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Label Class Base field Conductor norm Rank Torsion CM Sato-Tate Regulator Period Leading coeff j-invariant Weierstrass coefficients Weierstrass equation
375.2-a1 375.2-a Q(6)\Q(\sqrt{6}) 353 3 \cdot 5^{3} 11 Z/2Z\Z/2\Z SU(2)\mathrm{SU}(2) 1.0406251441.040625144 10.5325042310.53250423 4.474559968 20805875a+3355125 -\frac{208058}{75} a + \frac{33551}{25} [a+1 \bigl[a + 1 , a a , 1 1 , a4 a - 4 , a1] a - 1\bigr] y2+(a+1)xy+y=x3+ax2+(a4)x+a1{y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+a{x}^{2}+\left(a-4\right){x}+a-1
375.2-a2 375.2-a Q(6)\Q(\sqrt{6}) 353 3 \cdot 5^{3} 11 Z/2Z\Z/2\Z SU(2)\mathrm{SU}(2) 0.5203125720.520312572 5.2662521195.266252119 4.474559968 145502803091875a+356411861811875 \frac{14550280309}{1875} a + \frac{35641186181}{1875} [a+1 \bigl[a + 1 , a a , 1 1 , 34a69 -34 a - 69 , 112a+223] 112 a + 223\bigr] y2+(a+1)xy+y=x3+ax2+(34a69)x+112a+223{y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+a{x}^{2}+\left(-34a-69\right){x}+112a+223
375.2-b1 375.2-b Q(6)\Q(\sqrt{6}) 353 3 \cdot 5^{3} 0 Z/2Z\Z/2\Z SU(2)\mathrm{SU}(2) 11 5.3735927945.373592794 1.096880035 20805875a+3355125 -\frac{208058}{75} a + \frac{33551}{25} [1 \bigl[1 , a -a , 0 0 , 168a410 168 a - 410 , 1498a+3669] -1498 a + 3669\bigr] y2+xy=x3ax2+(168a410)x1498a+3669{y}^2+{x}{y}={x}^{3}-a{x}^{2}+\left(168a-410\right){x}-1498a+3669
375.2-b2 375.2-b Q(6)\Q(\sqrt{6}) 353 3 \cdot 5^{3} 0 Z/2Z\Z/2\Z SU(2)\mathrm{SU}(2) 11 2.6867963972.686796397 1.096880035 145502803091875a+356411861811875 \frac{14550280309}{1875} a + \frac{35641186181}{1875} [1 \bigl[1 , a -a , 0 0 , 247a+605 -247 a + 605 , 8721a+21362] -8721 a + 21362\bigr] y2+xy=x3ax2+(247a+605)x8721a+21362{y}^2+{x}{y}={x}^{3}-a{x}^{2}+\left(-247a+605\right){x}-8721a+21362
375.2-c1 375.2-c Q(6)\Q(\sqrt{6}) 353 3 \cdot 5^{3} 0 Z/2Z\Z/2\Z SU(2)\mathrm{SU}(2) 11 20.3898908020.38989080 4.162069031 8172025373977675a+6672421152467225 -\frac{81720253739776}{75} a + \frac{66724211524672}{25} [a \bigl[a , a+1 a + 1 , a+1 a + 1 , 1241a3040 1241 a - 3040 , 37209a+91141] -37209 a + 91141\bigr] y2+axy+(a+1)y=x3+(a+1)x2+(1241a3040)x37209a+91141{y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+\left(a+1\right){x}^{2}+\left(1241a-3040\right){x}-37209a+91141
375.2-c2 375.2-c Q(6)\Q(\sqrt{6}) 353 3 \cdot 5^{3} 0 Z/2Z\Z/2\Z SU(2)\mathrm{SU}(2) 11 4.0779781614.077978161 4.162069031 8297016064263671875a+15595752300887890625 -\frac{8297016064}{263671875} a + \frac{155957523008}{87890625} [a \bigl[a , a+1 a + 1 , a+1 a + 1 , 356a+870 356 a + 870 , 179a439] -179 a - 439\bigr] y2+axy+(a+1)y=x3+(a+1)x2+(356a+870)x179a439{y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+\left(a+1\right){x}^{2}+\left(356a+870\right){x}-179a-439
375.2-c3 375.2-c Q(6)\Q(\sqrt{6}) 353 3 \cdot 5^{3} 0 Z/2Z\Z/2\Z SU(2)\mathrm{SU}(2) 11 4.0779781614.077978161 4.162069031 109693837568759375a+270029745088759375 -\frac{109693837568}{759375} a + \frac{270029745088}{759375} [a \bigl[a , 1 1 , 1 1 , 11a44 11 a - 44 , 59a163] 59 a - 163\bigr] y2+axy+y=x3+x2+(11a44)x+59a163{y}^2+a{x}{y}+{y}={x}^{3}+{x}^{2}+\left(11a-44\right){x}+59a-163
375.2-c4 375.2-c Q(6)\Q(\sqrt{6}) 353 3 \cdot 5^{3} 0 Z/2Z\Z/2\Z SU(2)\mathrm{SU}(2) 11 20.3898908020.38989080 4.162069031 4539859201203215a+11120342013740815 \frac{45398592012032}{15} a + \frac{111203420137408}{15} [a \bigl[a , a+1 -a + 1 , 1 1 , 329a812 -329 a - 812 , 5101a+12497] 5101 a + 12497\bigr] y2+axy+y=x3+(a+1)x2+(329a812)x+5101a+12497{y}^2+a{x}{y}+{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-329a-812\right){x}+5101a+12497
375.2-d1 375.2-d Q(6)\Q(\sqrt{6}) 353 3 \cdot 5^{3} 11 Z/2Z\Z/2\Z SU(2)\mathrm{SU}(2) 5.5170657195.517065719 0.9056988960.905698896 2.039935193 8172025373977675a+6672421152467225 -\frac{81720253739776}{75} a + \frac{66724211524672}{25} [a \bigl[a , a+1 -a + 1 , a+1 a + 1 , 72a232 -72 a - 232 , 582a1712] -582 a - 1712\bigr] y2+axy+(a+1)y=x3+(a+1)x2+(72a232)x582a1712{y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-72a-232\right){x}-582a-1712
375.2-d2 375.2-d Q(6)\Q(\sqrt{6}) 353 3 \cdot 5^{3} 11 Z/10Z\Z/10\Z SU(2)\mathrm{SU}(2) 1.1034131431.103413143 4.5284944814.528494481 2.039935193 8297016064263671875a+15595752300887890625 -\frac{8297016064}{263671875} a + \frac{155957523008}{87890625} [a \bigl[a , 1 1 , a+1 a + 1 , 8a4 8 a - 4 , 5a+4] 5 a + 4\bigr] y2+axy+(a+1)y=x3+x2+(8a4)x+5a+4{y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+{x}^{2}+\left(8a-4\right){x}+5a+4
375.2-d3 375.2-d Q(6)\Q(\sqrt{6}) 353 3 \cdot 5^{3} 11 Z/10Z\Z/10\Z SU(2)\mathrm{SU}(2) 0.5517065710.551706571 9.0569889629.056988962 2.039935193 109693837568759375a+270029745088759375 -\frac{109693837568}{759375} a + \frac{270029745088}{759375} [a \bigl[a , a+1 a + 1 , 1 1 , 357a874 -357 a - 874 , 178a+436] 178 a + 436\bigr] y2+axy+y=x3+(a+1)x2+(357a874)x+178a+436{y}^2+a{x}{y}+{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-357a-874\right){x}+178a+436
375.2-d4 375.2-d Q(6)\Q(\sqrt{6}) 353 3 \cdot 5^{3} 11 Z/2Z\Z/2\Z SU(2)\mathrm{SU}(2) 2.7585328592.758532859 1.8113977921.811397792 2.039935193 4539859201203215a+11120342013740815 \frac{45398592012032}{15} a + \frac{111203420137408}{15} [a \bigl[a , a+1 a + 1 , 1 1 , 308a764 308 a - 764 , 4648a11434] 4648 a - 11434\bigr] y2+axy+y=x3+(a+1)x2+(308a764)x+4648a11434{y}^2+a{x}{y}+{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(308a-764\right){x}+4648a-11434
375.2-e1 375.2-e Q(6)\Q(\sqrt{6}) 353 3 \cdot 5^{3} 0 Z/2Z\Z/2\Z SU(2)\mathrm{SU}(2) 11 15.8348229715.83482297 3.232269705 107545675a+87763225 -\frac{1075456}{75} a + \frac{877632}{25} [a \bigl[a , 1 -1 , a+1 a + 1 , 13a36 13 a - 36 , 40a+95] -40 a + 95\bigr] y2+axy+(a+1)y=x3x2+(13a36)x40a+95{y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}-{x}^{2}+\left(13a-36\right){x}-40a+95
375.2-e2 375.2-e Q(6)\Q(\sqrt{6}) 353 3 \cdot 5^{3} 0 Z/2Z\Z/2\Z SU(2)\mathrm{SU}(2) 11 15.8348229715.83482297 3.232269705 1431045a+108332815 \frac{143104}{5} a + \frac{1083328}{15} [a \bigl[a , a1 -a - 1 , 1 1 , 4a6 -4 a - 6 , 3a7] -3 a - 7\bigr] y2+axy+y=x3+(a1)x2+(4a6)x3a7{y}^2+a{x}{y}+{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-4a-6\right){x}-3a-7
375.2-f1 375.2-f Q(6)\Q(\sqrt{6}) 353 3 \cdot 5^{3} 0 Z/2Z\Z/2\Z SU(2)\mathrm{SU}(2) 11 1.1276138231.127613823 2.762078493 3462131685673645a+8480447785073645 -\frac{346213168567}{3645} a + \frac{848044778507}{3645} [1 \bigl[1 , 0 0 , 1 1 , 154a387 -154 a - 387 , 4879a11963] -4879 a - 11963\bigr] y2+xy+y=x3+(154a387)x4879a11963{y}^2+{x}{y}+{y}={x}^{3}+\left(-154a-387\right){x}-4879a-11963
375.2-f2 375.2-f Q(6)\Q(\sqrt{6}) 353 3 \cdot 5^{3} 0 Z/2Z\Z/2\Z SU(2)\mathrm{SU}(2) 11 9.0209105849.020910584 2.762078493 1629245a+1359115 \frac{16292}{45} a + \frac{13591}{15} [1 \bigl[1 , 0 0 , 1 1 , 19a47 -19 a - 47 , 15a37] -15 a - 37\bigr] y2+xy+y=x3+(19a47)x15a37{y}^2+{x}{y}+{y}={x}^{3}+\left(-19a-47\right){x}-15a-37
375.2-f3 375.2-f Q(6)\Q(\sqrt{6}) 353 3 \cdot 5^{3} 0 Z/2ZZ/2Z\Z/2\Z\oplus\Z/2\Z SU(2)\mathrm{SU}(2) 11 4.5104552924.510455292 2.762078493 73011154675a+193909061675 \frac{73011154}{675} a + \frac{193909061}{675} [1 \bigl[1 , 0 0 , 1 1 , 229a562 -229 a - 562 , 2969a7273] -2969 a - 7273\bigr] y2+xy+y=x3+(229a562)x2969a7273{y}^2+{x}{y}+{y}={x}^{3}+\left(-229a-562\right){x}-2969a-7273
375.2-f4 375.2-f Q(6)\Q(\sqrt{6}) 353 3 \cdot 5^{3} 0 Z/2Z\Z/2\Z SU(2)\mathrm{SU}(2) 11 2.2552276462.255227646 2.762078493 3491974408317235625a+2851185231630191875 \frac{349197440831723}{5625} a + \frac{285118523163019}{1875} [1 \bigl[1 , a a , 1 1 , 3117a7635 3117 a - 7635 , 108499a+265765] -108499 a + 265765\bigr] y2+xy+y=x3+ax2+(3117a7635)x108499a+265765{y}^2+{x}{y}+{y}={x}^{3}+a{x}^{2}+\left(3117a-7635\right){x}-108499a+265765
375.2-g1 375.2-g Q(6)\Q(\sqrt{6}) 353 3 \cdot 5^{3} 11 Z/2Z\Z/2\Z SU(2)\mathrm{SU}(2) 0.0604937640.060493764 7.5364333717.536433371 2.233480139 3462131685673645a+8480447785073645 -\frac{346213168567}{3645} a + \frac{848044778507}{3645} [a+1 \bigl[a + 1 , 0 0 , 0 0 , 185a458 185 a - 458 , 2125a+5223] -2125 a + 5223\bigr] y2+(a+1)xy=x3+(185a458)x2125a+5223{y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(185a-458\right){x}-2125a+5223
375.2-g2 375.2-g Q(6)\Q(\sqrt{6}) 353 3 \cdot 5^{3} 11 Z/2Z\Z/2\Z SU(2)\mathrm{SU}(2) 0.2419750570.241975057 15.0728667415.07286674 2.233480139 1629245a+1359115 \frac{16292}{45} a + \frac{13591}{15} [a+1 \bigl[a + 1 , 0 0 , 0 0 , 2 2 , 2a+5] -2 a + 5\bigr] y2+(a+1)xy=x3+2x2a+5{y}^2+\left(a+1\right){x}{y}={x}^{3}+2{x}-2a+5
375.2-g3 375.2-g Q(6)\Q(\sqrt{6}) 353 3 \cdot 5^{3} 11 Z/2ZZ/2Z\Z/2\Z\oplus\Z/2\Z SU(2)\mathrm{SU}(2) 0.1209875280.120987528 15.0728667415.07286674 2.233480139 73011154675a+193909061675 \frac{73011154}{675} a + \frac{193909061}{675} [a+1 \bigl[a + 1 , 0 0 , 0 0 , 10a33 10 a - 33 , 30a+78] -30 a + 78\bigr] y2+(a+1)xy=x3+(10a33)x30a+78{y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(10a-33\right){x}-30a+78
375.2-g4 375.2-g Q(6)\Q(\sqrt{6}) 353 3 \cdot 5^{3} 11 Z/2Z\Z/2\Z SU(2)\mathrm{SU}(2) 0.2419750570.241975057 7.5364333717.536433371 2.233480139 3491974408317235625a+2851185231630191875 \frac{349197440831723}{5625} a + \frac{285118523163019}{1875} [a+1 \bigl[a + 1 , 0 0 , 0 0 , 5a168 -5 a - 168 , 273a+105] 273 a + 105\bigr] y2+(a+1)xy=x3+(5a168)x+273a+105{y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(-5a-168\right){x}+273a+105
375.2-h1 375.2-h Q(6)\Q(\sqrt{6}) 353 3 \cdot 5^{3} 11 Z/2Z\Z/2\Z SU(2)\mathrm{SU}(2) 0.1887974240.188797424 16.8458115416.84581154 1.298411572 107545675a+87763225 -\frac{1075456}{75} a + \frac{877632}{25} [a \bigl[a , a1 -a - 1 , a+1 a + 1 , a2 -a - 2 , a+2] a + 2\bigr] y2+axy+(a+1)y=x3+(a1)x2+(a2)x+a+2{y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-a-2\right){x}+a+2
375.2-h2 375.2-h Q(6)\Q(\sqrt{6}) 353 3 \cdot 5^{3} 11 Z/2Z\Z/2\Z SU(2)\mathrm{SU}(2) 0.0943987120.094398712 33.6916230833.69162308 1.298411572 1431045a+108332815 \frac{143104}{5} a + \frac{1083328}{15} [a \bigl[a , 1 -1 , 1 1 , 6a16 6 a - 16 , 5a+12] -5 a + 12\bigr] y2+axy+y=x3x2+(6a16)x5a+12{y}^2+a{x}{y}+{y}={x}^{3}-{x}^{2}+\left(6a-16\right){x}-5a+12
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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.