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Results (22 matches)

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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
32.1-a1 32.1-a 3.3.316.1 \( 2^{5} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $72.47588334$ 1.019271743 \( \frac{63684217}{2} a^{2} - 89592107 a + 35115877 \) \( \bigl[a^{2} - 2\) , \( -a^{2} - a + 2\) , \( a^{2} - 2\) , \( -602 a^{2} + 318 a + 2556\) , \( 12985 a^{2} - 6874 a - 55177\bigr] \) ${y}^2+\left(a^{2}-2\right){x}{y}+\left(a^{2}-2\right){y}={x}^{3}+\left(-a^{2}-a+2\right){x}^{2}+\left(-602a^{2}+318a+2556\right){x}+12985a^{2}-6874a-55177$
32.1-a2 32.1-a 3.3.316.1 \( 2^{5} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $36.23794167$ 1.019271743 \( \frac{1898088202191}{2} a^{2} + 1274493239347 a - 810136780017 \) \( \bigl[a\) , \( a^{2} + a - 2\) , \( a\) , \( 68 a^{2} - 33 a - 285\) , \( -445 a^{2} + 236 a + 1891\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^{3}+\left(a^{2}+a-2\right){x}^{2}+\left(68a^{2}-33a-285\right){x}-445a^{2}+236a+1891$
32.1-a3 32.1-a 3.3.316.1 \( 2^{5} \) 0 $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $144.9517666$ 1.019271743 \( \frac{1401505}{4} a^{2} + \frac{928349}{2} a - \frac{584947}{2} \) \( \bigl[a\) , \( a^{2} + a - 2\) , \( a\) , \( 13 a^{2} - 3 a - 50\) , \( 19 a^{2} - 7 a - 76\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^{3}+\left(a^{2}+a-2\right){x}^{2}+\left(13a^{2}-3a-50\right){x}+19a^{2}-7a-76$
32.1-a4 32.1-a 3.3.316.1 \( 2^{5} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $18.11897083$ 1.019271743 \( \frac{285267441}{256} a^{2} - \frac{401089939}{128} a + \frac{156913533}{128} \) \( \bigl[a\) , \( -a^{2} + a + 2\) , \( a\) , \( 14434589287 a^{2} - 7640467435 a - 61334598487\) , \( 1856721004039097 a^{2} - 982793212111362 a - 7889468486259131\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-a^{2}+a+2\right){x}^{2}+\left(14434589287a^{2}-7640467435a-61334598487\right){x}+1856721004039097a^{2}-982793212111362a-7889468486259131$
32.1-a5 32.1-a 3.3.316.1 \( 2^{5} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $18.11897083$ 1.019271743 \( -\frac{58508563841049}{4} a^{2} + \frac{15484776480827}{2} a + \frac{124305555260903}{2} \) \( \bigl[a\) , \( -a^{2} + a + 4\) , \( a\) , \( 26100179 a^{2} - 13815259 a - 110903333\) , \( 106175166175 a^{2} - 56200275854 a - 451153202737\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-a^{2}+a+4\right){x}^{2}+\left(26100179a^{2}-13815259a-110903333\right){x}+106175166175a^{2}-56200275854a-451153202737$
32.1-a6 32.1-a 3.3.316.1 \( 2^{5} \) 0 $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $72.47588334$ 1.019271743 \( -\frac{29580655}{16} a^{2} + \frac{7825805}{8} a + \frac{62873277}{8} \) \( \bigl[a\) , \( -a^{2} + a + 4\) , \( a\) , \( 1631309 a^{2} - 863479 a - 6931663\) , \( 1660636815 a^{2} - 879002600 a - 7056279211\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-a^{2}+a+4\right){x}^{2}+\left(1631309a^{2}-863479a-6931663\right){x}+1660636815a^{2}-879002600a-7056279211$
32.1-b1 32.1-b 3.3.316.1 \( 2^{5} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $22.49580122$ 1.898231533 \( \frac{5335424117455903}{8} a^{2} + \frac{3582532102104931}{4} a - \frac{2277251078226861}{4} \) \( \bigl[a^{2} - 2\) , \( a^{2} - 4\) , \( a^{2} - 2\) , \( -5 a^{2} - 10 a - 10\) , \( -44 a^{2} - 48 a + 75\bigr] \) ${y}^2+\left(a^{2}-2\right){x}{y}+\left(a^{2}-2\right){y}={x}^{3}+\left(a^{2}-4\right){x}^{2}+\left(-5a^{2}-10a-10\right){x}-44a^{2}-48a+75$
32.1-b2 32.1-b 3.3.316.1 \( 2^{5} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $67.48740366$ 1.898231533 \( \frac{33759}{2} a^{2} + 32803 a + 4371 \) \( \bigl[a^{2} - 2\) , \( a^{2} - 4\) , \( a^{2} - 2\) , \( 0\) , \( -1\bigr] \) ${y}^2+\left(a^{2}-2\right){x}{y}+\left(a^{2}-2\right){y}={x}^{3}+\left(a^{2}-4\right){x}^{2}-1$
32.1-b3 32.1-b 3.3.316.1 \( 2^{5} \) 0 $\Z/4\Z$ $\mathrm{SU}(2)$ $1$ $44.99160244$ 1.898231533 \( \frac{532560105997425}{4096} a^{2} - \frac{749207151764755}{2048} a + \frac{293646661918461}{2048} \) \( \bigl[a\) , \( a^{2} - a - 3\) , \( a\) , \( 122252877320 a^{2} - 64710474941 a - 519469656935\) , \( -34245221998777113 a^{2} + 18126563794145582 a + 145512761032249632\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^{3}+\left(a^{2}-a-3\right){x}^{2}+\left(122252877320a^{2}-64710474941a-519469656935\right){x}-34245221998777113a^{2}+18126563794145582a+145512761032249632$
32.1-b4 32.1-b 3.3.316.1 \( 2^{5} \) 0 $\Z/4\Z$ $\mathrm{SU}(2)$ $1$ $134.9748073$ 1.898231533 \( \frac{19825}{16} a^{2} - \frac{24115}{8} a + \frac{15581}{8} \) \( \bigl[a\) , \( a^{2} - a - 3\) , \( a\) , \( -4408566115 a^{2} + 2333527139 a + 18732616995\) , \( -249975088401133 a^{2} + 132315958909892 a + 1062179281647772\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^{3}+\left(a^{2}-a-3\right){x}^{2}+\left(-4408566115a^{2}+2333527139a+18732616995\right){x}-249975088401133a^{2}+132315958909892a+1062179281647772$
32.1-b5 32.1-b 3.3.316.1 \( 2^{5} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $44.99160244$ 1.898231533 \( -\frac{596658698344264096415}{8} a^{2} + \frac{157910670855855346189}{4} a + \frac{1267643331281111416669}{4} \) \( \bigl[a\) , \( -a^{2} + 4\) , \( a^{2} - 2\) , \( 202613715 a^{2} - 107246802 a - 860934154\) , \( -2295401845649 a^{2} + 1214994254958 a + 9753485033640\bigr] \) ${y}^2+a{x}{y}+\left(a^{2}-2\right){y}={x}^{3}+\left(-a^{2}+4\right){x}^{2}+\left(202613715a^{2}-107246802a-860934154\right){x}-2295401845649a^{2}+1214994254958a+9753485033640$
32.1-b6 32.1-b 3.3.316.1 \( 2^{5} \) 0 $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $89.98320488$ 1.898231533 \( -\frac{266664752495}{64} a^{2} + \frac{71121115277}{32} a + \frac{567573953693}{32} \) \( \bigl[a\) , \( -a^{2} + 4\) , \( a^{2} - 2\) , \( 12663355 a^{2} - 6702927 a - 53808379\) , \( -35853515497 a^{2} + 18977860206 a + 152346626128\bigr] \) ${y}^2+a{x}{y}+\left(a^{2}-2\right){y}={x}^{3}+\left(-a^{2}+4\right){x}^{2}+\left(12663355a^{2}-6702927a-53808379\right){x}-35853515497a^{2}+18977860206a+152346626128$
32.1-b7 32.1-b 3.3.316.1 \( 2^{5} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $134.9748073$ 1.898231533 \( \frac{2097153}{2} a^{2} - 6340607 a + 9585409 \) \( \bigl[a\) , \( -a^{2} + 4\) , \( a^{2} - 2\) , \( 2501490 a^{2} - 1324082 a - 10629184\) , \( -3145625497 a^{2} + 1665031730 a + 13366204816\bigr] \) ${y}^2+a{x}{y}+\left(a^{2}-2\right){y}={x}^{3}+\left(-a^{2}+4\right){x}^{2}+\left(2501490a^{2}-1324082a-10629184\right){x}-3145625497a^{2}+1665031730a+13366204816$
32.1-b8 32.1-b 3.3.316.1 \( 2^{5} \) 0 $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $269.9496146$ 1.898231533 \( \frac{113}{4} a^{2} - \frac{1939}{2} a + \frac{7773}{2} \) \( \bigl[a\) , \( -a^{2} + 4\) , \( a^{2} - 2\) , \( 170740 a^{2} - 90377 a - 725499\) , \( -39378439 a^{2} + 20843660 a + 167324520\bigr] \) ${y}^2+a{x}{y}+\left(a^{2}-2\right){y}={x}^{3}+\left(-a^{2}+4\right){x}^{2}+\left(170740a^{2}-90377a-725499\right){x}-39378439a^{2}+20843660a+167324520$
32.1-c1 32.1-c 3.3.316.1 \( 2^{5} \) $1$ $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $0.066041164$ $242.5005074$ 1.351372542 \( \frac{200481}{16} a^{2} - \frac{325027}{8} a + \frac{233973}{8} \) \( \bigl[a\) , \( a^{2} - 4\) , \( a^{2} + a - 2\) , \( 124431276076006 a^{2} - 65863537513620 a - 528725979385749\) , \( -1028177435994703261869 a^{2} + 544231364186354985038 a + 4368870423675193690762\bigr] \) ${y}^2+a{x}{y}+\left(a^{2}+a-2\right){y}={x}^{3}+\left(a^{2}-4\right){x}^{2}+\left(124431276076006a^{2}-65863537513620a-528725979385749\right){x}-1028177435994703261869a^{2}+544231364186354985038a+4368870423675193690762$
32.1-c2 32.1-c 3.3.316.1 \( 2^{5} \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $0.264164657$ $30.31256343$ 1.351372542 \( \frac{4108077233}{65536} a^{2} - \frac{5810733523}{32768} a + \frac{2294990397}{32768} \) \( \bigl[a\) , \( a^{2} - 3\) , \( a^{2} - 2\) , \( -77888706625301391598868 a^{2} + 41227783821563007723392 a + 330960060784047749989794\) , \( 28781005690695861341828735825476034 a^{2} - 15234263504867798437609722439797286 a - 122294538008473034126916564710880454\bigr] \) ${y}^2+a{x}{y}+\left(a^{2}-2\right){y}={x}^{3}+\left(a^{2}-3\right){x}^{2}+\left(-77888706625301391598868a^{2}+41227783821563007723392a+330960060784047749989794\right){x}+28781005690695861341828735825476034a^{2}-15234263504867798437609722439797286a-122294538008473034126916564710880454$
32.1-c3 32.1-c 3.3.316.1 \( 2^{5} \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $0.033020582$ $121.2502537$ 1.351372542 \( \frac{427}{4} a^{2} + \frac{383}{2} a - \frac{47}{2} \) \( \bigl[a\) , \( a^{2} - 3\) , \( a\) , \( -50918171471081616 a^{2} + 26951832389486757 a + 216358466525204405\) , \( -38951442097068833754512865 a^{2} + 20617644121906983248738693 a + 165510151633261046069659994\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^{3}+\left(a^{2}-3\right){x}^{2}+\left(-50918171471081616a^{2}+26951832389486757a+216358466525204405\right){x}-38951442097068833754512865a^{2}+20617644121906983248738693a+165510151633261046069659994$
32.1-c4 32.1-c 3.3.316.1 \( 2^{5} \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $0.264164657$ $30.31256343$ 1.351372542 \( \frac{89069256294443128323}{2} a^{2} - 125302919348047971845 a + 49111676741552886754 \) \( \bigl[a\) , \( a^{2} - 2\) , \( a^{2} + a - 2\) , \( 29 a^{2} + 72 a - 41\) , \( -5780 a^{2} - 7852 a + 4978\bigr] \) ${y}^2+a{x}{y}+\left(a^{2}+a-2\right){y}={x}^{3}+\left(a^{2}-2\right){x}^{2}+\left(29a^{2}+72a-41\right){x}-5780a^{2}-7852a+4978$
32.1-c5 32.1-c 3.3.316.1 \( 2^{5} \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $0.264164657$ $30.31256343$ 1.351372542 \( -\frac{10154621765056003}{2} a^{2} + 2687505089603077 a + 21574207961612782 \) \( \bigl[a\) , \( a^{2} + a - 2\) , \( a^{2} - 2\) , \( 486273921 a^{2} - 257393114 a - 2066246710\) , \( -8535646743838 a^{2} + 4518059339552 a + 36269162590988\bigr] \) ${y}^2+a{x}{y}+\left(a^{2}-2\right){y}={x}^{3}+\left(a^{2}+a-2\right){x}^{2}+\left(486273921a^{2}-257393114a-2066246710\right){x}-8535646743838a^{2}+4518059339552a+36269162590988$
32.1-c6 32.1-c 3.3.316.1 \( 2^{5} \) $1$ $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $0.132082328$ $121.2502537$ 1.351372542 \( \frac{8525185037}{4} a^{2} - \frac{12150636535}{2} a + \frac{5069473275}{2} \) \( \bigl[a\) , \( a^{2} + a - 2\) , \( a^{2} - 2\) , \( 30392171 a^{2} - 16087094 a - 129140630\) , \( -133378539946 a^{2} + 70599472536 a + 566744160836\bigr] \) ${y}^2+a{x}{y}+\left(a^{2}-2\right){y}={x}^{3}+\left(a^{2}+a-2\right){x}^{2}+\left(30392171a^{2}-16087094a-129140630\right){x}-133378539946a^{2}+70599472536a+566744160836$
32.1-c7 32.1-c 3.3.316.1 \( 2^{5} \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $0.264164657$ $30.31256343$ 1.351372542 \( \frac{32251567931279}{16} a^{2} + \frac{21655756210331}{8} a - \frac{13765401110581}{8} \) \( \bigl[a\) , \( a - 1\) , \( a^{2} - 2\) , \( 60199270876066245436 a^{2} - 31864472186369026517 a - 255795162245334633462\) , \( 371768135944838763461274232817 a^{2} - 196783038319195503754985629908 a - 1579695057228071638067406296651\bigr] \) ${y}^2+a{x}{y}+\left(a^{2}-2\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(60199270876066245436a^{2}-31864472186369026517a-255795162245334633462\right){x}+371768135944838763461274232817a^{2}-196783038319195503754985629908a-1579695057228071638067406296651$
32.1-c8 32.1-c 3.3.316.1 \( 2^{5} \) $1$ $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $0.132082328$ $121.2502537$ 1.351372542 \( \frac{130050481}{256} a^{2} + \frac{87514925}{128} a - \frac{54929731}{128} \) \( \bigl[a\) , \( a - 1\) , \( a^{2} - 2\) , \( 3966702684137806156 a^{2} - 2099641499155711377 a - 16855077177877245442\) , \( 5143048258086022485533521397 a^{2} - 2722300715407677981600101384 a - 21853534842989882938087538771\bigr] \) ${y}^2+a{x}{y}+\left(a^{2}-2\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(3966702684137806156a^{2}-2099641499155711377a-16855077177877245442\right){x}+5143048258086022485533521397a^{2}-2722300715407677981600101384a-21853534842989882938087538771$
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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.