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Results (32 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
1452.1-a1 1452.1-a \(\Q(\sqrt{21}) \) \( 2^{2} \cdot 3 \cdot 11^{2} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $1.214828373$ 2.120778277 \( -\frac{192100033}{2371842} \) \( \bigl[1\) , \( 1\) , \( 1\) , \( -12\) , \( -81\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}-12{x}-81$
1452.1-a2 1452.1-a \(\Q(\sqrt{21}) \) \( 2^{2} \cdot 3 \cdot 11^{2} \) 0 $\Z/4\Z$ $\mathrm{SU}(2)$ $1$ $19.43725397$ 2.120778277 \( \frac{912673}{528} \) \( \bigl[1\) , \( 1\) , \( 1\) , \( -2\) , \( -1\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}-2{x}-1$
1452.1-a3 1452.1-a \(\Q(\sqrt{21}) \) \( 2^{2} \cdot 3 \cdot 11^{2} \) 0 $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $4.859313493$ 2.120778277 \( \frac{1180932193}{4356} \) \( \bigl[1\) , \( 1\) , \( 1\) , \( -22\) , \( -49\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}-22{x}-49$
1452.1-a4 1452.1-a \(\Q(\sqrt{21}) \) \( 2^{2} \cdot 3 \cdot 11^{2} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $1.214828373$ 2.120778277 \( \frac{4824238966273}{66} \) \( \bigl[1\) , \( 1\) , \( 1\) , \( -352\) , \( -2689\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}-352{x}-2689$
1452.1-b1 1452.1-b \(\Q(\sqrt{21}) \) \( 2^{2} \cdot 3 \cdot 11^{2} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $0.884125736$ 3.858641056 \( -\frac{112427521449300721}{466873642818} \) \( \bigl[a\) , \( 1\) , \( a\) , \( 50275 a - 140771\) , \( -9317141 a + 26009932\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^{3}+{x}^{2}+\left(50275a-140771\right){x}-9317141a+26009932$
1452.1-b2 1452.1-b \(\Q(\sqrt{21}) \) \( 2^{2} \cdot 3 \cdot 11^{2} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $0.884125736$ 3.858641056 \( \frac{168105213359}{228637728} \) \( \bigl[a\) , \( 1\) , \( a\) , \( -575 a + 1609\) , \( 12889 a - 35978\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^{3}+{x}^{2}+\left(-575a+1609\right){x}+12889a-35978$
1452.1-b3 1452.1-b \(\Q(\sqrt{21}) \) \( 2^{2} \cdot 3 \cdot 11^{2} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $3.536502944$ 3.858641056 \( \frac{10091699281}{2737152} \) \( \bigl[a\) , \( 1\) , \( a\) , \( 225 a - 631\) , \( 2169 a - 6058\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^{3}+{x}^{2}+\left(225a-631\right){x}+2169a-6058$
1452.1-b4 1452.1-b \(\Q(\sqrt{21}) \) \( 2^{2} \cdot 3 \cdot 11^{2} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $3.536502944$ 3.858641056 \( \frac{112763292123580561}{1932612} \) \( \bigl[a + 1\) , \( -a + 1\) , \( a + 1\) , \( -50327 a - 90586\) , \( 9297650 a + 16657871\bigr] \) ${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-50327a-90586\right){x}+9297650a+16657871$
1452.1-c1 1452.1-c \(\Q(\sqrt{21}) \) \( 2^{2} \cdot 3 \cdot 11^{2} \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $0.102553931$ $5.787714375$ 4.144763299 \( -\frac{65315105246375}{3175524} a + \frac{91344237347125}{1587762} \) \( \bigl[1\) , \( a + 1\) , \( 0\) , \( -423 a - 860\) , \( 7025 a + 13001\bigr] \) ${y}^2+{x}{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-423a-860\right){x}+7025a+13001$
1452.1-c2 1452.1-c \(\Q(\sqrt{21}) \) \( 2^{2} \cdot 3 \cdot 11^{2} \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $0.205107862$ $11.57542875$ 4.144763299 \( \frac{42886322528375}{14256} a + \frac{25607299252625}{4752} \) \( \bigl[1\) , \( a + 1\) , \( 0\) , \( -443 a - 800\) , \( 7149 a + 12813\bigr] \) ${y}^2+{x}{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-443a-800\right){x}+7149a+12813$
1452.1-d1 1452.1-d \(\Q(\sqrt{21}) \) \( 2^{2} \cdot 3 \cdot 11^{2} \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $0.205107862$ $11.57542875$ 4.144763299 \( -\frac{42886322528375}{14256} a + \frac{59854110143125}{7128} \) \( \bigl[1\) , \( -a - 1\) , \( 1\) , \( 445 a - 1245\) , \( -7593 a + 21206\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(445a-1245\right){x}-7593a+21206$
1452.1-d2 1452.1-d \(\Q(\sqrt{21}) \) \( 2^{2} \cdot 3 \cdot 11^{2} \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $0.102553931$ $5.787714375$ 4.144763299 \( \frac{65315105246375}{3175524} a + \frac{39124456482625}{1058508} \) \( \bigl[1\) , \( -a - 1\) , \( 1\) , \( 425 a - 1285\) , \( -7449 a + 21310\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(425a-1285\right){x}-7449a+21310$
1452.1-e1 1452.1-e \(\Q(\sqrt{21}) \) \( 2^{2} \cdot 3 \cdot 11^{2} \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $0.195042991$ $4.813898015$ 3.278216031 \( -\frac{192100033}{2371842} \) \( \bigl[a\) , \( a + 1\) , \( 1\) , \( 62 a - 164\) , \( -1818 a + 5081\bigr] \) ${y}^2+a{x}{y}+{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(62a-164\right){x}-1818a+5081$
1452.1-e2 1452.1-e \(\Q(\sqrt{21}) \) \( 2^{2} \cdot 3 \cdot 11^{2} \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $0.195042991$ $19.25559206$ 3.278216031 \( \frac{912673}{528} \) \( \bigl[a\) , \( a + 1\) , \( 1\) , \( 12 a - 24\) , \( 2 a + 1\bigr] \) ${y}^2+a{x}{y}+{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(12a-24\right){x}+2a+1$
1452.1-e3 1452.1-e \(\Q(\sqrt{21}) \) \( 2^{2} \cdot 3 \cdot 11^{2} \) $1$ $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $0.390085982$ $19.25559206$ 3.278216031 \( \frac{1180932193}{4356} \) \( \bigl[a\) , \( a + 1\) , \( 1\) , \( 112 a - 304\) , \( -950 a + 2657\bigr] \) ${y}^2+a{x}{y}+{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(112a-304\right){x}-950a+2657$
1452.1-e4 1452.1-e \(\Q(\sqrt{21}) \) \( 2^{2} \cdot 3 \cdot 11^{2} \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $0.780171965$ $19.25559206$ 3.278216031 \( \frac{4824238966273}{66} \) \( \bigl[a\) , \( a + 1\) , \( 1\) , \( 1762 a - 4924\) , \( -61010 a + 170297\bigr] \) ${y}^2+a{x}{y}+{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(1762a-4924\right){x}-61010a+170297$
1452.1-f1 1452.1-f \(\Q(\sqrt{21}) \) \( 2^{2} \cdot 3 \cdot 11^{2} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $2.131863578$ 0.465210772 \( -\frac{42886322528375}{14256} a + \frac{59854110143125}{7128} \) \( \bigl[a + 1\) , \( -1\) , \( 0\) , \( -13 a - 112\) , \( -105 a - 486\bigr] \) ${y}^2+\left(a+1\right){x}{y}={x}^{3}-{x}^{2}+\left(-13a-112\right){x}-105a-486$
1452.1-f2 1452.1-f \(\Q(\sqrt{21}) \) \( 2^{2} \cdot 3 \cdot 11^{2} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $1.065931789$ 0.465210772 \( \frac{65315105246375}{3175524} a + \frac{39124456482625}{1058508} \) \( \bigl[a + 1\) , \( -1\) , \( 0\) , \( -493 a - 972\) , \( -9949 a - 18118\bigr] \) ${y}^2+\left(a+1\right){x}{y}={x}^{3}-{x}^{2}+\left(-493a-972\right){x}-9949a-18118$
1452.1-g1 1452.1-g \(\Q(\sqrt{21}) \) \( 2^{2} \cdot 3 \cdot 11^{2} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $1.065931789$ 0.465210772 \( -\frac{65315105246375}{3175524} a + \frac{91344237347125}{1587762} \) \( \bigl[a\) , \( -a\) , \( 0\) , \( 493 a - 1465\) , \( 9949 a - 28067\bigr] \) ${y}^2+a{x}{y}={x}^{3}-a{x}^{2}+\left(493a-1465\right){x}+9949a-28067$
1452.1-g2 1452.1-g \(\Q(\sqrt{21}) \) \( 2^{2} \cdot 3 \cdot 11^{2} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $2.131863578$ 0.465210772 \( \frac{42886322528375}{14256} a + \frac{25607299252625}{4752} \) \( \bigl[a\) , \( -a\) , \( 0\) , \( 13 a - 125\) , \( 105 a - 591\bigr] \) ${y}^2+a{x}{y}={x}^{3}-a{x}^{2}+\left(13a-125\right){x}+105a-591$
1452.1-h1 1452.1-h \(\Q(\sqrt{21}) \) \( 2^{2} \cdot 3 \cdot 11^{2} \) 0 $\Z/6\Z$ $\mathrm{SU}(2)$ $1$ $2.444595345$ 2.133817754 \( -\frac{7357983625}{127552392} \) \( \bigl[a\) , \( 1\) , \( a + 1\) , \( 202 a - 568\) , \( -13136 a + 36667\bigr] \) ${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+{x}^{2}+\left(202a-568\right){x}-13136a+36667$
1452.1-h2 1452.1-h \(\Q(\sqrt{21}) \) \( 2^{2} \cdot 3 \cdot 11^{2} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $2.444595345$ 2.133817754 \( \frac{9938375}{176418} \) \( \bigl[a\) , \( 1\) , \( a + 1\) , \( -23 a + 62\) , \( 463 a - 1295\bigr] \) ${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+{x}^{2}+\left(-23a+62\right){x}+463a-1295$
1452.1-h3 1452.1-h \(\Q(\sqrt{21}) \) \( 2^{2} \cdot 3 \cdot 11^{2} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $9.778381380$ 2.133817754 \( \frac{18609625}{1188} \) \( \bigl[a\) , \( 1\) , \( a + 1\) , \( 27 a - 78\) , \( 129 a - 363\bigr] \) ${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+{x}^{2}+\left(27a-78\right){x}+129a-363$
1452.1-h4 1452.1-h \(\Q(\sqrt{21}) \) \( 2^{2} \cdot 3 \cdot 11^{2} \) 0 $\Z/6\Z$ $\mathrm{SU}(2)$ $1$ $9.778381380$ 2.133817754 \( \frac{57736239625}{255552} \) \( \bigl[a\) , \( 1\) , \( a + 1\) , \( 402 a - 1128\) , \( -6408 a + 17883\bigr] \) ${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+{x}^{2}+\left(402a-1128\right){x}-6408a+17883$
1452.1-i1 1452.1-i \(\Q(\sqrt{21}) \) \( 2^{2} \cdot 3 \cdot 11^{2} \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $9.780331572$ $0.056797834$ 2.424407990 \( -\frac{112427521449300721}{466873642818} \) \( \bigl[1\) , \( 0\) , \( 0\) , \( -10055\) , \( -390309\bigr] \) ${y}^2+{x}{y}={x}^{3}-10055{x}-390309$
1452.1-i2 1452.1-i \(\Q(\sqrt{21}) \) \( 2^{2} \cdot 3 \cdot 11^{2} \) $1$ $\Z/10\Z$ $\mathrm{SU}(2)$ $1.956066314$ $1.419945868$ 2.424407990 \( \frac{168105213359}{228637728} \) \( \bigl[1\) , \( 0\) , \( 0\) , \( 115\) , \( 561\bigr] \) ${y}^2+{x}{y}={x}^{3}+115{x}+561$
1452.1-i3 1452.1-i \(\Q(\sqrt{21}) \) \( 2^{2} \cdot 3 \cdot 11^{2} \) $1$ $\Z/10\Z$ $\mathrm{SU}(2)$ $0.978033157$ $5.679783475$ 2.424407990 \( \frac{10091699281}{2737152} \) \( \bigl[1\) , \( 0\) , \( 0\) , \( -45\) , \( 81\bigr] \) ${y}^2+{x}{y}={x}^{3}-45{x}+81$
1452.1-i4 1452.1-i \(\Q(\sqrt{21}) \) \( 2^{2} \cdot 3 \cdot 11^{2} \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $4.890165786$ $0.227191339$ 2.424407990 \( \frac{112763292123580561}{1932612} \) \( \bigl[1\) , \( 0\) , \( 0\) , \( -10065\) , \( -389499\bigr] \) ${y}^2+{x}{y}={x}^{3}-10065{x}-389499$
1452.1-j1 1452.1-j \(\Q(\sqrt{21}) \) \( 2^{2} \cdot 3 \cdot 11^{2} \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $1.088014913$ $0.635354791$ 5.430552431 \( -\frac{7357983625}{127552392} \) \( \bigl[1\) , \( 0\) , \( 1\) , \( -41\) , \( -556\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}-41{x}-556$
1452.1-j2 1452.1-j \(\Q(\sqrt{21}) \) \( 2^{2} \cdot 3 \cdot 11^{2} \) $1$ $\Z/6\Z$ $\mathrm{SU}(2)$ $3.264044740$ $5.718193122$ 5.430552431 \( \frac{9938375}{176418} \) \( \bigl[1\) , \( 0\) , \( 1\) , \( 4\) , \( 20\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}+4{x}+20$
1452.1-j3 1452.1-j \(\Q(\sqrt{21}) \) \( 2^{2} \cdot 3 \cdot 11^{2} \) $1$ $\Z/6\Z$ $\mathrm{SU}(2)$ $1.632022370$ $22.87277248$ 5.430552431 \( \frac{18609625}{1188} \) \( \bigl[1\) , \( 0\) , \( 1\) , \( -6\) , \( 4\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}-6{x}+4$
1452.1-j4 1452.1-j \(\Q(\sqrt{21}) \) \( 2^{2} \cdot 3 \cdot 11^{2} \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $0.544007456$ $2.541419165$ 5.430552431 \( \frac{57736239625}{255552} \) \( \bigl[1\) , \( 0\) , \( 1\) , \( -81\) , \( -284\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}-81{x}-284$
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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.