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Label Class Base field Conductor norm Rank Torsion CM Regulator Period Leading coeff j-invariant Weierstrass coefficients Weierstrass equation
8.1-a1 8.1-a 3.3.229.1 \( 2^{3} \) $0$ $\Z/6\Z$ $1$ $182.6574446$ 0.670574649 \( \frac{4847}{32} a^{2} - \frac{17157}{32} a + \frac{14147}{32} \) \( \bigl[a^{2} - 2\) , \( -a^{2} - a + 4\) , \( a\) , \( -3 a^{2} + a + 9\) , \( -3 a^{2} + 3 a + 6\bigr] \) ${y}^2+\left(a^{2}-2\right){x}{y}+a{y}={x}^{3}+\left(-a^{2}-a+4\right){x}^{2}+\left(-3a^{2}+a+9\right){x}-3a^{2}+3a+6$
8.1-a2 8.1-a 3.3.229.1 \( 2^{3} \) $0$ $\Z/2\Z$ $1$ $6.765090543$ 0.670574649 \( \frac{5149908848399}{32768} a^{2} - \frac{9582969548701}{32768} a - \frac{2767591890197}{32768} \) \( \bigl[a^{2} - 2\) , \( -a^{2} - a + 4\) , \( a\) , \( -78 a^{2} + 141 a + 49\) , \( -725 a^{2} + 1346 a + 393\bigr] \) ${y}^2+\left(a^{2}-2\right){x}{y}+a{y}={x}^{3}+\left(-a^{2}-a+4\right){x}^{2}+\left(-78a^{2}+141a+49\right){x}-725a^{2}+1346a+393$
8.1-a3 8.1-a 3.3.229.1 \( 2^{3} \) $0$ $\Z/6\Z$ $1$ $36.53148893$ 0.670574649 \( \frac{410180291815113}{1024} a^{2} - \frac{381468430679405}{512} a - \frac{221127400043935}{1024} \) \( \bigl[a^{2} - 2\) , \( -a^{2} - a + 4\) , \( a\) , \( -403 a^{2} + 746 a + 214\) , \( 7473 a^{2} - 13910 a - 4017\bigr] \) ${y}^2+\left(a^{2}-2\right){x}{y}+a{y}={x}^{3}+\left(-a^{2}-a+4\right){x}^{2}+\left(-403a^{2}+746a+214\right){x}+7473a^{2}-13910a-4017$
8.1-a4 8.1-a 3.3.229.1 \( 2^{3} \) $0$ $\Z/6\Z$ $1$ $36.53148893$ 0.670574649 \( -\frac{304458198456664063}{2} a^{2} + \frac{1237813476398146963}{32} a + \frac{19170794207295639649}{32} \) \( \bigl[a\) , \( a^{2} - a - 2\) , \( a^{2} - 2\) , \( 1227 a^{2} - 425 a - 5034\) , \( -35239 a^{2} + 7997 a + 136900\bigr] \) ${y}^2+a{x}{y}+\left(a^{2}-2\right){y}={x}^{3}+\left(a^{2}-a-2\right){x}^{2}+\left(1227a^{2}-425a-5034\right){x}-35239a^{2}+7997a+136900$
8.1-a5 8.1-a 3.3.229.1 \( 2^{3} \) $0$ $\Z/2\Z$ $1$ $6.765090543$ 0.670574649 \( -\frac{550001475734697}{1073741824} a^{2} + \frac{154648619367179}{1073741824} a + \frac{2158976306071891}{1073741824} \) \( \bigl[a\) , \( a^{2} - a - 2\) , \( a^{2} - 2\) , \( 52 a^{2} - 30 a - 229\) , \( 275 a^{2} - 119 a - 1172\bigr] \) ${y}^2+a{x}{y}+\left(a^{2}-2\right){y}={x}^{3}+\left(a^{2}-a-2\right){x}^{2}+\left(52a^{2}-30a-229\right){x}+275a^{2}-119a-1172$
8.1-a6 8.1-a 3.3.229.1 \( 2^{3} \) $0$ $\Z/6\Z$ $1$ $182.6574446$ 0.670574649 \( \frac{13210743}{1024} a^{2} + \frac{29758379}{1024} a + \frac{11183859}{1024} \) \( \bigl[a\) , \( a^{2} - a - 2\) , \( a^{2} - 2\) , \( 2 a^{2} - 5 a - 9\) , \( -2 a^{2} + a + 11\bigr] \) ${y}^2+a{x}{y}+\left(a^{2}-2\right){y}={x}^{3}+\left(a^{2}-a-2\right){x}^{2}+\left(2a^{2}-5a-9\right){x}-2a^{2}+a+11$
8.1-a7 8.1-a 3.3.229.1 \( 2^{3} \) $0$ $\Z/2\Z$ $1$ $1.353018108$ 0.670574649 \( -\frac{9591905236373162715}{1073741824} a^{2} - \frac{20286002608069784023}{1073741824} a - \frac{2267690473188435537}{536870912} \) \( \bigl[a\) , \( -a + 1\) , \( 1\) , \( 433 a^{2} - 66 a - 1835\) , \( -18127 a^{2} + 4359 a + 71774\bigr] \) ${y}^2+a{x}{y}+{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(433a^{2}-66a-1835\right){x}-18127a^{2}+4359a+71774$
8.1-a8 8.1-a 3.3.229.1 \( 2^{3} \) $0$ $\Z/2\Z$ $1$ $1.353018108$ 0.670574649 \( \frac{24628729701449988584212043}{32768} a^{2} + \frac{52087486182589166202672597}{32768} a + \frac{2911324634581045729032995}{8192} \) \( \bigl[1\) , \( a^{2} - 4\) , \( a + 1\) , \( 782 a^{2} - 1290 a - 896\) , \( 79104 a^{2} - 149643 a - 37909\bigr] \) ${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(a^{2}-4\right){x}^{2}+\left(782a^{2}-1290a-896\right){x}+79104a^{2}-149643a-37909$
8.1-b1 8.1-b 3.3.229.1 \( 2^{3} \) $0$ $\Z/2\Z$ $1$ $0.411398833$ 1.019475005 \( \frac{24628729701449988584212043}{32768} a^{2} + \frac{52087486182589166202672597}{32768} a + \frac{2911324634581045729032995}{8192} \) \( \bigl[a^{2} - 2\) , \( 0\) , \( a + 1\) , \( 2232 a^{2} - 4377 a - 1289\) , \( -519466 a^{2} + 964390 a + 278508\bigr] \) ${y}^2+\left(a^{2}-2\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(2232a^{2}-4377a-1289\right){x}-519466a^{2}+964390a+278508$
8.1-b2 8.1-b 3.3.229.1 \( 2^{3} \) $0$ $\Z/2\Z$ $1$ $1.234196500$ 1.019475005 \( \frac{410180291815113}{1024} a^{2} - \frac{381468430679405}{512} a - \frac{221127400043935}{1024} \) \( \bigl[1\) , \( -a^{2} - a + 3\) , \( a\) , \( -76 a^{2} + 206 a - 95\) , \( -1041 a^{2} + 2329 a - 271\bigr] \) ${y}^2+{x}{y}+a{y}={x}^{3}+\left(-a^{2}-a+3\right){x}^{2}+\left(-76a^{2}+206a-95\right){x}-1041a^{2}+2329a-271$
8.1-b3 8.1-b 3.3.229.1 \( 2^{3} \) $0$ $\Z/2\Z$ $1$ $0.411398833$ 1.019475005 \( -\frac{9591905236373162715}{1073741824} a^{2} - \frac{20286002608069784023}{1073741824} a - \frac{2267690473188435537}{536870912} \) \( \bigl[1\) , \( -a^{2} - a + 3\) , \( a\) , \( -106 a^{2} + 176 a - 60\) , \( -971 a^{2} + 2082 a - 692\bigr] \) ${y}^2+{x}{y}+a{y}={x}^{3}+\left(-a^{2}-a+3\right){x}^{2}+\left(-106a^{2}+176a-60\right){x}-971a^{2}+2082a-692$
8.1-b4 8.1-b 3.3.229.1 \( 2^{3} \) $0$ $\Z/10\Z$ $1$ $154.2745625$ 1.019475005 \( \frac{4847}{32} a^{2} - \frac{17157}{32} a + \frac{14147}{32} \) \( \bigl[1\) , \( -a^{2} - a + 3\) , \( a\) , \( -a^{2} + a + 5\) , \( -a^{2} + 2\bigr] \) ${y}^2+{x}{y}+a{y}={x}^{3}+\left(-a^{2}-a+3\right){x}^{2}+\left(-a^{2}+a+5\right){x}-a^{2}+2$
8.1-b5 8.1-b 3.3.229.1 \( 2^{3} \) $0$ $\Z/10\Z$ $1$ $51.42485419$ 1.019475005 \( \frac{5149908848399}{32768} a^{2} - \frac{9582969548701}{32768} a - \frac{2767591890197}{32768} \) \( \bigl[1\) , \( -a^{2} - a + 3\) , \( a\) , \( -21 a^{2} + 41 a + 10\) , \( 87 a^{2} - 165 a - 43\bigr] \) ${y}^2+{x}{y}+a{y}={x}^{3}+\left(-a^{2}-a+3\right){x}^{2}+\left(-21a^{2}+41a+10\right){x}+87a^{2}-165a-43$
8.1-b6 8.1-b 3.3.229.1 \( 2^{3} \) $0$ $\Z/2\Z$ $1$ $1.234196500$ 1.019475005 \( -\frac{304458198456664063}{2} a^{2} + \frac{1237813476398146963}{32} a + \frac{19170794207295639649}{32} \) \( \bigl[1\) , \( -a^{2} + 4\) , \( a^{2} + a - 3\) , \( -131 a^{2} - 464 a - 415\) , \( -2913 a^{2} - 7754 a - 4350\bigr] \) ${y}^2+{x}{y}+\left(a^{2}+a-3\right){y}={x}^{3}+\left(-a^{2}+4\right){x}^{2}+\left(-131a^{2}-464a-415\right){x}-2913a^{2}-7754a-4350$
8.1-b7 8.1-b 3.3.229.1 \( 2^{3} \) $0$ $\Z/10\Z$ $1$ $51.42485419$ 1.019475005 \( -\frac{550001475734697}{1073741824} a^{2} + \frac{154648619367179}{1073741824} a + \frac{2158976306071891}{1073741824} \) \( \bigl[1\) , \( -a^{2} + 4\) , \( a^{2} + a - 3\) , \( -26 a^{2} - 59 a - 20\) , \( -163 a^{2} - 344 a - 76\bigr] \) ${y}^2+{x}{y}+\left(a^{2}+a-3\right){y}={x}^{3}+\left(-a^{2}+4\right){x}^{2}+\left(-26a^{2}-59a-20\right){x}-163a^{2}-344a-76$
8.1-b8 8.1-b 3.3.229.1 \( 2^{3} \) $0$ $\Z/10\Z$ $1$ $154.2745625$ 1.019475005 \( \frac{13210743}{1024} a^{2} + \frac{29758379}{1024} a + \frac{11183859}{1024} \) \( \bigl[1\) , \( -a^{2} + 4\) , \( a^{2} + a - 3\) , \( -6 a^{2} - 9 a + 5\) , \( 10 a^{2} + 21 a + 4\bigr] \) ${y}^2+{x}{y}+\left(a^{2}+a-3\right){y}={x}^{3}+\left(-a^{2}+4\right){x}^{2}+\left(-6a^{2}-9a+5\right){x}+10a^{2}+21a+4$
13.1-a1 13.1-a 3.3.229.1 \( 13 \) $0$ $\Z/2\Z\oplus\Z/2\Z$ $1$ $153.1181165$ 1.264791243 \( -\frac{2911512}{169} a^{2} + \frac{1025865}{169} a + \frac{12442564}{169} \) \( \bigl[a^{2} - 2\) , \( a^{2} - 4\) , \( a^{2} - 3\) , \( -2 a^{2} + 3 a + 1\) , \( 2 a^{2} - 3 a - 4\bigr] \) ${y}^2+\left(a^{2}-2\right){x}{y}+\left(a^{2}-3\right){y}={x}^{3}+\left(a^{2}-4\right){x}^{2}+\left(-2a^{2}+3a+1\right){x}+2a^{2}-3a-4$
13.1-a2 13.1-a 3.3.229.1 \( 13 \) $0$ $\Z/2\Z$ $1$ $19.13976456$ 1.264791243 \( -\frac{37002219875353}{28561} a^{2} + \frac{9402056060606}{28561} a + \frac{145620309456504}{28561} \) \( \bigl[a^{2} - 2\) , \( a^{2} - 4\) , \( a^{2} - 3\) , \( -12 a^{2} + 23 a + 6\) , \( -40 a^{2} + 75 a + 19\bigr] \) ${y}^2+\left(a^{2}-2\right){x}{y}+\left(a^{2}-3\right){y}={x}^{3}+\left(a^{2}-4\right){x}^{2}+\left(-12a^{2}+23a+6\right){x}-40a^{2}+75a+19$
13.1-a3 13.1-a 3.3.229.1 \( 13 \) $0$ $\Z/2\Z$ $1$ $76.55905826$ 1.264791243 \( \frac{109709855}{13} a^{2} + \frac{205310236}{13} a + \frac{45085962}{13} \) \( \bigl[a\) , \( -a^{2} + a + 4\) , \( a\) , \( -7 a^{2} - 11 a + 2\) , \( -21 a^{2} - 44 a - 10\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-a^{2}+a+4\right){x}^{2}+\left(-7a^{2}-11a+2\right){x}-21a^{2}-44a-10$
13.1-a4 13.1-a 3.3.229.1 \( 13 \) $0$ $\Z/4\Z$ $1$ $306.2362330$ 1.264791243 \( \frac{4451}{13} a^{2} + \frac{17718}{13} a + \frac{31630}{13} \) \( \bigl[1\) , \( -a^{2} + 4\) , \( a^{2} - 3\) , \( -2 a^{2} + 7\) , \( 0\bigr] \) ${y}^2+{x}{y}+\left(a^{2}-3\right){y}={x}^{3}+\left(-a^{2}+4\right){x}^{2}+\left(-2a^{2}+7\right){x}$
13.1-b1 13.1-b 3.3.229.1 \( 13 \) $1$ $\Z/2\Z$ $0.236027789$ $56.91991814$ 0.665841604 \( \frac{109709855}{13} a^{2} + \frac{205310236}{13} a + \frac{45085962}{13} \) \( \bigl[a^{2} - 2\) , \( a^{2} - a - 4\) , \( 0\) , \( -a^{2} - 3 a - 1\) , \( -31 a^{2} + 4 a + 115\bigr] \) ${y}^2+\left(a^{2}-2\right){x}{y}={x}^{3}+\left(a^{2}-a-4\right){x}^{2}+\left(-a^{2}-3a-1\right){x}-31a^{2}+4a+115$
13.1-b2 13.1-b 3.3.229.1 \( 13 \) $1$ $\Z/2\Z$ $0.059006947$ $227.6796725$ 0.665841604 \( \frac{4451}{13} a^{2} + \frac{17718}{13} a + \frac{31630}{13} \) \( \bigl[a\) , \( a^{2} - a - 2\) , \( a^{2} + a - 2\) , \( 2 a^{2} - 3 a - 7\) , \( -2 a - 1\bigr] \) ${y}^2+a{x}{y}+\left(a^{2}+a-2\right){y}={x}^{3}+\left(a^{2}-a-2\right){x}^{2}+\left(2a^{2}-3a-7\right){x}-2a-1$
13.1-b3 13.1-b 3.3.229.1 \( 13 \) $1$ $\Z/2\Z$ $0.059006947$ $113.8398362$ 0.665841604 \( -\frac{37002219875353}{28561} a^{2} + \frac{9402056060606}{28561} a + \frac{145620309456504}{28561} \) \( \bigl[1\) , \( a\) , \( 1\) , \( 6 a - 11\) , \( 4 a^{2} - 14 a + 12\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}+a{x}^{2}+\left(6a-11\right){x}+4a^{2}-14a+12$
13.1-b4 13.1-b 3.3.229.1 \( 13 \) $1$ $\Z/2\Z\oplus\Z/2\Z$ $0.118013894$ $227.6796725$ 0.665841604 \( -\frac{2911512}{169} a^{2} + \frac{1025865}{169} a + \frac{12442564}{169} \) \( \bigl[1\) , \( a\) , \( 1\) , \( a - 1\) , \( 0\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}+a{x}^{2}+\left(a-1\right){x}$
14.1-a1 14.1-a 3.3.229.1 \( 2 \cdot 7 \) $0$ $\Z/2\Z\oplus\Z/2\Z$ $1$ $7.028265236$ 1.393322519 \( \frac{144450740091078986229263}{885842380864} a^{2} + \frac{305499959947366052778019}{885842380864} a + \frac{68301210357720562240171}{885842380864} \) \( \bigl[a^{2} - 2\) , \( a^{2} + a - 3\) , \( 1\) , \( -625 a^{2} + 1168 a + 329\) , \( -2987 a^{2} + 5550 a + 1618\bigr] \) ${y}^2+\left(a^{2}-2\right){x}{y}+{y}={x}^{3}+\left(a^{2}+a-3\right){x}^{2}+\left(-625a^{2}+1168a+329\right){x}-2987a^{2}+5550a+1618$
14.1-a2 14.1-a 3.3.229.1 \( 2 \cdot 7 \) $0$ $\Z/8\Z$ $1$ $56.22612189$ 1.393322519 \( \frac{19171931555165458625}{5754585088} a^{2} - \frac{35675235167864071379}{5754585088} a - \frac{10303029851568696283}{5754585088} \) \( \bigl[a^{2} - 2\) , \( -a^{2} + a + 3\) , \( a^{2} + a - 3\) , \( -52 a^{2} + 88 a + 26\) , \( 372 a^{2} - 703 a - 204\bigr] \) ${y}^2+\left(a^{2}-2\right){x}{y}+\left(a^{2}+a-3\right){y}={x}^{3}+\left(-a^{2}+a+3\right){x}^{2}+\left(-52a^{2}+88a+26\right){x}+372a^{2}-703a-204$
14.1-a3 14.1-a 3.3.229.1 \( 2 \cdot 7 \) $0$ $\Z/4\Z$ $1$ $168.6783656$ 1.393322519 \( -\frac{138925}{28} a^{2} + \frac{38211}{28} a + \frac{552719}{28} \) \( \bigl[a\) , \( -1\) , \( a\) , \( -a\) , \( -4 a^{2} + 7 a + 2\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^{3}-{x}^{2}-a{x}-4a^{2}+7a+2$
14.1-a4 14.1-a 3.3.229.1 \( 2 \cdot 7 \) $0$ $\Z/4\Z$ $1$ $56.22612189$ 1.393322519 \( -\frac{35449278183454201}{21952} a^{2} + \frac{9007721434929467}{21952} a + \frac{139508235502484995}{21952} \) \( \bigl[a\) , \( -1\) , \( a\) , \( -5 a^{2} + 9 a\) , \( 101 a^{2} - 190 a - 52\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^{3}-{x}^{2}+\left(-5a^{2}+9a\right){x}+101a^{2}-190a-52$
14.1-a5 14.1-a 3.3.229.1 \( 2 \cdot 7 \) $0$ $\Z/8\Z$ $1$ $168.6783656$ 1.393322519 \( \frac{4089546065}{1792} a^{2} + \frac{8645765501}{1792} a + \frac{1934066933}{1792} \) \( \bigl[a\) , \( a + 1\) , \( 0\) , \( -6 a^{2} + 3 a + 26\) , \( 14 a^{2} - 3 a - 54\bigr] \) ${y}^2+a{x}{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-6a^{2}+3a+26\right){x}+14a^{2}-3a-54$
14.1-a6 14.1-a 3.3.229.1 \( 2 \cdot 7 \) $0$ $\Z/2\Z$ $1$ $2.635599463$ 1.393322519 \( -\frac{285193138089447737033}{11529602} a^{2} + \frac{72468057958216640193}{11529602} a + \frac{1122358296368399397537}{11529602} \) \( \bigl[a\) , \( -a^{2} + 4\) , \( a^{2} + a - 3\) , \( 27 a^{2} + 67 a + 17\) , \( -780 a^{2} - 1637 a - 372\bigr] \) ${y}^2+a{x}{y}+\left(a^{2}+a-3\right){y}={x}^{3}+\left(-a^{2}+4\right){x}^{2}+\left(27a^{2}+67a+17\right){x}-780a^{2}-1637a-372$
14.1-a7 14.1-a 3.3.229.1 \( 2 \cdot 7 \) $0$ $\Z/2\Z$ $1$ $0.878533154$ 1.393322519 \( -\frac{219768203370710958657491381}{1532649851044531315208} a^{2} - \frac{422256959586277880827223561}{1532649851044531315208} a - \frac{22234843138942680536190377}{1532649851044531315208} \) \( \bigl[1\) , \( -a^{2} + a + 3\) , \( 1\) , \( 80 a^{2} - 296 a - 821\) , \( 695 a^{2} - 3738 a - 9368\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}+\left(-a^{2}+a+3\right){x}^{2}+\left(80a^{2}-296a-821\right){x}+695a^{2}-3738a-9368$
14.1-a8 14.1-a 3.3.229.1 \( 2 \cdot 7 \) $0$ $\Z/2\Z$ $1$ $0.878533154$ 1.393322519 \( \frac{235714709275320239218607561029}{941192} a^{2} + \frac{498514816283375773212941728729}{941192} a + \frac{111453907394329888778466345977}{941192} \) \( \bigl[1\) , \( -a^{2} + a + 3\) , \( 1\) , \( -1940 a^{2} - 3886 a - 531\) , \( -95053 a^{2} - 199862 a - 42792\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}+\left(-a^{2}+a+3\right){x}^{2}+\left(-1940a^{2}-3886a-531\right){x}-95053a^{2}-199862a-42792$
14.1-a9 14.1-a 3.3.229.1 \( 2 \cdot 7 \) $0$ $\Z/2\Z\oplus\Z/4\Z$ $1$ $56.22612189$ 1.393322519 \( -\frac{239467329359737}{481890304} a^{2} + \frac{193379148122235}{481890304} a + \frac{1259678493551939}{481890304} \) \( \bigl[1\) , \( -a^{2} + a + 3\) , \( 1\) , \( 15 a^{2} - 21 a - 91\) , \( -85 a^{2} - 38 a + 224\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}+\left(-a^{2}+a+3\right){x}^{2}+\left(15a^{2}-21a-91\right){x}-85a^{2}-38a+224$
14.1-a10 14.1-a 3.3.229.1 \( 2 \cdot 7 \) $0$ $\Z/2\Z$ $1$ $2.635599463$ 1.393322519 \( \frac{3082823789666319289}{98} a^{2} - \frac{5736536546416283697}{98} a - \frac{1656714364858512497}{98} \) \( \bigl[1\) , \( -a^{2} + a + 3\) , \( 1\) , \( -15 a^{2} - 46 a - 51\) , \( -91 a^{2} - 294 a - 250\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}+\left(-a^{2}+a+3\right){x}^{2}+\left(-15a^{2}-46a-51\right){x}-91a^{2}-294a-250$
14.1-a11 14.1-a 3.3.229.1 \( 2 \cdot 7 \) $0$ $\Z/2\Z\oplus\Z/2\Z$ $1$ $21.08479570$ 1.393322519 \( \frac{649494835763}{9604} a^{2} - \frac{1247873756341}{9604} a - \frac{265826789201}{9604} \) \( \bigl[1\) , \( -a^{2} + a + 3\) , \( 1\) , \( 10 a^{2} - 6 a - 46\) , \( 41 a^{2} - 16 a - 172\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}+\left(-a^{2}+a+3\right){x}^{2}+\left(10a^{2}-6a-46\right){x}+41a^{2}-16a-172$
14.1-a12 14.1-a 3.3.229.1 \( 2 \cdot 7 \) $0$ $\Z/2\Z\oplus\Z/4\Z$ $1$ $168.6783656$ 1.393322519 \( \frac{2334119}{784} a^{2} - \frac{3847349}{784} a + \frac{1948435}{784} \) \( \bigl[1\) , \( -a^{2} + a + 3\) , \( 1\) , \( -a - 1\) , \( a^{2} - 4\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}+\left(-a^{2}+a+3\right){x}^{2}+\left(-a-1\right){x}+a^{2}-4$
14.1-b1 14.1-b 3.3.229.1 \( 2 \cdot 7 \) $0$ $\Z/2\Z$ $1$ $1.584878311$ 0.628390240 \( -\frac{219768203370710958657491381}{1532649851044531315208} a^{2} - \frac{422256959586277880827223561}{1532649851044531315208} a - \frac{22234843138942680536190377}{1532649851044531315208} \) \( \bigl[a^{2} - 2\) , \( a^{2} - a - 2\) , \( 1\) , \( -501 a^{2} - 1104 a - 295\) , \( -14257 a^{2} - 30089 a - 6588\bigr] \) ${y}^2+\left(a^{2}-2\right){x}{y}+{y}={x}^{3}+\left(a^{2}-a-2\right){x}^{2}+\left(-501a^{2}-1104a-295\right){x}-14257a^{2}-30089a-6588$
14.1-b2 14.1-b 3.3.229.1 \( 2 \cdot 7 \) $0$ $\Z/6\Z$ $1$ $42.79171441$ 0.628390240 \( -\frac{285193138089447737033}{11529602} a^{2} + \frac{72468057958216640193}{11529602} a + \frac{1122358296368399397537}{11529602} \) \( \bigl[a^{2} - 2\) , \( a^{2} - a - 2\) , \( 1\) , \( 19 a^{2} + 11 a - 45\) , \( -115 a^{2} - 157 a + 106\bigr] \) ${y}^2+\left(a^{2}-2\right){x}{y}+{y}={x}^{3}+\left(a^{2}-a-2\right){x}^{2}+\left(19a^{2}+11a-45\right){x}-115a^{2}-157a+106$
14.1-b3 14.1-b 3.3.229.1 \( 2 \cdot 7 \) $0$ $\Z/2\Z\oplus\Z/2\Z$ $1$ $12.67902649$ 0.628390240 \( -\frac{239467329359737}{481890304} a^{2} + \frac{193379148122235}{481890304} a + \frac{1259678493551939}{481890304} \) \( \bigl[a^{2} - 2\) , \( a^{2} - a - 2\) , \( 1\) , \( -31 a^{2} - 69 a - 20\) , \( -237 a^{2} - 501 a - 116\bigr] \) ${y}^2+\left(a^{2}-2\right){x}{y}+{y}={x}^{3}+\left(a^{2}-a-2\right){x}^{2}+\left(-31a^{2}-69a-20\right){x}-237a^{2}-501a-116$
14.1-b4 14.1-b 3.3.229.1 \( 2 \cdot 7 \) $0$ $\Z/2\Z\oplus\Z/6\Z$ $1$ $171.1668576$ 0.628390240 \( \frac{649494835763}{9604} a^{2} - \frac{1247873756341}{9604} a - \frac{265826789201}{9604} \) \( \bigl[a^{2} - 2\) , \( a^{2} - a - 2\) , \( 1\) , \( -6 a^{2} - 14 a - 5\) , \( -23 a^{2} - 47 a - 8\bigr] \) ${y}^2+\left(a^{2}-2\right){x}{y}+{y}={x}^{3}+\left(a^{2}-a-2\right){x}^{2}+\left(-6a^{2}-14a-5\right){x}-23a^{2}-47a-8$
14.1-b5 14.1-b 3.3.229.1 \( 2 \cdot 7 \) $0$ $\Z/2\Z\oplus\Z/6\Z$ $1$ $342.3337153$ 0.628390240 \( \frac{2334119}{784} a^{2} - \frac{3847349}{784} a + \frac{1948435}{784} \) \( \bigl[a^{2} - 2\) , \( a^{2} - a - 2\) , \( 1\) , \( -a^{2} - 4 a\) , \( a^{2} + a\bigr] \) ${y}^2+\left(a^{2}-2\right){x}{y}+{y}={x}^{3}+\left(a^{2}-a-2\right){x}^{2}+\left(-a^{2}-4a\right){x}+a^{2}+a$
14.1-b6 14.1-b 3.3.229.1 \( 2 \cdot 7 \) $0$ $\Z/2\Z$ $1$ $6.339513247$ 0.628390240 \( -\frac{35449278183454201}{21952} a^{2} + \frac{9007721434929467}{21952} a + \frac{139508235502484995}{21952} \) \( \bigl[a^{2} - 2\) , \( -a^{2} + 3\) , \( a\) , \( 9 a^{2} - a - 41\) , \( 29 a^{2} + 18 a - 169\bigr] \) ${y}^2+\left(a^{2}-2\right){x}{y}+a{y}={x}^{3}+\left(-a^{2}+3\right){x}^{2}+\left(9a^{2}-a-41\right){x}+29a^{2}+18a-169$
14.1-b7 14.1-b 3.3.229.1 \( 2 \cdot 7 \) $0$ $\Z/6\Z$ $1$ $171.1668576$ 0.628390240 \( -\frac{138925}{28} a^{2} + \frac{38211}{28} a + \frac{552719}{28} \) \( \bigl[a^{2} - 2\) , \( -a^{2} + 3\) , \( a\) , \( -a^{2} - a + 4\) , \( -a + 1\bigr] \) ${y}^2+\left(a^{2}-2\right){x}{y}+a{y}={x}^{3}+\left(-a^{2}+3\right){x}^{2}+\left(-a^{2}-a+4\right){x}-a+1$
14.1-b8 14.1-b 3.3.229.1 \( 2 \cdot 7 \) $0$ $\Z/6\Z$ $1$ $42.79171441$ 0.628390240 \( \frac{3082823789666319289}{98} a^{2} - \frac{5736536546416283697}{98} a - \frac{1656714364858512497}{98} \) \( \bigl[a\) , \( -a\) , \( 0\) , \( 168 a^{2} - 54 a - 685\) , \( -2241 a^{2} + 541 a + 8767\bigr] \) ${y}^2+a{x}{y}={x}^{3}-a{x}^{2}+\left(168a^{2}-54a-685\right){x}-2241a^{2}+541a+8767$
14.1-b9 14.1-b 3.3.229.1 \( 2 \cdot 7 \) $0$ $\Z/2\Z$ $1$ $1.584878311$ 0.628390240 \( \frac{235714709275320239218607561029}{941192} a^{2} + \frac{498514816283375773212941728729}{941192} a + \frac{111453907394329888778466345977}{941192} \) \( \bigl[a\) , \( -a\) , \( 0\) , \( -1752 a^{2} - 534 a + 5070\) , \( 14642 a^{2} - 26939 a - 100827\bigr] \) ${y}^2+a{x}{y}={x}^{3}-a{x}^{2}+\left(-1752a^{2}-534a+5070\right){x}+14642a^{2}-26939a-100827$
14.1-b10 14.1-b 3.3.229.1 \( 2 \cdot 7 \) $0$ $\Z/2\Z$ $1$ $6.339513247$ 0.628390240 \( \frac{19171931555165458625}{5754585088} a^{2} - \frac{35675235167864071379}{5754585088} a - \frac{10303029851568696283}{5754585088} \) \( \bigl[1\) , \( a^{2} - a - 3\) , \( a + 1\) , \( -11 a^{2} + 24 a - 7\) , \( -59 a^{2} + 120 a + 7\bigr] \) ${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(a^{2}-a-3\right){x}^{2}+\left(-11a^{2}+24a-7\right){x}-59a^{2}+120a+7$
14.1-b11 14.1-b 3.3.229.1 \( 2 \cdot 7 \) $0$ $\Z/6\Z$ $1$ $171.1668576$ 0.628390240 \( \frac{4089546065}{1792} a^{2} + \frac{8645765501}{1792} a + \frac{1934066933}{1792} \) \( \bigl[1\) , \( a^{2} - a - 3\) , \( a + 1\) , \( -a^{2} - a + 3\) , \( -1\bigr] \) ${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(a^{2}-a-3\right){x}^{2}+\left(-a^{2}-a+3\right){x}-1$
14.1-b12 14.1-b 3.3.229.1 \( 2 \cdot 7 \) $0$ $\Z/2\Z\oplus\Z/2\Z$ $1$ $6.339513247$ 0.628390240 \( \frac{144450740091078986229263}{885842380864} a^{2} + \frac{305499959947366052778019}{885842380864} a + \frac{68301210357720562240171}{885842380864} \) \( \bigl[1\) , \( a^{2} + a - 3\) , \( a^{2} - 3\) , \( -138 a^{2} + 327 a - 71\) , \( 637 a^{2} - 1062 a - 603\bigr] \) ${y}^2+{x}{y}+\left(a^{2}-3\right){y}={x}^{3}+\left(a^{2}+a-3\right){x}^{2}+\left(-138a^{2}+327a-71\right){x}+637a^{2}-1062a-603$
16.3-a1 16.3-a 3.3.229.1 \( 2^{4} \) $0$ $\Z/2\Z$ $1$ $36.37942472$ 1.202010026 \( \frac{180079}{8} a^{2} - \frac{324541}{8} a - \frac{108845}{8} \) \( \bigl[a^{2} - 3\) , \( a^{2} + a - 3\) , \( a + 1\) , \( a^{2} + a - 3\) , \( a^{2} - 4\bigr] \) ${y}^2+\left(a^{2}-3\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a^{2}+a-3\right){x}^{2}+\left(a^{2}+a-3\right){x}+a^{2}-4$
16.3-a2 16.3-a 3.3.229.1 \( 2^{4} \) $0$ $\Z/2\Z$ $1$ $18.18971236$ 1.202010026 \( -\frac{4350984313}{16777216} a^{2} + \frac{2200640379}{16777216} a + \frac{14807078979}{16777216} \) \( \bigl[a^{2} - 3\) , \( -a + 1\) , \( a + 1\) , \( -3 a^{2} + 2 a + 7\) , \( 3 a^{2} - 8 a\bigr] \) ${y}^2+\left(a^{2}-3\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-3a^{2}+2a+7\right){x}+3a^{2}-8a$
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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.