}{2401} a + \frac{1561357008}{2401} \) \( \bigl[2 a^{4} + a^{3} - 9 a^{2} - 4 a + 5\) , \( a^{4} - 4 a^{2} + 2\) , \( a^{3} - 3 a + 1\) , \( -4 a^{3} - 10 a^{2} - a + 7\) , \( -11 a^{4} - 23 a^{3} + 5 a^{2} + 15 a - 1\bigr] \) ${y}^2+\left(2a^{4}+a^{3}-9a^{2}-4a+5\right){x}{y}+\left(a^{3}-3a+1\right){y}={x}^{3}+\left(a^{4}-4a^{2}+2\right){x}^{2}+\left(-4a^{3}-10a^{2}-a+7\right){x}-11a^{4}-23a^{3}+5a^{2}+15a-1$
49.1-b1 49.1-b 5.5.38569.1 \( 7^{2} \) $0$ $\Z/2\Z$ $1$ $243.3916011$ 1.239328389 \( -\frac{5175181428463393170}{5764801} a^{4} - \frac{4092193575688521122}{5764801} a^{3} + \frac{22640069243029692952}{5764801} a^{2} + \frac{17902279789885167463}{5764801} a - \frac{6544778460145840534}{5764801} \) \( \bigl[a^{2} + a - 2\) , \( 2 a^{4} + a^{3} - 9 a^{2} - 5 a + 3\) , \( 2 a^{4} + a^{3} - 9 a^{2} - 4 a + 4\) , \( 20 a^{4} + 19 a^{3} - 96 a^{2} - 67 a + 27\) , \( -119 a^{4} - 76 a^{3} + 494 a^{2} + 383 a - 143\bigr] \) ${y}^2+\left(a^{2}+a-2\right){x}{y}+\left(2a^{4}+a^{3}-9a^{2}-4a+4\right){y}={x}^{3}+\left(2a^{4}+a^{3}-9a^{2}-5a+3\right){x}^{2}+\left(20a^{4}+19a^{3}-96a^{2}-67a+27\right){x}-119a^{4}-76a^{3}+494a^{2}+383a-143$
49.1-b2 49.1-b 5.5.38569.1 \( 7^{2} \) $0$ $\Z/2\Z$ $1$ $486.7832023$ 1.239328389 \( \frac{1243808100}{2401} a^{4} + \frac{1002203176}{2401} a^{3} - \frac{5388495975}{2401} a^{2} - \frac{4276678300}{2401} a + \frac{1561357008}{2401} \) \( \bigl[a^{2} + a - 2\) , \( 2 a^{4} + a^{3} - 9 a^{2} - 5 a + 3\) , \( 2 a^{4} + a^{3} - 9 a^{2} - 4 a + 4\) , \( -a^{3} - a^{2} + 3 a + 2\) , \( -2 a^{4} - a^{3} + 7 a^{2} + 5 a - 3\bigr] \) ${y}^2+\left(a^{2}+a-2\right){x}{y}+\left(2a^{4}+a^{3}-9a^{2}-4a+4\right){y}={x}^{3}+\left(2a^{4}+a^{3}-9a^{2}-5a+3\right){x}^{2}+\left(-a^{3}-a^{2}+3a+2\right){x}-2a^{4}-a^{3}+7a^{2}+5a-3$
73.1-a1 73.1-a 5.5.38569.1 \( 73 \) $1$ $\mathsf{trivial}$ $0.006899557$ $13633.89651$ 2.394925608 \( \frac{1339615}{73} a^{4} + \frac{391026}{73} a^{3} - \frac{6659602}{73} a^{2} - \frac{1812753}{73} a + \frac{4880044}{73} \) \( \bigl[a^{2} + a - 2\) , \( -a^{3} + a^{2} + 3 a - 3\) , \( 2 a^{4} + a^{3} - 9 a^{2} - 4 a + 5\) , \( -a\) , \( -a^{4} + 5 a^{2} - 4\bigr] \) ${y}^2+\left(a^{2}+a-2\right){x}{y}+\left(2a^{4}+a^{3}-9a^{2}-4a+5\right){y}={x}^{3}+\left(-a^{3}+a^{2}+3a-3\right){x}^{2}-a{x}-a^{4}+5a^{2}-4$
73.1-a2 73.1-a 5.5.38569.1 \( 73 \) $1$ $\mathsf{trivial}$ $0.020698671$ $4544.632172$ 2.394925608 \( -\frac{4005895010964759}{389017} a^{4} + \frac{8209363168524430}{389017} a^{3} + \frac{3566257207321731}{389017} a^{2} - \frac{8377320503431615}{389017} a + \frac{1890337860286333}{389017} \) \( \bigl[a^{2} + a - 2\) , \( -a^{3} + a^{2} + 3 a - 3\) , \( 2 a^{4} + a^{3} - 9 a^{2} - 4 a + 5\) , \( 15 a^{4} - 10 a^{3} - 50 a^{2} + 34 a - 35\) , \( -66 a^{4} + 65 a^{3} + 225 a^{2} - 234 a + 131\bigr] \) ${y}^2+\left(a^{2}+a-2\right){x}{y}+\left(2a^{4}+a^{3}-9a^{2}-4a+5\right){y}={x}^{3}+\left(-a^{3}+a^{2}+3a-3\right){x}^{2}+\left(15a^{4}-10a^{3}-50a^{2}+34a-35\right){x}-66a^{4}+65a^{3}+225a^{2}-234a+131$
73.1-b1 73.1-b 5.5.38569.1 \( 73 \) $0$ $\Z/3\Z$ $1$ $1922.427000$ 1.087647481 \( \frac{1339615}{73} a^{4} + \frac{391026}{73} a^{3} - \frac{6659602}{73} a^{2} - \frac{1812753}{73} a + \frac{4880044}{73} \) \( \bigl[2 a^{4} + a^{3} - 9 a^{2} - 3 a + 4\) , \( -a^{4} - a^{3} + 4 a^{2} + 3 a\) , \( a^{4} + a^{3} - 4 a^{2} - 3 a + 1\) , \( -2 a^{4} - 2 a^{3} + 8 a^{2} + 6 a - 1\) , \( -a^{4} - a^{3} + 4 a^{2} + 3 a - 1\bigr] \) ${y}^2+\left(2a^{4}+a^{3}-9a^{2}-3a+4\right){x}{y}+\left(a^{4}+a^{3}-4a^{2}-3a+1\right){y}={x}^{3}+\left(-a^{4}-a^{3}+4a^{2}+3a\right){x}^{2}+\left(-2a^{4}-2a^{3}+8a^{2}+6a-1\right){x}-a^{4}-a^{3}+4a^{2}+3a-1$
73.1-b2 73.1-b 5.5.38569.1 \( 73 \) $0$ $\mathsf{trivial}$ $1$ $7.911222223$ 1.087647481 \( -\frac{4005895010964759}{389017} a^{4} + \frac{8209363168524430}{389017} a^{3} + \frac{3566257207321731}{389017} a^{2} - \frac{8377320503431615}{389017} a + \frac{1890337860286333}{389017} \) \( \bigl[-a^{4} + 5 a^{2} - 3\) , \( a^{4} + a^{3} - 5 a^{2} - 5 a + 4\) , \( 1\) , \( -123 a^{4} - 33 a^{3} + 608 a^{2} + 165 a - 453\) , \( -1097 a^{4} - 306 a^{3} + 5403 a^{2} + 1501 a - 3989\bigr] \) ${y}^2+\left(-a^{4}+5a^{2}-3\right){x}{y}+{y}={x}^{3}+\left(a^{4}+a^{3}-5a^{2}-5a+4\right){x}^{2}+\left(-123a^{4}-33a^{3}+608a^{2}+165a-453\right){x}-1097a^{4}-306a^{3}+5403a^{2}+1501a-3989$
73.2-a1 73.2-a 5.5.38569.1 \( 73 \) $0$ $\Z/6\Z$ $1$ $12420.84750$ 1.756829194 \( -\frac{5584014}{73} a^{4} - \frac{11394131}{73} a^{3} + \frac{4542950}{73} a^{2} + \frac{9362375}{73} a - \frac{2435239}{73} \) \( \bigl[a^{3} - 3 a + 1\) , \( a^{3} - a^{2} - 5 a + 1\) , \( 0\) , \( -2 a^{4} + a^{3} + 8 a^{2} - 3 a\) , \( 0\bigr] \) ${y}^2+\left(a^{3}-3a+1\right){x}{y}={x}^{3}+\left(a^{3}-a^{2}-5a+1\right){x}^{2}+\left(-2a^{4}+a^{3}+8a^{2}-3a\right){x}$
73.2-a2 73.2-a 5.5.38569.1 \( 73 \) $0$ $\Z/2\Z$ $1$ $51.11459879$ 1.756829194 \( -\frac{3137541036040698}{389017} a^{4} + \frac{5489070488218751}{389017} a^{3} + \frac{10233014795067686}{389017} a^{2} - \frac{21603512212125382}{389017} a + \frac{9197081196456878}{389017} \) \( \bigl[2 a^{4} + a^{3} - 9 a^{2} - 4 a + 4\) , \( 2 a^{4} - 9 a^{2} + 3\) , \( a^{2} + a - 1\) , \( -198 a^{4} - 66 a^{3} + 986 a^{2} + 315 a - 754\) , \( -2188 a^{4} - 618 a^{3} + 10803 a^{2} + 3048 a - 8004\bigr] \) ${y}^2+\left(2a^{4}+a^{3}-9a^{2}-4a+4\right){x}{y}+\left(a^{2}+a-1\right){y}={x}^{3}+\left(2a^{4}-9a^{2}+3\right){x}^{2}+\left(-198a^{4}-66a^{3}+986a^{2}+315a-754\right){x}-2188a^{4}-618a^{3}+10803a^{2}+3048a-8004$
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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.