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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
1452.1-a1 1452.1-a \(\Q(\sqrt{3}) \) \( 2^{2} \cdot 3 \cdot 11^{2} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $2.092358537$ 1.208023764 \( -\frac{3209452}{9801} a - \frac{2627288}{9801} \) \( \bigl[a + 1\) , \( -a + 1\) , \( 0\) , \( -6 a + 4\) , \( 2 a - 18\bigr] \) ${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-6a+4\right){x}+2a-18$
1452.1-a2 1452.1-a \(\Q(\sqrt{3}) \) \( 2^{2} \cdot 3 \cdot 11^{2} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $8.369434150$ 1.208023764 \( \frac{60218368}{99} a + \frac{104983888}{99} \) \( \bigl[a + 1\) , \( -a + 1\) , \( 0\) , \( -a - 6\) , \( -12\bigr] \) ${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-a-6\right){x}-12$
1452.1-b1 1452.1-b \(\Q(\sqrt{3}) \) \( 2^{2} \cdot 3 \cdot 11^{2} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $0.634035360$ 2.745453647 \( -\frac{3196715008}{649539} \) \( \bigl[0\) , \( 1\) , \( 0\) , \( -77\) , \( -330\bigr] \) ${y}^2={x}^{3}+{x}^{2}-77{x}-330$
1452.1-b2 1452.1-b \(\Q(\sqrt{3}) \) \( 2^{2} \cdot 3 \cdot 11^{2} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $0.634035360$ 2.745453647 \( -\frac{114750605652090357244}{395307} a + \frac{7361254784861301480}{14641} \) \( \bigl[a + 1\) , \( -a\) , \( 0\) , \( 20777 a - 36011\) , \( 2159496 a - 3740397\bigr] \) ${y}^2+\left(a+1\right){x}{y}={x}^{3}-a{x}^{2}+\left(20777a-36011\right){x}+2159496a-3740397$
1452.1-b3 1452.1-b \(\Q(\sqrt{3}) \) \( 2^{2} \cdot 3 \cdot 11^{2} \) 0 $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $1.268070721$ 2.745453647 \( \frac{932410994128}{29403} \) \( \bigl[a + 1\) , \( -a\) , \( 0\) , \( 1292 a - 2261\) , \( 34335 a - 59514\bigr] \) ${y}^2+\left(a+1\right){x}{y}={x}^{3}-a{x}^{2}+\left(1292a-2261\right){x}+34335a-59514$
1452.1-b4 1452.1-b \(\Q(\sqrt{3}) \) \( 2^{2} \cdot 3 \cdot 11^{2} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $0.634035360$ 2.745453647 \( \frac{114750605652090357244}{395307} a + \frac{7361254784861301480}{14641} \) \( \bigl[a + 1\) , \( -a\) , \( 0\) , \( 1247 a - 2531\) , \( 30564 a - 55707\bigr] \) ${y}^2+\left(a+1\right){x}{y}={x}^{3}-a{x}^{2}+\left(1247a-2531\right){x}+30564a-55707$
1452.1-c1 1452.1-c \(\Q(\sqrt{3}) \) \( 2^{2} \cdot 3 \cdot 11^{2} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $2.092358537$ 1.208023764 \( \frac{3209452}{9801} a - \frac{2627288}{9801} \) \( \bigl[a + 1\) , \( 1\) , \( 0\) , \( 6 a + 4\) , \( -2 a - 18\bigr] \) ${y}^2+\left(a+1\right){x}{y}={x}^{3}+{x}^{2}+\left(6a+4\right){x}-2a-18$
1452.1-c2 1452.1-c \(\Q(\sqrt{3}) \) \( 2^{2} \cdot 3 \cdot 11^{2} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $8.369434150$ 1.208023764 \( -\frac{60218368}{99} a + \frac{104983888}{99} \) \( \bigl[a + 1\) , \( 1\) , \( 0\) , \( a - 6\) , \( -12\bigr] \) ${y}^2+\left(a+1\right){x}{y}={x}^{3}+{x}^{2}+\left(a-6\right){x}-12$
1452.1-d1 1452.1-d \(\Q(\sqrt{3}) \) \( 2^{2} \cdot 3 \cdot 11^{2} \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $0.311641691$ $9.243056976$ 2.494605153 \( \frac{131072}{99} \) \( \bigl[0\) , \( -1\) , \( 0\) , \( 3\) , \( 0\bigr] \) ${y}^2={x}^{3}-{x}^{2}+3{x}$
1452.1-d2 1452.1-d \(\Q(\sqrt{3}) \) \( 2^{2} \cdot 3 \cdot 11^{2} \) $1$ $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $0.155820845$ $18.48611395$ 2.494605153 \( \frac{810448}{363} \) \( \bigl[a + 1\) , \( 1\) , \( 0\) , \( 13 a - 20\) , \( -10 a + 18\bigr] \) ${y}^2+\left(a+1\right){x}{y}={x}^{3}+{x}^{2}+\left(13a-20\right){x}-10a+18$
1452.1-d3 1452.1-d \(\Q(\sqrt{3}) \) \( 2^{2} \cdot 3 \cdot 11^{2} \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $0.311641691$ $9.243056976$ 2.494605153 \( -\frac{21610512004}{43923} a + \frac{13346636520}{14641} \) \( \bigl[a + 1\) , \( 1\) , \( 0\) , \( 168 a - 290\) , \( -1494 a + 2586\bigr] \) ${y}^2+\left(a+1\right){x}{y}={x}^{3}+{x}^{2}+\left(168a-290\right){x}-1494a+2586$
1452.1-d4 1452.1-d \(\Q(\sqrt{3}) \) \( 2^{2} \cdot 3 \cdot 11^{2} \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $0.311641691$ $9.243056976$ 2.494605153 \( \frac{21610512004}{43923} a + \frac{13346636520}{14641} \) \( \bigl[a + 1\) , \( 1\) , \( 0\) , \( 98 a - 170\) , \( 724 a - 1254\bigr] \) ${y}^2+\left(a+1\right){x}{y}={x}^{3}+{x}^{2}+\left(98a-170\right){x}+724a-1254$
1452.1-e1 1452.1-e \(\Q(\sqrt{3}) \) \( 2^{2} \cdot 3 \cdot 11^{2} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $7.056084593$ 2.036916169 \( \frac{131072}{99} \) \( \bigl[0\) , \( 1\) , \( 0\) , \( 3\) , \( 0\bigr] \) ${y}^2={x}^{3}+{x}^{2}+3{x}$
1452.1-e2 1452.1-e \(\Q(\sqrt{3}) \) \( 2^{2} \cdot 3 \cdot 11^{2} \) 0 $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $14.11216918$ 2.036916169 \( \frac{810448}{363} \) \( \bigl[a + 1\) , \( -a\) , \( a + 1\) , \( 11 a - 23\) , \( 22 a - 40\bigr] \) ${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}-a{x}^{2}+\left(11a-23\right){x}+22a-40$
1452.1-e3 1452.1-e \(\Q(\sqrt{3}) \) \( 2^{2} \cdot 3 \cdot 11^{2} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $7.056084593$ 2.036916169 \( -\frac{21610512004}{43923} a + \frac{13346636520}{14641} \) \( \bigl[a + 1\) , \( -a\) , \( a + 1\) , \( 166 a - 293\) , \( 1661 a - 2878\bigr] \) ${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}-a{x}^{2}+\left(166a-293\right){x}+1661a-2878$
1452.1-e4 1452.1-e \(\Q(\sqrt{3}) \) \( 2^{2} \cdot 3 \cdot 11^{2} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $7.056084593$ 2.036916169 \( \frac{21610512004}{43923} a + \frac{13346636520}{14641} \) \( \bigl[a + 1\) , \( -a\) , \( a + 1\) , \( 96 a - 173\) , \( -627 a + 1082\bigr] \) ${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}-a{x}^{2}+\left(96a-173\right){x}-627a+1082$
1452.1-f1 1452.1-f \(\Q(\sqrt{3}) \) \( 2^{2} \cdot 3 \cdot 11^{2} \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $0.037908947$ $6.730048416$ 3.535171865 \( \frac{3209452}{9801} a - \frac{2627288}{9801} \) \( \bigl[a + 1\) , \( -a\) , \( a + 1\) , \( 4 a + 1\) , \( 7 a + 20\bigr] \) ${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}-a{x}^{2}+\left(4a+1\right){x}+7a+20$
1452.1-f2 1452.1-f \(\Q(\sqrt{3}) \) \( 2^{2} \cdot 3 \cdot 11^{2} \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $0.075817895$ $26.92019366$ 3.535171865 \( -\frac{60218368}{99} a + \frac{104983888}{99} \) \( \bigl[a + 1\) , \( -a\) , \( a + 1\) , \( -a - 9\) , \( 4\bigr] \) ${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}-a{x}^{2}+\left(-a-9\right){x}+4$
1452.1-g1 1452.1-g \(\Q(\sqrt{3}) \) \( 2^{2} \cdot 3 \cdot 11^{2} \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $1.993305343$ $4.791232579$ 2.756959975 \( -\frac{3196715008}{649539} \) \( \bigl[0\) , \( -1\) , \( 0\) , \( -77\) , \( 330\bigr] \) ${y}^2={x}^{3}-{x}^{2}-77{x}+330$
1452.1-g2 1452.1-g \(\Q(\sqrt{3}) \) \( 2^{2} \cdot 3 \cdot 11^{2} \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $1.993305343$ $4.791232579$ 2.756959975 \( -\frac{114750605652090357244}{395307} a + \frac{7361254784861301480}{14641} \) \( \bigl[a + 1\) , \( 1\) , \( a + 1\) , \( 20777 a - 36012\) , \( -2138719 a + 3704385\bigr] \) ${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+{x}^{2}+\left(20777a-36012\right){x}-2138719a+3704385$
1452.1-g3 1452.1-g \(\Q(\sqrt{3}) \) \( 2^{2} \cdot 3 \cdot 11^{2} \) $1$ $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $0.996652671$ $9.582465158$ 2.756959975 \( \frac{932410994128}{29403} \) \( \bigl[a + 1\) , \( 1\) , \( a + 1\) , \( 1292 a - 2262\) , \( -33043 a + 57252\bigr] \) ${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+{x}^{2}+\left(1292a-2262\right){x}-33043a+57252$
1452.1-g4 1452.1-g \(\Q(\sqrt{3}) \) \( 2^{2} \cdot 3 \cdot 11^{2} \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $1.993305343$ $4.791232579$ 2.756959975 \( \frac{114750605652090357244}{395307} a + \frac{7361254784861301480}{14641} \) \( \bigl[a + 1\) , \( 1\) , \( a + 1\) , \( 1247 a - 2532\) , \( -29317 a + 53175\bigr] \) ${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+{x}^{2}+\left(1247a-2532\right){x}-29317a+53175$
1452.1-h1 1452.1-h \(\Q(\sqrt{3}) \) \( 2^{2} \cdot 3 \cdot 11^{2} \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $0.037908947$ $6.730048416$ 3.535171865 \( -\frac{3209452}{9801} a - \frac{2627288}{9801} \) \( \bigl[a + 1\) , \( 0\) , \( a + 1\) , \( -6 a + 1\) , \( -8 a + 20\bigr] \) ${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-6a+1\right){x}-8a+20$
1452.1-h2 1452.1-h \(\Q(\sqrt{3}) \) \( 2^{2} \cdot 3 \cdot 11^{2} \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $0.075817895$ $26.92019366$ 3.535171865 \( \frac{60218368}{99} a + \frac{104983888}{99} \) \( \bigl[a + 1\) , \( 0\) , \( a + 1\) , \( -a - 9\) , \( -a + 4\bigr] \) ${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a-9\right){x}-a+4$
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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.