Learn more

Refine search


Results (29 matches)

  displayed columns for results
Label Class Base field Conductor norm Rank Torsion CM Sato-Tate Regulator Period Leading coeff j-invariant Weierstrass coefficients Weierstrass equation
28224.1-a1 28224.1-a \(\Q(\sqrt{-3}) \) \( 2^{6} \cdot 3^{2} \cdot 7^{2} \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $0.303994586$ $2.018890495$ 2.834705677 \( 77808 a - 64752 \) \( \bigl[0\) , \( a + 1\) , \( 0\) , \( 8 a - 28\) , \( -24 a + 44\bigr] \) ${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(8a-28\right){x}-24a+44$
28224.1-a2 28224.1-a \(\Q(\sqrt{-3}) \) \( 2^{6} \cdot 3^{2} \cdot 7^{2} \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $0.151997293$ $4.037780990$ 2.834705677 \( -768 a + 1536 \) \( \bigl[0\) , \( a + 1\) , \( 0\) , \( 3 a - 3\) , \( 2 a - 2\bigr] \) ${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(3a-3\right){x}+2a-2$
28224.1-b1 28224.1-b \(\Q(\sqrt{-3}) \) \( 2^{6} \cdot 3^{2} \cdot 7^{2} \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $1.976637884$ $0.338531005$ 3.090686286 \( -\frac{325140500}{21} a - \frac{202293500}{21} \) \( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 1286 a - 2365\) , \( 31223 a - 37739\bigr] \) ${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(1286a-2365\right){x}+31223a-37739$
28224.1-b2 28224.1-b \(\Q(\sqrt{-3}) \) \( 2^{6} \cdot 3^{2} \cdot 7^{2} \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $3.953275769$ $0.169265502$ 3.090686286 \( \frac{11086896250}{3969} a - \frac{3415354000}{3969} \) \( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -6994 a + 2075\) , \( 201359 a - 182147\bigr] \) ${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(-6994a+2075\right){x}+201359a-182147$
28224.1-b3 28224.1-b \(\Q(\sqrt{-3}) \) \( 2^{6} \cdot 3^{2} \cdot 7^{2} \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $3.953275769$ $0.169265502$ 3.090686286 \( -\frac{27056768750}{17294403} a - \frac{239701516000}{17294403} \) \( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -1474 a + 3035\) , \( 45599 a + 13693\bigr] \) ${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(-1474a+3035\right){x}+45599a+13693$
28224.1-b4 28224.1-b \(\Q(\sqrt{-3}) \) \( 2^{6} \cdot 3^{2} \cdot 7^{2} \) $1$ $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $0.988318942$ $0.677062010$ 3.090686286 \( \frac{746000}{147} a - \frac{488000}{147} \) \( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 86 a - 145\) , \( 455 a - 575\bigr] \) ${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(86a-145\right){x}+455a-575$
28224.1-b5 28224.1-b \(\Q(\sqrt{-3}) \) \( 2^{6} \cdot 3^{2} \cdot 7^{2} \) $1$ $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $1.976637884$ $0.338531005$ 3.090686286 \( -\frac{22841500}{21609} a - \frac{363500}{7203} \) \( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -394 a + 155\) , \( 4343 a - 3299\bigr] \) ${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(-394a+155\right){x}+4343a-3299$
28224.1-b6 28224.1-b \(\Q(\sqrt{-3}) \) \( 2^{6} \cdot 3^{2} \cdot 7^{2} \) $1$ $\Z/4\Z$ $\mathrm{SU}(2)$ $0.494159471$ $1.354124020$ 3.090686286 \( -\frac{160000}{21} a + \frac{32000}{21} \) \( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 41 a - 25\) , \( -94 a + 7\bigr] \) ${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(41a-25\right){x}-94a+7$
28224.1-c1 28224.1-c \(\Q(\sqrt{-3}) \) \( 2^{6} \cdot 3^{2} \cdot 7^{2} \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $0.220721263$ $0.793297756$ 3.234966217 \( \frac{73696}{3} a - \frac{624368}{3} \) \( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 25 a + 181\) , \( 1115 a - 816\bigr] \) ${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(25a+181\right){x}+1115a-816$
28224.1-c2 28224.1-c \(\Q(\sqrt{-3}) \) \( 2^{6} \cdot 3^{2} \cdot 7^{2} \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $0.220721263$ $0.793297756$ 3.234966217 \( -\frac{73696}{3} a - \frac{550672}{3} \) \( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -170 a + 211\) , \( -277 a - 975\bigr] \) ${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(-170a+211\right){x}-277a-975$
28224.1-c3 28224.1-c \(\Q(\sqrt{-3}) \) \( 2^{6} \cdot 3^{2} \cdot 7^{2} \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $3.531540208$ $0.198324439$ 3.234966217 \( \frac{207646}{6561} \) \( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -140 a + 376\) , \( -10516 a + 19224\bigr] \) ${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(-140a+376\right){x}-10516a+19224$
28224.1-c4 28224.1-c \(\Q(\sqrt{-3}) \) \( 2^{6} \cdot 3^{2} \cdot 7^{2} \) $1$ $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $0.441442526$ $1.586595513$ 3.234966217 \( \frac{2048}{3} \) \( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -5 a + 16\) , \( 14 a - 36\bigr] \) ${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(-5a+16\right){x}+14a-36$
28224.1-c5 28224.1-c \(\Q(\sqrt{-3}) \) \( 2^{6} \cdot 3^{2} \cdot 7^{2} \) $1$ $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $0.882885052$ $0.793297756$ 3.234966217 \( \frac{35152}{9} \) \( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 40 a - 104\) , \( 164 a - 240\bigr] \) ${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(40a-104\right){x}+164a-240$
28224.1-c6 28224.1-c \(\Q(\sqrt{-3}) \) \( 2^{6} \cdot 3^{2} \cdot 7^{2} \) $1$ $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $1.765770104$ $0.396648878$ 3.234966217 \( \frac{1556068}{81} \) \( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 220 a - 584\) , \( -2596 a + 5160\bigr] \) ${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(220a-584\right){x}-2596a+5160$
28224.1-c7 28224.1-c \(\Q(\sqrt{-3}) \) \( 2^{6} \cdot 3^{2} \cdot 7^{2} \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $1.765770104$ $0.396648878$ 3.234966217 \( \frac{28756228}{3} \) \( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 580 a - 1544\) , \( 12044 a - 21336\bigr] \) ${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(580a-1544\right){x}+12044a-21336$
28224.1-c8 28224.1-c \(\Q(\sqrt{-3}) \) \( 2^{6} \cdot 3^{2} \cdot 7^{2} \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $3.531540208$ $0.198324439$ 3.234966217 \( \frac{3065617154}{9} \) \( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 3460 a - 9224\) , \( -173236 a + 326136\bigr] \) ${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(3460a-9224\right){x}-173236a+326136$
28224.1-d1 28224.1-d \(\Q(\sqrt{-3}) \) \( 2^{6} \cdot 3^{2} \cdot 7^{2} \) 0 $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $0.464193648$ 2.144018622 \( -\frac{14733184}{7203} a - \frac{75724112}{7203} \) \( \bigl[0\) , \( a + 1\) , \( 0\) , \( -88 a + 368\) , \( 2764 a - 316\bigr] \) ${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(-88a+368\right){x}+2764a-316$
28224.1-d2 28224.1-d \(\Q(\sqrt{-3}) \) \( 2^{6} \cdot 3^{2} \cdot 7^{2} \) 0 $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $0.928387296$ 2.144018622 \( \frac{647168}{441} a - \frac{231424}{147} \) \( \bigl[0\) , \( a + 1\) , \( 0\) , \( 47 a + 8\) , \( 46 a + 170\bigr] \) ${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(47a+8\right){x}+46a+170$
28224.1-d3 28224.1-d \(\Q(\sqrt{-3}) \) \( 2^{6} \cdot 3^{2} \cdot 7^{2} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $0.232096824$ 2.144018622 \( -\frac{16918844552}{17294403} a - \frac{6343701788}{17294403} \) \( \bigl[0\) , \( a + 1\) , \( 0\) , \( -868 a + 488\) , \( 10516 a - 12364\bigr] \) ${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(-868a+488\right){x}+10516a-12364$
28224.1-d4 28224.1-d \(\Q(\sqrt{-3}) \) \( 2^{6} \cdot 3^{2} \cdot 7^{2} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $0.464193648$ 2.144018622 \( -\frac{2145056}{567} a + \frac{395120}{567} \) \( \bigl[0\) , \( a + 1\) , \( 0\) , \( 62 a - 277\) , \( -1019 a + 1883\bigr] \) ${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(62a-277\right){x}-1019a+1883$
28224.1-d5 28224.1-d \(\Q(\sqrt{-3}) \) \( 2^{6} \cdot 3^{2} \cdot 7^{2} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $0.464193648$ 2.144018622 \( -\frac{97542176}{21} a + \frac{59625200}{21} \) \( \bigl[0\) , \( a + 1\) , \( 0\) , \( 857 a + 53\) , \( -323 a + 10268\bigr] \) ${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(857a+53\right){x}-323a+10268$
28224.1-d6 28224.1-d \(\Q(\sqrt{-3}) \) \( 2^{6} \cdot 3^{2} \cdot 7^{2} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $0.232096824$ 2.144018622 \( \frac{7384301576}{147} a + \frac{17955092684}{147} \) \( \bigl[0\) , \( a + 1\) , \( 0\) , \( -1468 a + 6008\) , \( 167524 a - 27292\bigr] \) ${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(-1468a+6008\right){x}+167524a-27292$
28224.1-e1 28224.1-e \(\Q(\sqrt{-3}) \) \( 2^{6} \cdot 3^{2} \cdot 7^{2} \) 0 $\mathsf{trivial}$ $\mathrm{SU}(2)$ $1$ $0.841467970$ 1.943287036 \( 1024 a + 2048 \) \( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -75 a + 72\) , \( -6 a - 195\bigr] \) ${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(-75a+72\right){x}-6a-195$
28224.1-f1 28224.1-f \(\Q(\sqrt{-3}) \) \( 2^{6} \cdot 3^{2} \cdot 7^{2} \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $0.293072232$ $1.228270874$ 3.325279703 \( \frac{3840}{7} a - \frac{768}{7} \) \( \bigl[0\) , \( 0\) , \( 0\) , \( -9 a + 24\) , \( -75 a + 53\bigr] \) ${y}^2={x}^{3}+\left(-9a+24\right){x}-75a+53$
28224.1-f2 28224.1-f \(\Q(\sqrt{-3}) \) \( 2^{6} \cdot 3^{2} \cdot 7^{2} \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $0.586144464$ $0.614135437$ 3.325279703 \( -\frac{242448}{49} a + \frac{302304}{49} \) \( \bigl[0\) , \( 0\) , \( 0\) , \( 156 a - 171\) , \( -852 a + 410\bigr] \) ${y}^2={x}^{3}+\left(156a-171\right){x}-852a+410$
28224.1-g1 28224.1-g \(\Q(\sqrt{-3}) \) \( 2^{6} \cdot 3^{2} \cdot 7^{2} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $0.839337644$ 1.938367259 \( \frac{41728}{9} a - \frac{14336}{9} \) \( \bigl[0\) , \( a + 1\) , \( 0\) , \( -92 a + 52\) , \( 103 a - 276\bigr] \) ${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(-92a+52\right){x}+103a-276$
28224.1-g2 28224.1-g \(\Q(\sqrt{-3}) \) \( 2^{6} \cdot 3^{2} \cdot 7^{2} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $0.419668822$ 1.938367259 \( -\frac{29968}{27} a + \frac{11248}{27} \) \( \bigl[0\) , \( a + 1\) , \( 0\) , \( 178 a + 67\) , \( 1765 a - 2013\bigr] \) ${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(178a+67\right){x}+1765a-2013$
28224.1-h1 28224.1-h \(\Q(\sqrt{-3}) \) \( 2^{6} \cdot 3^{2} \cdot 7^{2} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $0.440558024$ 2.034850352 \( 77808 a - 64752 \) \( \bigl[0\) , \( 0\) , \( 0\) , \( 252 a + 357\) , \( 4344 a - 5018\bigr] \) ${y}^2={x}^{3}+\left(252a+357\right){x}+4344a-5018$
28224.1-h2 28224.1-h \(\Q(\sqrt{-3}) \) \( 2^{6} \cdot 3^{2} \cdot 7^{2} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $0.881116048$ 2.034850352 \( -768 a + 1536 \) \( \bigl[0\) , \( 0\) , \( 0\) , \( -3 a + 57\) , \( -87 a - 62\bigr] \) ${y}^2={x}^{3}+\left(-3a+57\right){x}-87a-62$
  displayed columns for results

  *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.