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Results (28 matches)

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Label Class Base field Conductor norm Rank Torsion CM Regulator Period Leading coeff j-invariant Weierstrass coefficients Weierstrass equation
28224.2-a1 28224.2-a \(\Q(\sqrt{-3}) \) \( 2^{6} \cdot 3^{2} \cdot 7^{2} \) $0$ $\Z/2\Z$ $1$ $0.606358791$ 1.400325646 \( \frac{70330790}{117649} a - \frac{91085936}{117649} \) \( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 73 a - 107\) , \( -529 a + 768\bigr] \) ${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(73a-107\right){x}-529a+768$
28224.2-a2 28224.2-a \(\Q(\sqrt{-3}) \) \( 2^{6} \cdot 3^{2} \cdot 7^{2} \) $0$ $\Z/2\Z$ $1$ $1.212717583$ 1.400325646 \( -\frac{2555300}{343} a + \frac{1035204}{343} \) \( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -47 a + 13\) , \( -97 a + 72\bigr] \) ${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(-47a+13\right){x}-97a+72$
28224.2-b1 28224.2-b \(\Q(\sqrt{-3}) \) \( 2^{6} \cdot 3^{2} \cdot 7^{2} \) $0$ $\Z/2\Z$ $1$ $1.212717583$ 1.400325646 \( \frac{2555300}{343} a - \frac{1520096}{343} \) \( \bigl[0\) , \( a + 1\) , \( 0\) , \( 49 a - 35\) , \( 145 a - 60\bigr] \) ${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(49a-35\right){x}+145a-60$
28224.2-b2 28224.2-b \(\Q(\sqrt{-3}) \) \( 2^{6} \cdot 3^{2} \cdot 7^{2} \) $0$ $\Z/2\Z$ $1$ $0.606358791$ 1.400325646 \( -\frac{70330790}{117649} a - \frac{20755146}{117649} \) \( \bigl[0\) , \( a + 1\) , \( 0\) , \( -71 a - 35\) , \( 457 a + 204\bigr] \) ${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(-71a-35\right){x}+457a+204$
28224.2-c1 28224.2-c \(\Q(\sqrt{-3}) \) \( 2^{6} \cdot 3^{2} \cdot 7^{2} \) $1$ $\Z/2\Z$ $0.515123520$ $1.287365174$ 3.062968257 \( \frac{12853728}{2401} a - \frac{20030544}{2401} \) \( \bigl[0\) , \( 0\) , \( 0\) , \( 45 a - 21\) , \( 84 a + 30\bigr] \) ${y}^2={x}^{3}+\left(45a-21\right){x}+84a+30$
28224.2-c2 28224.2-c \(\Q(\sqrt{-3}) \) \( 2^{6} \cdot 3^{2} \cdot 7^{2} \) $1$ $\Z/2\Z$ $0.515123520$ $1.287365174$ 3.062968257 \( -\frac{12853728}{2401} a - \frac{7176816}{2401} \) \( \bigl[0\) , \( 0\) , \( 0\) , \( -45 a + 24\) , \( -84 a + 114\bigr] \) ${y}^2={x}^{3}+\left(-45a+24\right){x}-84a+114$
28224.2-c3 28224.2-c \(\Q(\sqrt{-3}) \) \( 2^{6} \cdot 3^{2} \cdot 7^{2} \) $1$ $\Z/2\Z\oplus\Z/2\Z$ $0.257561760$ $2.574730348$ 3.062968257 \( -\frac{55296}{49} \) \( \bigl[0\) , \( 0\) , \( 0\) , \( -6\) , \( 9\bigr] \) ${y}^2={x}^{3}-6{x}+9$
28224.2-c4 28224.2-c \(\Q(\sqrt{-3}) \) \( 2^{6} \cdot 3^{2} \cdot 7^{2} \) $1$ $\Z/2\Z$ $0.515123520$ $1.287365174$ 3.062968257 \( \frac{21882096}{7} \) \( \bigl[0\) , \( 0\) , \( 0\) , \( -111\) , \( 450\bigr] \) ${y}^2={x}^{3}-111{x}+450$
28224.2-d1 28224.2-d \(\Q(\sqrt{-3}) \) \( 2^{6} \cdot 3^{2} \cdot 7^{2} \) $1$ $\Z/2\Z$ $0.418913130$ $0.834893235$ 3.230831214 \( \frac{334159992}{2401} a - \frac{339280596}{2401} \) \( \bigl[0\) , \( 0\) , \( 0\) , \( -69 a - 120\) , \( 504 a + 446\bigr] \) ${y}^2={x}^{3}+\left(-69a-120\right){x}+504a+446$
28224.2-d2 28224.2-d \(\Q(\sqrt{-3}) \) \( 2^{6} \cdot 3^{2} \cdot 7^{2} \) $1$ $\Z/2\Z$ $0.418913130$ $0.834893235$ 3.230831214 \( -\frac{334159992}{2401} a - \frac{5120604}{2401} \) \( \bigl[0\) , \( 0\) , \( 0\) , \( -189 a + 120\) , \( -504 a + 950\bigr] \) ${y}^2={x}^{3}+\left(-189a+120\right){x}-504a+950$
28224.2-d3 28224.2-d \(\Q(\sqrt{-3}) \) \( 2^{6} \cdot 3^{2} \cdot 7^{2} \) $1$ $\Z/2\Z\oplus\Z/2\Z$ $0.209456565$ $1.669786470$ 3.230831214 \( \frac{11664}{49} \) \( \bigl[0\) , \( 0\) , \( 0\) , \( -9 a\) , \( 26\bigr] \) ${y}^2={x}^{3}-9a{x}+26$
28224.2-d4 28224.2-d \(\Q(\sqrt{-3}) \) \( 2^{6} \cdot 3^{2} \cdot 7^{2} \) $1$ $\Z/2\Z$ $0.418913130$ $3.339572940$ 3.230831214 \( \frac{55296}{7} \) \( \bigl[0\) , \( 0\) , \( 0\) , \( 6 a\) , \( 5\bigr] \) ${y}^2={x}^{3}+6a{x}+5$
28224.2-e1 28224.2-e \(\Q(\sqrt{-3}) \) \( 2^{6} \cdot 3^{2} \cdot 7^{2} \) $0$ $\Z/2\Z$ $1$ $0.441968146$ 2.041363425 \( \frac{540572762}{194481} a - \frac{147359740}{21609} \) \( \bigl[0\) , \( a + 1\) , \( 0\) , \( 57 a - 339\) , \( 441 a - 2772\bigr] \) ${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(57a-339\right){x}+441a-2772$
28224.2-e2 28224.2-e \(\Q(\sqrt{-3}) \) \( 2^{6} \cdot 3^{2} \cdot 7^{2} \) $0$ $\Z/2\Z$ $1$ $1.767872584$ 2.041363425 \( -\frac{64528}{21} a - 3264 \) \( \bigl[0\) , \( a + 1\) , \( 0\) , \( -3 a + 21\) , \( 45 a\bigr] \) ${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(-3a+21\right){x}+45a$
28224.2-e3 28224.2-e \(\Q(\sqrt{-3}) \) \( 2^{6} \cdot 3^{2} \cdot 7^{2} \) $0$ $\Z/2\Z\oplus\Z/2\Z$ $1$ $0.883936292$ 2.041363425 \( \frac{53428}{441} a - \frac{746932}{441} \) \( \bigl[0\) , \( a + 1\) , \( 0\) , \( -63 a + 21\) , \( 201 a - 204\bigr] \) ${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(-63a+21\right){x}+201a-204$
28224.2-e4 28224.2-e \(\Q(\sqrt{-3}) \) \( 2^{6} \cdot 3^{2} \cdot 7^{2} \) $0$ $\Z/2\Z$ $1$ $0.441968146$ 2.041363425 \( -\frac{4146758318}{7203} a + \frac{13316821740}{2401} \) \( \bigl[0\) , \( a + 1\) , \( 0\) , \( -1143 a + 381\) , \( 11865 a - 11652\bigr] \) ${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(-1143a+381\right){x}+11865a-11652$
28224.2-f1 28224.2-f \(\Q(\sqrt{-3}) \) \( 2^{6} \cdot 3^{2} \cdot 7^{2} \) $0$ $\Z/2\Z$ $1$ $0.645884175$ 2.237408416 \( -\frac{2837874944}{3087} a - \frac{2609921648}{1029} \) \( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -192 a + 504\) , \( -3468 a - 480\bigr] \) ${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(-192a+504\right){x}-3468a-480$
28224.2-f2 28224.2-f \(\Q(\sqrt{-3}) \) \( 2^{6} \cdot 3^{2} \cdot 7^{2} \) $0$ $\Z/2\Z$ $1$ $0.161471043$ 2.237408416 \( -\frac{2501041836936508}{124571584809} a - \frac{179475886366954}{41523861603} \) \( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -3492 a + 2664\) , \( -27972 a + 77976\bigr] \) ${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(-3492a+2664\right){x}-27972a+77976$
28224.2-f3 28224.2-f \(\Q(\sqrt{-3}) \) \( 2^{6} \cdot 3^{2} \cdot 7^{2} \) $0$ $\Z/2\Z\oplus\Z/2\Z$ $1$ $0.322942087$ 2.237408416 \( \frac{18014530528}{9529569} a - \frac{4291022956}{9529569} \) \( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -252 a + 504\) , \( -4212 a + 648\bigr] \) ${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(-252a+504\right){x}-4212a+648$
28224.2-f4 28224.2-f \(\Q(\sqrt{-3}) \) \( 2^{6} \cdot 3^{2} \cdot 7^{2} \) $0$ $\Z/2\Z$ $1$ $0.161471043$ 2.237408416 \( -\frac{37641895204}{15752961} a + \frac{10103566538}{5250987} \) \( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 2028 a - 1656\) , \( -29988 a - 3528\bigr] \) ${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(2028a-1656\right){x}-29988a-3528$
28224.2-g1 28224.2-g \(\Q(\sqrt{-3}) \) \( 2^{6} \cdot 3^{2} \cdot 7^{2} \) $0$ $\Z/2\Z$ $1$ $1.767872584$ 2.041363425 \( \frac{64528}{21} a - \frac{133072}{21} \) \( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 18 a - 21\) , \( -45 a + 45\bigr] \) ${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(18a-21\right){x}-45a+45$
28224.2-g2 28224.2-g \(\Q(\sqrt{-3}) \) \( 2^{6} \cdot 3^{2} \cdot 7^{2} \) $0$ $\Z/2\Z$ $1$ $0.441968146$ 2.041363425 \( -\frac{540572762}{194481} a - \frac{785664898}{194481} \) \( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -282 a + 339\) , \( -441 a - 2331\bigr] \) ${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(-282a+339\right){x}-441a-2331$
28224.2-g3 28224.2-g \(\Q(\sqrt{-3}) \) \( 2^{6} \cdot 3^{2} \cdot 7^{2} \) $0$ $\Z/2\Z\oplus\Z/2\Z$ $1$ $0.883936292$ 2.041363425 \( -\frac{53428}{441} a - \frac{11008}{7} \) \( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -42 a - 21\) , \( -201 a - 3\bigr] \) ${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(-42a-21\right){x}-201a-3$
28224.2-g4 28224.2-g \(\Q(\sqrt{-3}) \) \( 2^{6} \cdot 3^{2} \cdot 7^{2} \) $0$ $\Z/2\Z$ $1$ $0.441968146$ 2.041363425 \( \frac{4146758318}{7203} a + \frac{35803706902}{7203} \) \( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -762 a - 381\) , \( -11865 a + 213\bigr] \) ${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(-762a-381\right){x}-11865a+213$
28224.2-h1 28224.2-h \(\Q(\sqrt{-3}) \) \( 2^{6} \cdot 3^{2} \cdot 7^{2} \) $0$ $\Z/2\Z$ $1$ $0.645884175$ 2.237408416 \( \frac{2837874944}{3087} a - \frac{10667639888}{3087} \) \( \bigl[0\) , \( a + 1\) , \( 0\) , \( -503 a + 193\) , \( 3157 a - 3444\bigr] \) ${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(-503a+193\right){x}+3157a-3444$
28224.2-h2 28224.2-h \(\Q(\sqrt{-3}) \) \( 2^{6} \cdot 3^{2} \cdot 7^{2} \) $0$ $\Z/2\Z$ $1$ $0.161471043$ 2.237408416 \( \frac{2501041836936508}{124571584809} a - \frac{3039469496037370}{124571584809} \) \( \bigl[0\) , \( a + 1\) , \( 0\) , \( -2663 a + 3493\) , \( 28801 a + 52668\bigr] \) ${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(-2663a+3493\right){x}+28801a+52668$
28224.2-h3 28224.2-h \(\Q(\sqrt{-3}) \) \( 2^{6} \cdot 3^{2} \cdot 7^{2} \) $0$ $\Z/2\Z$ $1$ $0.161471043$ 2.237408416 \( \frac{37641895204}{15752961} a - \frac{7331195590}{15752961} \) \( \bigl[0\) , \( a + 1\) , \( 0\) , \( 1657 a - 2027\) , \( 29617 a - 35172\bigr] \) ${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(1657a-2027\right){x}+29617a-35172$
28224.2-h4 28224.2-h \(\Q(\sqrt{-3}) \) \( 2^{6} \cdot 3^{2} \cdot 7^{2} \) $0$ $\Z/2\Z\oplus\Z/2\Z$ $1$ $0.322942087$ 2.237408416 \( -\frac{18014530528}{9529569} a + \frac{4574502524}{3176523} \) \( \bigl[0\) , \( a + 1\) , \( 0\) , \( -503 a + 253\) , \( 3961 a - 3060\bigr] \) ${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(-503a+253\right){x}+3961a-3060$
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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.