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Results (23 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
14112.2-a1 14112.2-a \(\Q(\sqrt{-7}) \) \( 2^{5} \cdot 3^{2} \cdot 7^{2} \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $1.420862494$ $1.191573554$ 2.559669408 \( \frac{519158333}{589824} a + \frac{1760396843}{884736} \) \( \bigl[a\) , \( a - 1\) , \( a\) , \( -29 a + 17\) , \( -9 a + 81\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-29a+17\right){x}-9a+81$
14112.2-a2 14112.2-a \(\Q(\sqrt{-7}) \) \( 2^{5} \cdot 3^{2} \cdot 7^{2} \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $0.710431247$ $1.191573554$ 2.559669408 \( -\frac{1076146307}{62208} a + \frac{2632399595}{93312} \) \( \bigl[a\) , \( a\) , \( 0\) , \( -15 a + 65\) , \( 144 a + 32\bigr] \) ${y}^2+a{x}{y}={x}^{3}+a{x}^{2}+\left(-15a+65\right){x}+144a+32$
14112.2-b1 14112.2-b \(\Q(\sqrt{-7}) \) \( 2^{5} \cdot 3^{2} \cdot 7^{2} \) 0 $\mathsf{trivial}$ $\mathrm{SU}(2)$ $1$ $0.144416270$ 1.528358148 \( -\frac{6329617441}{279936} \) \( \bigl[a\) , \( -a\) , \( 0\) , \( -2961 a + 1974\) , \( -41391 a + 101178\bigr] \) ${y}^2+a{x}{y}={x}^{3}-a{x}^{2}+\left(-2961a+1974\right){x}-41391a+101178$
14112.2-b2 14112.2-b \(\Q(\sqrt{-7}) \) \( 2^{5} \cdot 3^{2} \cdot 7^{2} \) 0 $\mathsf{trivial}$ $\mathrm{SU}(2)$ $1$ $1.010913893$ 1.528358148 \( -\frac{2401}{6} \) \( \bigl[a\) , \( -a\) , \( 0\) , \( -21 a + 14\) , \( 63 a - 154\bigr] \) ${y}^2+a{x}{y}={x}^{3}-a{x}^{2}+\left(-21a+14\right){x}+63a-154$
14112.2-c1 14112.2-c \(\Q(\sqrt{-7}) \) \( 2^{5} \cdot 3^{2} \cdot 7^{2} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $0.517880747$ 1.565924189 \( \frac{12134104351}{1376256} a - \frac{12253997573}{1376256} \) \( \bigl[a\) , \( 0\) , \( a\) , \( -204 a + 62\) , \( -1071 a + 1605\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-204a+62\right){x}-1071a+1605$
14112.2-c2 14112.2-c \(\Q(\sqrt{-7}) \) \( 2^{5} \cdot 3^{2} \cdot 7^{2} \) 0 $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $0.517880747$ 1.565924189 \( -\frac{7189057}{16128} \) \( \bigl[a\) , \( -a + 1\) , \( a\) , \( -85 a + 57\) , \( -439 a + 1023\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-85a+57\right){x}-439a+1023$
14112.2-c3 14112.2-c \(\Q(\sqrt{-7}) \) \( 2^{5} \cdot 3^{2} \cdot 7^{2} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $0.517880747$ 1.565924189 \( -\frac{12134104351}{1376256} a - \frac{59946611}{688128} \) \( \bigl[a\) , \( a + 1\) , \( a\) , \( -189 a + 201\) , \( -353 a + 2079\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-189a+201\right){x}-353a+2079$
14112.2-c4 14112.2-c \(\Q(\sqrt{-7}) \) \( 2^{5} \cdot 3^{2} \cdot 7^{2} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $0.064735093$ 1.565924189 \( \frac{6359387729183}{4218578658} \) \( \bigl[a\) , \( -a + 1\) , \( a\) , \( 8105 a - 5403\) , \( -69655 a + 175071\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(8105a-5403\right){x}-69655a+175071$
14112.2-c5 14112.2-c \(\Q(\sqrt{-7}) \) \( 2^{5} \cdot 3^{2} \cdot 7^{2} \) 0 $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $0.129470186$ 1.565924189 \( \frac{124475734657}{63011844} \) \( \bigl[a\) , \( -a + 1\) , \( a\) , \( -2185 a + 1457\) , \( -9287 a + 21407\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-2185a+1457\right){x}-9287a+21407$
14112.2-c6 14112.2-c \(\Q(\sqrt{-7}) \) \( 2^{5} \cdot 3^{2} \cdot 7^{2} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $0.064735093$ 1.565924189 \( \frac{84448510979617}{933897762} \) \( \bigl[a\) , \( -a + 1\) , \( a\) , \( -19195 a + 12797\) , \( 662041 a - 1629697\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-19195a+12797\right){x}+662041a-1629697$
14112.2-c7 14112.2-c \(\Q(\sqrt{-7}) \) \( 2^{5} \cdot 3^{2} \cdot 7^{2} \) 0 $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $0.258940373$ 1.565924189 \( \frac{65597103937}{63504} \) \( \bigl[a\) , \( -a + 1\) , \( a\) , \( -1765 a + 1177\) , \( -18807 a + 44927\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-1765a+1177\right){x}-18807a+44927$
14112.2-c8 14112.2-c \(\Q(\sqrt{-7}) \) \( 2^{5} \cdot 3^{2} \cdot 7^{2} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $0.129470186$ 1.565924189 \( \frac{268498407453697}{252} \) \( \bigl[a\) , \( -a + 1\) , \( a\) , \( -28225 a + 18817\) , \( -1197159 a + 2909663\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-28225a+18817\right){x}-1197159a+2909663$
14112.2-d1 14112.2-d \(\Q(\sqrt{-7}) \) \( 2^{5} \cdot 3^{2} \cdot 7^{2} \) $1$ $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $0.399664649$ $0.499124703$ 6.031783824 \( \frac{5744242075}{580608} a - \frac{638675959}{41472} \) \( \bigl[a\) , \( a\) , \( a\) , \( 229 a - 184\) , \( 1494 a - 45\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^{3}+a{x}^{2}+\left(229a-184\right){x}+1494a-45$
14112.2-d2 14112.2-d \(\Q(\sqrt{-7}) \) \( 2^{5} \cdot 3^{2} \cdot 7^{2} \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $0.799329299$ $0.249562351$ 6.031783824 \( \frac{218546645}{1143072} a - \frac{2541633511}{5143824} \) \( \bigl[a\) , \( a\) , \( a\) , \( -51 a - 464\) , \( 2614 a + 6899\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^{3}+a{x}^{2}+\left(-51a-464\right){x}+2614a+6899$
14112.2-d3 14112.2-d \(\Q(\sqrt{-7}) \) \( 2^{5} \cdot 3^{2} \cdot 7^{2} \) $1$ $\Z/4\Z$ $\mathrm{SU}(2)$ $0.199832324$ $0.499124703$ 6.031783824 \( -\frac{100686965405}{66060288} a + \frac{11094110413}{11010048} \) \( \bigl[a\) , \( a - 1\) , \( 0\) , \( -63 a + 203\) , \( -336 a - 812\bigr] \) ${y}^2+a{x}{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-63a+203\right){x}-336a-812$
14112.2-d4 14112.2-d \(\Q(\sqrt{-7}) \) \( 2^{5} \cdot 3^{2} \cdot 7^{2} \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $0.799329299$ $0.499124703$ 6.031783824 \( -\frac{446668992275}{2016} a + \frac{21665210083}{336} \) \( \bigl[a\) , \( -1\) , \( a\) , \( -105 a - 1195\) , \( 2072 a + 16461\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^{3}-{x}^{2}+\left(-105a-1195\right){x}+2072a+16461$
14112.2-e1 14112.2-e \(\Q(\sqrt{-7}) \) \( 2^{5} \cdot 3^{2} \cdot 7^{2} \) $1$ $\mathsf{trivial}$ $\mathrm{SU}(2)$ $0.036107404$ $2.054306579$ 5.831440488 \( \frac{1334593}{8192} a + \frac{23502151}{12288} \) \( \bigl[a\) , \( a\) , \( a\) , \( 2 a + 10\) , \( 8 a - 9\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^{3}+a{x}^{2}+\left(2a+10\right){x}+8a-9$
14112.2-f1 14112.2-f \(\Q(\sqrt{-7}) \) \( 2^{5} \cdot 3^{2} \cdot 7^{2} \) $1$ $\mathsf{trivial}$ $\mathrm{SU}(2)$ $0.126591401$ $0.541165759$ 6.214364745 \( -\frac{16591834777}{98304} \) \( \bigl[a\) , \( -a + 1\) , \( 0\) , \( -305 a + 203\) , \( -1374 a + 3178\bigr] \) ${y}^2+a{x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-305a+203\right){x}-1374a+3178$
14112.2-f2 14112.2-f \(\Q(\sqrt{-7}) \) \( 2^{5} \cdot 3^{2} \cdot 7^{2} \) $1$ $\mathsf{trivial}$ $\mathrm{SU}(2)$ $0.042197133$ $1.623497278$ 6.214364745 \( \frac{596183}{864} \) \( \bigl[a\) , \( -a + 1\) , \( 0\) , \( 10 a - 7\) , \( -9 a + 28\bigr] \) ${y}^2+a{x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(10a-7\right){x}-9a+28$
14112.2-g1 14112.2-g \(\Q(\sqrt{-7}) \) \( 2^{5} \cdot 3^{2} \cdot 7^{2} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $0.639934178$ 3.869958154 \( \frac{125632169}{196} a - \frac{968559785}{294} \) \( \bigl[a\) , \( 0\) , \( 0\) , \( 3 a - 450\) , \( -75 a + 3750\bigr] \) ${y}^2+a{x}{y}={x}^{3}+\left(3a-450\right){x}-75a+3750$
14112.2-g2 14112.2-g \(\Q(\sqrt{-7}) \) \( 2^{5} \cdot 3^{2} \cdot 7^{2} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $1.279868357$ 3.869958154 \( -\frac{14150117}{756} a + \frac{157757}{1134} \) \( \bigl[a\) , \( -a\) , \( a\) , \( -25 a - 27\) , \( 110 a + 25\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^{3}-a{x}^{2}+\left(-25a-27\right){x}+110a+25$
14112.2-g3 14112.2-g \(\Q(\sqrt{-7}) \) \( 2^{5} \cdot 3^{2} \cdot 7^{2} \) 0 $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $1.279868357$ 3.869958154 \( \frac{413801}{336} a + \frac{191711}{504} \) \( \bigl[a\) , \( 0\) , \( 0\) , \( 3 a - 30\) , \( 9 a + 54\bigr] \) ${y}^2+a{x}{y}={x}^{3}+\left(3a-30\right){x}+9a+54$
14112.2-g4 14112.2-g \(\Q(\sqrt{-7}) \) \( 2^{5} \cdot 3^{2} \cdot 7^{2} \) 0 $\Z/4\Z$ $\mathrm{SU}(2)$ $1$ $1.279868357$ 3.869958154 \( -\frac{2117957}{1792} a + \frac{4119197}{2688} \) \( \bigl[a\) , \( -a + 1\) , \( 0\) , \( -18 a - 7\) , \( 39 a + 4\bigr] \) ${y}^2+a{x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-18a-7\right){x}+39a+4$
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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.