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Results (24 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
726.1-a1 726.1-a \(\Q(\sqrt{6}) \) \( 2 \cdot 3 \cdot 11^{2} \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $0.195042991$ $4.813898015$ 1.533245153 \( -\frac{192100033}{2371842} \) \( \bigl[a + 1\) , \( -a + 1\) , \( a\) , \( 239 a - 589\) , \( -14693 a + 35989\bigr] \) ${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(239a-589\right){x}-14693a+35989$
726.1-a2 726.1-a \(\Q(\sqrt{6}) \) \( 2 \cdot 3 \cdot 11^{2} \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $0.195042991$ $19.25559206$ 1.533245153 \( \frac{912673}{528} \) \( \bigl[a + 1\) , \( -a + 1\) , \( a\) , \( 39 a - 99\) , \( 57 a - 141\bigr] \) ${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(39a-99\right){x}+57a-141$
726.1-a3 726.1-a \(\Q(\sqrt{6}) \) \( 2 \cdot 3 \cdot 11^{2} \) $1$ $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $0.390085982$ $19.25559206$ 1.533245153 \( \frac{1180932193}{4356} \) \( \bigl[a + 1\) , \( 1\) , \( a\) , \( -440 a - 1079\) , \( 7267 a + 17799\bigr] \) ${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+{x}^{2}+\left(-440a-1079\right){x}+7267a+17799$
726.1-a4 726.1-a \(\Q(\sqrt{6}) \) \( 2 \cdot 3 \cdot 11^{2} \) $1$ $\Z/4\Z$ $\mathrm{SU}(2)$ $0.780171965$ $19.25559206$ 1.533245153 \( \frac{4824238966273}{66} \) \( \bigl[a + 1\) , \( -a + 1\) , \( a\) , \( 7039 a - 17249\) , \( -494017 a + 1210089\bigr] \) ${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(7039a-17249\right){x}-494017a+1210089$
726.1-b1 726.1-b \(\Q(\sqrt{6}) \) \( 2 \cdot 3 \cdot 11^{2} \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $8.015579573$ $0.056797834$ 3.717244094 \( -\frac{112427521449300721}{466873642818} \) \( \bigl[1\) , \( 0\) , \( 0\) , \( -10055\) , \( -390309\bigr] \) ${y}^2+{x}{y}={x}^{3}-10055{x}-390309$
726.1-b2 726.1-b \(\Q(\sqrt{6}) \) \( 2 \cdot 3 \cdot 11^{2} \) $1$ $\Z/10\Z$ $\mathrm{SU}(2)$ $1.603115914$ $1.419945868$ 3.717244094 \( \frac{168105213359}{228637728} \) \( \bigl[1\) , \( 0\) , \( 0\) , \( 115\) , \( 561\bigr] \) ${y}^2+{x}{y}={x}^{3}+115{x}+561$
726.1-b3 726.1-b \(\Q(\sqrt{6}) \) \( 2 \cdot 3 \cdot 11^{2} \) $1$ $\Z/10\Z$ $\mathrm{SU}(2)$ $0.801557957$ $5.679783475$ 3.717244094 \( \frac{10091699281}{2737152} \) \( \bigl[1\) , \( 0\) , \( 0\) , \( -45\) , \( 81\bigr] \) ${y}^2+{x}{y}={x}^{3}-45{x}+81$
726.1-b4 726.1-b \(\Q(\sqrt{6}) \) \( 2 \cdot 3 \cdot 11^{2} \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $4.007789786$ $0.227191339$ 3.717244094 \( \frac{112763292123580561}{1932612} \) \( \bigl[1\) , \( 0\) , \( 0\) , \( -10065\) , \( -389499\bigr] \) ${y}^2+{x}{y}={x}^{3}-10065{x}-389499$
726.1-c1 726.1-c \(\Q(\sqrt{6}) \) \( 2 \cdot 3 \cdot 11^{2} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $1.214828373$ 3.967612853 \( -\frac{192100033}{2371842} \) \( \bigl[1\) , \( 1\) , \( 1\) , \( -12\) , \( -81\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}-12{x}-81$
726.1-c2 726.1-c \(\Q(\sqrt{6}) \) \( 2 \cdot 3 \cdot 11^{2} \) 0 $\Z/4\Z$ $\mathrm{SU}(2)$ $1$ $19.43725397$ 3.967612853 \( \frac{912673}{528} \) \( \bigl[1\) , \( 1\) , \( 1\) , \( -2\) , \( -1\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}-2{x}-1$
726.1-c3 726.1-c \(\Q(\sqrt{6}) \) \( 2 \cdot 3 \cdot 11^{2} \) 0 $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $4.859313493$ 3.967612853 \( \frac{1180932193}{4356} \) \( \bigl[1\) , \( 1\) , \( 1\) , \( -22\) , \( -49\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}-22{x}-49$
726.1-c4 726.1-c \(\Q(\sqrt{6}) \) \( 2 \cdot 3 \cdot 11^{2} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $1.214828373$ 3.967612853 \( \frac{4824238966273}{66} \) \( \bigl[1\) , \( 1\) , \( 1\) , \( -352\) , \( -2689\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}-352{x}-2689$
726.1-d1 726.1-d \(\Q(\sqrt{6}) \) \( 2 \cdot 3 \cdot 11^{2} \) $1$ $\Z/6\Z$ $\mathrm{SU}(2)$ $1.548328844$ $2.444595345$ 6.180940330 \( -\frac{7357983625}{127552392} \) \( \bigl[a + 1\) , \( 0\) , \( 0\) , \( 811 a - 1984\) , \( -109228 a + 267554\bigr] \) ${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(811a-1984\right){x}-109228a+267554$
726.1-d2 726.1-d \(\Q(\sqrt{6}) \) \( 2 \cdot 3 \cdot 11^{2} \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $0.516109614$ $2.444595345$ 6.180940330 \( \frac{9938375}{176418} \) \( \bigl[a + 1\) , \( -a\) , \( 0\) , \( 89 a + 221\) , \( -3920 a - 9601\bigr] \) ${y}^2+\left(a+1\right){x}{y}={x}^{3}-a{x}^{2}+\left(89a+221\right){x}-3920a-9601$
726.1-d3 726.1-d \(\Q(\sqrt{6}) \) \( 2 \cdot 3 \cdot 11^{2} \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $0.258054807$ $9.778381380$ 6.180940330 \( \frac{18609625}{1188} \) \( \bigl[a + 1\) , \( -a\) , \( 0\) , \( -111 a - 269\) , \( -952 a - 2331\bigr] \) ${y}^2+\left(a+1\right){x}{y}={x}^{3}-a{x}^{2}+\left(-111a-269\right){x}-952a-2331$
726.1-d4 726.1-d \(\Q(\sqrt{6}) \) \( 2 \cdot 3 \cdot 11^{2} \) $1$ $\Z/6\Z$ $\mathrm{SU}(2)$ $0.774164422$ $9.778381380$ 6.180940330 \( \frac{57736239625}{255552} \) \( \bigl[a + 1\) , \( 0\) , \( 0\) , \( 1611 a - 3944\) , \( -54572 a + 133674\bigr] \) ${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(1611a-3944\right){x}-54572a+133674$
726.1-e1 726.1-e \(\Q(\sqrt{6}) \) \( 2 \cdot 3 \cdot 11^{2} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $0.884125736$ 3.609428203 \( -\frac{112427521449300721}{466873642818} \) \( \bigl[a + 1\) , \( 0\) , \( a + 1\) , \( 201100 a - 492698\) , \( -77080082 a + 188807168\bigr] \) ${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(201100a-492698\right){x}-77080082a+188807168$
726.1-e2 726.1-e \(\Q(\sqrt{6}) \) \( 2 \cdot 3 \cdot 11^{2} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $0.884125736$ 3.609428203 \( \frac{168105213359}{228637728} \) \( \bigl[a + 1\) , \( -a\) , \( a + 1\) , \( 2298 a + 5632\) , \( -108779 a - 266452\bigr] \) ${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}-a{x}^{2}+\left(2298a+5632\right){x}-108779a-266452$
726.1-e3 726.1-e \(\Q(\sqrt{6}) \) \( 2 \cdot 3 \cdot 11^{2} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $3.536502944$ 3.609428203 \( \frac{10091699281}{2737152} \) \( \bigl[a + 1\) , \( -a\) , \( a + 1\) , \( -902 a - 2208\) , \( -16939 a - 41492\bigr] \) ${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}-a{x}^{2}+\left(-902a-2208\right){x}-16939a-41492$
726.1-e4 726.1-e \(\Q(\sqrt{6}) \) \( 2 \cdot 3 \cdot 11^{2} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $3.536502944$ 3.609428203 \( \frac{112763292123580561}{1932612} \) \( \bigl[a + 1\) , \( -a\) , \( a + 1\) , \( -201302 a - 493188\) , \( 76919501 a + 188413828\bigr] \) ${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}-a{x}^{2}+\left(-201302a-493188\right){x}+76919501a+188413828$
726.1-f1 726.1-f \(\Q(\sqrt{6}) \) \( 2 \cdot 3 \cdot 11^{2} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $0.635354791$ 1.556295044 \( -\frac{7357983625}{127552392} \) \( \bigl[1\) , \( 0\) , \( 1\) , \( -41\) , \( -556\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}-41{x}-556$
726.1-f2 726.1-f \(\Q(\sqrt{6}) \) \( 2 \cdot 3 \cdot 11^{2} \) 0 $\Z/6\Z$ $\mathrm{SU}(2)$ $1$ $5.718193122$ 1.556295044 \( \frac{9938375}{176418} \) \( \bigl[1\) , \( 0\) , \( 1\) , \( 4\) , \( 20\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}+4{x}+20$
726.1-f3 726.1-f \(\Q(\sqrt{6}) \) \( 2 \cdot 3 \cdot 11^{2} \) 0 $\Z/6\Z$ $\mathrm{SU}(2)$ $1$ $22.87277248$ 1.556295044 \( \frac{18609625}{1188} \) \( \bigl[1\) , \( 0\) , \( 1\) , \( -6\) , \( 4\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}-6{x}+4$
726.1-f4 726.1-f \(\Q(\sqrt{6}) \) \( 2 \cdot 3 \cdot 11^{2} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $2.541419165$ 1.556295044 \( \frac{57736239625}{255552} \) \( \bigl[1\) , \( 0\) , \( 1\) , \( -81\) , \( -284\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}-81{x}-284$
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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.