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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
882.1-a1 882.1-a \(\Q(\sqrt{2}) \) \( 2 \cdot 3^{2} \cdot 7^{2} \) 0 $\Z/8\Z$ $\mathrm{SU}(2)$ $1$ $12.07873502$ 2.135238861 \( -\frac{7189057}{16128} \) \( \bigl[1\) , \( 1\) , \( 1\) , \( -4\) , \( 5\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}-4{x}+5$
882.1-a2 882.1-a \(\Q(\sqrt{2}) \) \( 2 \cdot 3^{2} \cdot 7^{2} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $0.188730234$ 2.135238861 \( -\frac{1700921006729998152378353}{598192750252818} a + \frac{133636975245726467337960}{33232930569601} \) \( \bigl[1\) , \( 1\) , \( 1\) , \( 5085 a - 7394\) , \( 232452 a - 355327\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}+\left(5085a-7394\right){x}+232452a-355327$
882.1-a3 882.1-a \(\Q(\sqrt{2}) \) \( 2 \cdot 3^{2} \cdot 7^{2} \) 0 $\Z/4\Z$ $\mathrm{SU}(2)$ $1$ $0.754920939$ 2.135238861 \( \frac{6359387729183}{4218578658} \) \( \bigl[1\) , \( 1\) , \( 1\) , \( 386\) , \( 1277\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}+386{x}+1277$
882.1-a4 882.1-a \(\Q(\sqrt{2}) \) \( 2 \cdot 3^{2} \cdot 7^{2} \) 0 $\Z/2\Z\oplus\Z/4\Z$ $\mathrm{SU}(2)$ $1$ $3.019683757$ 2.135238861 \( \frac{124475734657}{63011844} \) \( \bigl[1\) , \( 1\) , \( 1\) , \( -104\) , \( 101\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}-104{x}+101$
882.1-a5 882.1-a \(\Q(\sqrt{2}) \) \( 2 \cdot 3^{2} \cdot 7^{2} \) 0 $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $0.754920939$ 2.135238861 \( \frac{84448510979617}{933897762} \) \( \bigl[1\) , \( 1\) , \( 1\) , \( -914\) , \( -10915\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}-914{x}-10915$
882.1-a6 882.1-a \(\Q(\sqrt{2}) \) \( 2 \cdot 3^{2} \cdot 7^{2} \) 0 $\Z/2\Z\oplus\Z/8\Z$ $\mathrm{SU}(2)$ $1$ $12.07873502$ 2.135238861 \( \frac{65597103937}{63504} \) \( \bigl[1\) , \( 1\) , \( 1\) , \( -84\) , \( 261\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}-84{x}+261$
882.1-a7 882.1-a \(\Q(\sqrt{2}) \) \( 2 \cdot 3^{2} \cdot 7^{2} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $0.188730234$ 2.135238861 \( \frac{1700921006729998152378353}{598192750252818} a + \frac{133636975245726467337960}{33232930569601} \) \( \bigl[1\) , \( 1\) , \( 1\) , \( -5085 a - 7394\) , \( -232452 a - 355327\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}+\left(-5085a-7394\right){x}-232452a-355327$
882.1-a8 882.1-a \(\Q(\sqrt{2}) \) \( 2 \cdot 3^{2} \cdot 7^{2} \) 0 $\Z/8\Z$ $\mathrm{SU}(2)$ $1$ $12.07873502$ 2.135238861 \( \frac{268498407453697}{252} \) \( \bigl[1\) , \( 1\) , \( 1\) , \( -1344\) , \( 18405\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}-1344{x}+18405$
882.1-b1 882.1-b \(\Q(\sqrt{2}) \) \( 2 \cdot 3^{2} \cdot 7^{2} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $6.130830253$ 2.167575823 \( \frac{2655587}{3087} a + \frac{179831}{2058} \) \( \bigl[a + 1\) , \( -1\) , \( 1\) , \( a - 1\) , \( a - 1\bigr] \) ${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}-{x}^{2}+\left(a-1\right){x}+a-1$
882.1-b2 882.1-b \(\Q(\sqrt{2}) \) \( 2 \cdot 3^{2} \cdot 7^{2} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $6.130830253$ 2.167575823 \( -\frac{780255600743}{705894} a + \frac{552523185269}{352947} \) \( \bigl[a + 1\) , \( -1\) , \( 1\) , \( 16 a - 31\) , \( 49 a - 67\bigr] \) ${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}-{x}^{2}+\left(16a-31\right){x}+49a-67$
882.1-c1 882.1-c \(\Q(\sqrt{2}) \) \( 2 \cdot 3^{2} \cdot 7^{2} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $2.980796834$ 1.053870827 \( -\frac{1654553343595}{154893312} a - \frac{1493179606537}{103262208} \) \( \bigl[a + 1\) , \( -a\) , \( 1\) , \( -52 a - 36\) , \( 190 a + 176\bigr] \) ${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}-a{x}^{2}+\left(-52a-36\right){x}+190a+176$
882.1-c2 882.1-c \(\Q(\sqrt{2}) \) \( 2 \cdot 3^{2} \cdot 7^{2} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $2.980796834$ 1.053870827 \( \frac{17609102787747678607}{54235247808} a + \frac{12451626415479149645}{27117623904} \) \( \bigl[a + 1\) , \( -a\) , \( 1\) , \( -532 a - 996\) , \( 10366 a + 13424\bigr] \) ${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}-a{x}^{2}+\left(-532a-996\right){x}+10366a+13424$
882.1-d1 882.1-d \(\Q(\sqrt{2}) \) \( 2 \cdot 3^{2} \cdot 7^{2} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $6.130830253$ 2.167575823 \( -\frac{2655587}{3087} a + \frac{179831}{2058} \) \( \bigl[a + 1\) , \( -a - 1\) , \( 1\) , \( -2 a - 1\) , \( -a - 1\bigr] \) ${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-2a-1\right){x}-a-1$
882.1-d2 882.1-d \(\Q(\sqrt{2}) \) \( 2 \cdot 3^{2} \cdot 7^{2} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $6.130830253$ 2.167575823 \( \frac{780255600743}{705894} a + \frac{552523185269}{352947} \) \( \bigl[a + 1\) , \( -a - 1\) , \( 1\) , \( -17 a - 31\) , \( -49 a - 67\bigr] \) ${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-17a-31\right){x}-49a-67$
882.1-e1 882.1-e \(\Q(\sqrt{2}) \) \( 2 \cdot 3^{2} \cdot 7^{2} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $2.980796834$ 1.053870827 \( \frac{1654553343595}{154893312} a - \frac{1493179606537}{103262208} \) \( \bigl[a + 1\) , \( 0\) , \( 1\) , \( 51 a - 36\) , \( -190 a + 176\bigr] \) ${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+\left(51a-36\right){x}-190a+176$
882.1-e2 882.1-e \(\Q(\sqrt{2}) \) \( 2 \cdot 3^{2} \cdot 7^{2} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $2.980796834$ 1.053870827 \( -\frac{17609102787747678607}{54235247808} a + \frac{12451626415479149645}{27117623904} \) \( \bigl[a + 1\) , \( 0\) , \( 1\) , \( 531 a - 996\) , \( -10366 a + 13424\bigr] \) ${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+\left(531a-996\right){x}-10366a+13424$
882.1-f1 882.1-f \(\Q(\sqrt{2}) \) \( 2 \cdot 3^{2} \cdot 7^{2} \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $0.130451768$ $17.23629450$ 1.589933200 \( -\frac{99733}{147} a + \frac{771443}{588} \) \( \bigl[a + 1\) , \( -a + 1\) , \( a\) , \( 2 a - 4\) , \( 4 a - 6\bigr] \) ${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(2a-4\right){x}+4a-6$
882.1-f2 882.1-f \(\Q(\sqrt{2}) \) \( 2 \cdot 3^{2} \cdot 7^{2} \) $1$ $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $0.065225884$ $17.23629450$ 1.589933200 \( -\frac{384494749}{21609} a + \frac{150700299}{4802} \) \( \bigl[1\) , \( -a\) , \( 1\) , \( -18 a - 27\) , \( 51 a + 72\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}-a{x}^{2}+\left(-18a-27\right){x}+51a+72$
882.1-f3 882.1-f \(\Q(\sqrt{2}) \) \( 2 \cdot 3^{2} \cdot 7^{2} \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $0.130451768$ $4.309073625$ 1.589933200 \( \frac{127949540041}{34588806} a + \frac{2442796570097}{466948881} \) \( \bigl[a + 1\) , \( -a + 1\) , \( a\) , \( -3 a - 4\) , \( -213 a + 292\bigr] \) ${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-3a-4\right){x}-213a+292$
882.1-f4 882.1-f \(\Q(\sqrt{2}) \) \( 2 \cdot 3^{2} \cdot 7^{2} \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $0.130451768$ $17.23629450$ 1.589933200 \( -\frac{15707330441833}{14406} a + \frac{11319802754221}{7203} \) \( \bigl[1\) , \( -a\) , \( 1\) , \( -273 a - 417\) , \( 3189 a + 4560\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}-a{x}^{2}+\left(-273a-417\right){x}+3189a+4560$
882.1-g1 882.1-g \(\Q(\sqrt{2}) \) \( 2 \cdot 3^{2} \cdot 7^{2} \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $0.130451768$ $4.309073625$ 1.589933200 \( -\frac{127949540041}{34588806} a + \frac{2442796570097}{466948881} \) \( \bigl[a + 1\) , \( 1\) , \( a\) , \( 2 a - 4\) , \( 213 a + 292\bigr] \) ${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+{x}^{2}+\left(2a-4\right){x}+213a+292$
882.1-g2 882.1-g \(\Q(\sqrt{2}) \) \( 2 \cdot 3^{2} \cdot 7^{2} \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $0.130451768$ $17.23629450$ 1.589933200 \( \frac{99733}{147} a + \frac{771443}{588} \) \( \bigl[a + 1\) , \( 1\) , \( a\) , \( -3 a - 4\) , \( -4 a - 6\bigr] \) ${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+{x}^{2}+\left(-3a-4\right){x}-4a-6$
882.1-g3 882.1-g \(\Q(\sqrt{2}) \) \( 2 \cdot 3^{2} \cdot 7^{2} \) $1$ $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $0.065225884$ $17.23629450$ 1.589933200 \( \frac{384494749}{21609} a + \frac{150700299}{4802} \) \( \bigl[1\) , \( a\) , \( 1\) , \( 18 a - 27\) , \( -51 a + 72\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}+a{x}^{2}+\left(18a-27\right){x}-51a+72$
882.1-g4 882.1-g \(\Q(\sqrt{2}) \) \( 2 \cdot 3^{2} \cdot 7^{2} \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $0.130451768$ $17.23629450$ 1.589933200 \( \frac{15707330441833}{14406} a + \frac{11319802754221}{7203} \) \( \bigl[1\) , \( a\) , \( 1\) , \( 273 a - 417\) , \( -3189 a + 4560\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}+a{x}^{2}+\left(273a-417\right){x}-3189a+4560$
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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.